tests/rtest_integrate.mac

   1 /* A collection of about 730 integrals with power functions.
   2    The integrals are taken from functions.wolfram.com
   3
   4    OK   - The integral is solved by Maxima
   5    NEW  - Solution after extension of the integrator (rev. 1.34)
   6    NOUN - No solution a noun form is returned.
   7 */
   8
   9 (kill(all),
  10   declare(z,complex,n,integer),
  11   assume(n>0),
  12   assume(notequal(v,0)),
  13   domain:complex,
  14   radexpand:true,
  15
  16   /* This function checks if we get back the integrand.
  17    *
  18    * integral is the result of an integration,
  19    * var the integration variable, and
  20    * simplifier a simplifying function.
  21    */
  22   diffcheck(integral,var,simplifier):=
  23      if op(integral)=nounify(integrate) then
  24         integral
  25      else
  26         simplifier(diff(integral,var)),
  27
  28   factor_radcan(expr):=factor(radcan(expr)),
  29   done);
  30 done;
  31
  32 /* ----- Involving only one direct function --------------------------------- */
  33
  34 /* Problem 2: OK */
  35 integrate(a^(c*z),z);
  36 a^(c*z)/(log(a)*c);
  37
  38 /* Problem 3: OK */
  39 integrate(a^z,z);
  40 a^z/log(a);
  41
  42 /* Problem 4: OK */
  43 integrate(%e^(a*z+b),z);
  44 %e^(a*z+b)/a;
  45
  46 /* Problem 5: OK */
  47 integrate(%e^(a*z),z);
  48 %e^(a*z)/a;
  49
  50 /* Problem 6: OK */
  51 integrate(%e^z,z);
  52 %e^z;
  53
  54 /* ----- Power arguments and base a ----------------------------------------- */
  55
  56 /* Problem 7: NEW Type 1 */
  57 integrate(a^(b*z^r),z);
  58 z*gamma_incomplete(1/r,-b*z^r*log(a))*(-b*z^r*log(a))^(-1/r)/-r;
  59
  60 /* Problem 9: OK */
  61 assume(a>1,b>0);
  62 [a>1,b>0];
  63 integrate(a^(b*z^2),z),erf_representation:erfi,trigsign:true;
  64 -sqrt(%pi)*%i*erfi(%i*sqrt(-log(a)*b)*z)/(2*sqrt(-log(a)*b))$
  65 forget(a>1,b>0);
  66 [a>1,b>0];
  67
  68 /* Problem 11: OK */
  69 integrate(a^(b*sqrt(z)),z),radcan,factor;
  70 2*(log(a)*b*sqrt(z)-1)*a^(b*sqrt(z))/(log(a)^2*b^2);
  71
  72 /* Problem 12: NEW Type 1 */
  73 integrate(a^(b*(z^r)^p),z);
  74 z*gamma_incomplete(1/(p*r),-log(a)*b*(z^r)^p)
  75   /(-p*r*(-b*log(a)*(z^r)^p)^(1/(p*r)));
  76
  77 /* Problem 13: Expected failure
  78  * (z^r)^(1/r) simplifies to z which is not correct in general.
  79  * rischint does not respect the complex character of z.
  80  * The result of rischint is only correct for z>0.
  81  */
  82 integrate(a^(b*(z^r)^(1/r)),z), domain:real, radcan;
  83 a^(b*z)/(log(a)*b)$
  84
  85 /* Problem 14: Expected failure
  86  * sqrt(z^2) simplifies to z, which is not correct in general.
  87  * rischint does not respect the complex character of z.
  88  * The result of rischint is only correct for z>0.
  89  */
  90 integrate(a^(b*sqrt(z^2)),z), radcan;
  91 a^(b*z)/(log(a)*b)$
  92
  93 /* ----- Power arguments and base %e ---------------------------------------- */
  94
  95 /* Problem 15: NEW Type 1 */
  96 integrate(%e^(a*z^r),z);
  97 -z*gamma_incomplete(1/r,-a*z^r)/(r*(-a*z^r)^(1/r));
  98
  99 /* Problem 17: OK */
 100 assume(a>0);
 101 [a>0];
 102 integrate(%e^(a*z^2),z),erf_representation:erfi;
 103 -sqrt(%pi)*%i*erfi(%i*sqrt(-a)*z)/(2*sqrt(-a))$
 104 forget(a>0);
 105 [a>0];
 106
 107 /* Problem 19: OK */
 108 integrate(%e^(a*sqrt(z)),z);
 109 2*(a*sqrt(z)-1)*%e^(a*sqrt(z))/a^2;
 110
 111 /* Problem 20: NEW Type 1 */
 112 integrate(%e^(a*(z^r)^p),z);
 113 -z*gamma_incomplete(1/(p*r),-a*(z^r)^p)/(p*r*(-a*(z^r)^p)^(1/(p*r)));
 114
 115 /* Problem 21: Expected failure
 116  * See problem 13
 117  */
 118 integrate(%e^(a*(z^r)^(1/r)),z), domain:real;
 119 %e^(a*z)/a$
 120
 121 /* Problem 22: Expected failure
 122  * See problem 14
 123  */
 124 integrate(%e^(a*sqrt(z^2)),z);
 125 %e^(a*z)/a$
 126
 127 /* ----- Involving z^(v-1), arguments b*z and base a ------------------------ */
 128
 129 /* Problem 23: NEW Type 2 */
 130 integrate(z^(v-1)*a^(b*z),z);
 131 -z^v*gamma_incomplete(v,-log(a)*b*z)/(-b*z*log(a))^v;
 132
 133 /* Problem 24: NEW Type 2 */
 134 integrate(a^(b*z)/z,z),gamma_expand:true,logcontract;
 135 expintegral_ei(b*z*log(a));
 136
 137 /* Problem 25: NEW Type 2 */
 138 integrate(z^(v-1)*a^z,z);
 139 -gamma_incomplete(v,-log(a)*z)*z^v/(-log(a)*z)^v;
 140
 141 /* Problem 26: NEW Type 2 */
 142 integrate(a^z/z,z),gamma_expand:true,logcontract;
 143 expintegral_ei(z*log(a));
 144
 145
 146 /* ----- Involving z^(v-1), arguments a*z and base %e ----------------------- */
 147
 148 /* Problem 27: NEW Type 2 */
 149 integrate(z^(v-1)*%e^(a*z),z);
 150 -gamma_incomplete(v,-a*z)*z^v/(-a*z)^v;
 151
 152 /* Problem 28: NEW Type 2 */
 153 integrate(z^(v-1)*%e^z,z);
 154 -gamma_incomplete(v,-z)*z^v/(-z)^v;
 155
 156 /* Problem 29: NEW Type 2 */
 157 integrate(z^n*%e^(a*z),z),factor;
 158 a^(-n-1)*(-1)^n*gamma_incomplete(n+1,-a*z);
 159
 160 /* Problem 30: New Type 2 */
 161 integrate(%e^(a*z)/z^n,z),factor;
 162 a^(n-1)*(-1)^n*gamma_incomplete(1-n,-a*z);
 163
 164 /* Problem 31: OK */
 165 integrate(z*%e^(a*z),z);
 166 (a*z-1)*%e^(a*z)/a^2;
 167
 168 /* Problem 32: Expected failure
 169  * Simplifies sqrt(z^2) -> z, which is correct only for z>0.
 170  * The problem is in rischint.
 171  */
 172 integrate(sqrt(z^2)*%e^(a*z),z);
 173 (a*z-1)*%e^(a*z)/a^2$
 174
 175 /* Problem 33: OK */
 176 integrate(z^2*%e^(a*z),z);
 177 (a^2*z^2-2*a*z+2)*%e^(a*z)/a^3;
 178
 179 /* Problem 34: OK */
 180 integrate(z^3*%e^(a*z),z);
 181 (a^3*z^3-3*a^2*z^2+6*a*z-6)*%e^(a*z)/a^4;
 182
 183 /* Problem 35: OK */
 184 integrate(z^4*%e^(a*z),z);
 185 (a^4*z^4-4*a^3*z^3+12*a^2*z^2-24*a*z+24)*%e^(a*z)/a^5;
 186
 187 /* Problem 36: OK */
 188 integrate(z^5*%e^(a*z),z);
 189 (a^5*z^5-5*a^4*z^4+20*a^3*z^3-60*a^2*z^2+120*a*z-120)*%e^(a*z)/a^6;
 190
 191 /* Problem 37: OK */
 192 integrate(z^6*%e^(a*z),z);
 193 (a^6*z^6-6*a^5*z^5+30*a^4*z^4-120*a^3*z^3+360*a^2*z^2-720*a*z+720)
 194         *%e^(a*z)
 195         /a^7;
 196
 197 /* Problem 38: OK */
 198 integrate(z^7*%e^(a*z),z);
 199 (a^7*z^7-7*a^6*z^6+42*a^5*z^5-210*a^4*z^4+840*a^3*z^3-2520*a^2*z^2
 200                +5040*a*z-5040)
 201         *%e^(a*z)
 202         /a^8;
 203
 204 /* Problem 39: OK */
 205 integrate(z^8*%e^(a*z),z);
 206 (a^8*z^8-8*a^7*z^7+56*a^6*z^6-336*a^5*z^5+1680*a^4*z^4-6720*a^3*z^3
 207                +20160*a^2*z^2-40320*a*z+40320)
 208         *%e^(a*z)
 209         /a^9;
 210
 211 /* Problem 40: NEW Type 2 */
 212 integrate(%e^(a*z)/z,z),gamma_expand:true,logcontract;
 213 expintegral_ei(a*z);
 214
 215 /* Problem 41: NEW Type 2 */
 216 integrate(%e^(a*z)/z^2,z),gamma_expand:true,logcontract,ratsimp;
 217 (a*z*expintegral_ei(a*z)-%e^(a*z))/z;
 218
 219 /* Problem 42: NEW Type 2 */
 220 integrate(%e^(a*z)/z^3,z),gamma_expand:true,logcontract,ratsimp;
 221 (a^2*z^2*expintegral_ei(a*z)+(-a*z-1)*%e^(a*z))/(2*z^2);
 222
 223 /* Problem 43: NEW Type 2 */
 224 integrate(%e^(a*z)/z^4,z),gamma_expand:true,logcontract,ratsimp;
 225 (a^3*z^3*expintegral_ei(a*z)+(-a^2*z^2-a*z-2)*%e^(a*z))/(6*z^3);
 226
 227 /* Problem 44: NEW Type 2 */
 228 integrate(%e^(a*z)/z^5,z),gamma_expand:true,logcontract,ratsimp;
 229 (a^4*z^4*expintegral_ei(a*z)+(-a^3*z^3-a^2*z^2-2*a*z-6)*%e^(a*z))/(24*z^4);
 230
 231 /* Problem 45: NEW Type 2 (OK)
 232  * The following gives sqrt(z)/sqrt(-z) and not sqrt(-z)/sqrt(z),
 233  * but the phase is correct.
 234  */
 235 integrate(z^(1/2+n)*%e^(a*z),z),ratsimp;
 236 a^(-n-1)*(-1)^n*gamma_incomplete((2*n+3)/2,-a*z)*sqrt(z)/sqrt(-a*z);
 237
 238 /* Problem 47: OK */
 239 assume(a>0);
 240 [a>0];
 241 integrate(sqrt(z)*%e^(a*z),z),erf_representation:erfi,expand;
 242 sqrt(z)*%e^(a*z)/a+sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(2*sqrt(-a)*a)$
 243 forget(a>0);
 244 [a>0];
 245
 246 /* Problem 50: OK */
 247 assume(a>0);
 248 [a>0];
 249 multthru(integrate(z^(3/2)*%e^(a*z),z)),erf_representation:erfi;
 250 (2*a*z^(3/2)-3*sqrt(z))*%e^(a*z)/(2*a^2)
 251  -3*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(4*sqrt(-a)*a^2)$
 252 forget(a>0);
 253 [a>0];
 254
 255 /* Problem 53: OK */
 256 assume(a>0);
 257 [a>0];
 258 multthru(integrate(z^(5/2)*%e^(a*z),z)),erf_representation:erfi;
 259 (4*a^2*z^(5/2)-10*a*z^(3/2)+15*sqrt(z))*%e^(a*z)/(4*a^3)
 260  +15*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(8*sqrt(-a)*a^3);
 261 forget(a>0);
 262 [a>0];
 263
 264 /* Problem 56: OK */
 265 assume(a>0);
 266 [a>0];
 267 multthru(integrate(z^(7/2)*%e^(a*z),z)),erf_representation:erfi;
 268 (8*a^3*z^(7/2)-28*a^2*z^(5/2)+70*a*z^(3/2)-105*sqrt(z))*%e^(a*z)/(8*a^4)
 269  -105*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(16*sqrt(-a)*a^4);
 270 forget(a>0);
 271 [a>0];
 272
 273 /* Problem 59: OK */
 274 assume(a>0);
 275 [a>0];
 276 multthru(integrate(z^(9/2)*%e^(a*z),z)),erf_representation:erfi;
 277 (16*a^4*z^(9/2)-72*a^3*z^(7/2)+252*a^2*z^(5/2)-630*a*z^(3/2)+945*sqrt(z))
 278  *%e^(a*z)
 279  /(16*a^5)
 280  +945*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/(32*sqrt(-a)*a^5)$
 281 forget(a>0);
 282 [a>0];
 283
 284 /* Problem 62: OK */
 285 assume(a>0);
 286 [a>0];
 287 integrate(%e^(a*z)/sqrt(z),z),erf_representation:erfi;
 288 -sqrt(%pi)*%i*erfi(%i*sqrt(-a)*sqrt(z))/sqrt(-a)$
 289 forget(a>0);
 290 [a>0];
 291
 292 /* Problem 64: NEW Type 2 (OK)
 293  * We have a problem to simplify this integral to an erfi representation,
 294  * because of expression like sqrt(-z), which do not simplify to %i*sqrt(z).
 295  * We give the results in term of the erfc function.
 296  * The same for No. 48, 49, 50, 51
 297  */
 298 multthru(integrate(%e^(a*z)/z^(3/2),z)),gamma_expand:true;
 299 2*sqrt(%pi)*sqrt(-a*z)*erfc(sqrt(-a*z))/sqrt(z)-2*%e^(a*z)/sqrt(z);
 300
 301 /* Problem 65: NEW Type 2 (OK)
 302  * Maxima simplifies z/sqrt(z^3) -> 1/sqrt(z). Therefore, we get the same
 303  * result for Problem 64 and 65.
 304  * Because of revision 1.125 of simp.lisp Maxima no longer simplifies
 305  * z/sqrt(z^3) -> 1/sqrt(z). We get a noun form.
 306  */
 307 multthru(integrate(%e^(a*z)/sqrt(z^3),z)),gamma_expand:true, domain:real;
 308 2*sqrt(%pi)*sqrt(-a*z)*erfc(sqrt(-a*z))/sqrt(z)-2*%e^(a*z)/sqrt(z)$
 309 /*'integrate(%e^(a*z)/sqrt(z^3),z);*/
 310
 311 /* Problem 66: NEW Type 2 (OK) */
 312 multthru(integrate(%e^(a*z)/z^(5/2),z)),gamma_expand:true;
 313 (-4*a*z/3-2/3)*%e^(a*z)/z^(3/2)-4*sqrt(%pi)*(-a*z)^(3/2)*erfc(sqrt(-a*z))
 314                                 /(3*z^(3/2));
 315
 316 /* Problem 67: NEW Type 2 (OK) */
 317 multthru(integrate(%e^(a*z)/z^(7/2),z)),gamma_expand:true;
 318 8*sqrt(%pi)*(-a*z)^(5/2)*erfc(sqrt(-a*z))/(15*z^(5/2))
 319  +(-8*a^2*z^2/15-4*a*z/15-2/5)*%e^(a*z)/z^(5/2);
 320
 321 /* Problem 68: NEW Type 2 (OK) */
 322 multthru(integrate(%e^(a*z)/z^(9/2),z)),gamma_expand:true;
 323 (-16*a^3*z^3/105-8*a^2*z^2/105-4*a*z/35-2/7)*%e^(a*z)/z^(7/2)
 324  -16*sqrt(%pi)*(-a*z)^(7/2)*erfc(sqrt(-a*z))/(105*z^(7/2));
 325
 326 /* ----- Involving z^(v-1), arguments b*z+d and base a ---------------------- */
 327
 328 /* Problem 69: NEW Type 2 */
 329 integrate(z^(v-1)*a^(b*z+d),z);
 330 -a^d*gamma_incomplete(v,-log(a)*b*z)*z^v/(-log(a)*b*z)^v$
 331
 332 /* Problem 70: NEW 2 */
 333 integrate(a^(b*z+d)/z,z),gamma_expand:true,logcontract;
 334 a^d*expintegral_ei(b*z*log(a));
 335
 336 /* ----- Involving z^(v-1), arguments b*z+d and base %e --------------------- */
 337
 338 /* Problem 71: NEW 2 */
 339 diffcheck(integrate(z^(v-1)*%e^(a*z+b),z),z,factor);
 340 z^(v-1)*%e^(a*z+b);
 341
 342 /* Problem 72: NEW 2 */
 343 integrate(z^n*%e^(a*z+b),z),factor;
 344 a^(-n-1)*%e^b*(-1)^n*gamma_incomplete(n+1,-a*z);
 345
 346 /* Problem 73: OK */
 347 integrate(z*%e^(a*z+b),z),factor;
 348 (a*z-1)*%e^(a*z+b)/a^2;
 349
 350 /* Problem 74: NEW 2 */
 351 integrate(%e^(a*z+b)/z,z),gamma_expand:true,logcontract;
 352 %e^b*expintegral_ei(a*z);
 353
 354 /* Problem 76: OK */
 355 assume(a>0);
 356 [a>0];
 357 integrate(%e^(a*z+b)/sqrt(z),z),erf_representation:erfi;
 358 -sqrt(%pi)*%i*%e^b*erfi(%i*sqrt(-a)*sqrt(z))/sqrt(-a)$
 359 forget(a>0);
 360 [a>0];
 361
 362 /* ----- Involving z^(v-1), arguments b*z^r and base a ---------------------- */
 363
 364 /* Problem 77: NEW 2 */
 365 integrate(z^(v-1)*a^(b*z^r),z);
 366 -gamma_incomplete(v/r,-log(a)*b*z^r)*z^v/(r*(-log(a)*b*z^r)^(v/r))$
 367
 368 /* Problem 79: NEW 2 */
 369 integrate(a^(b*z^r)/z,z),gamma_expand:true,logcontract;
 370 expintegral_ei(log(a)*b*z^r)/r;
 371
 372 /* ----- Involving z^(v-1), arguments a*z^r and base %e --------------------- */
 373
 374 /* Problem 80: NEW 2 */
 375 integrate(z^(v-1)*%e^(a*z^r),z);
 376 -gamma_incomplete(v/r,-a*z^r)*z^v/(r*(-a*z^r)^(v/r))$
 377
 378 /* Problem 81: NEW 2 */
 379 integrate(%e^(a*z^r)/z,z),gamma_expand:true,logcontract;
 380 expintegral_ei(a*z^r)/r;
 381
 382 /* Problem 82: NEW 2 */
 383 integrate(z^(2*n)*%e^(a*z^2),z),factor;
 384 -(-1)^n*gamma_incomplete((2*n+1)/2,-a*z^2)*z/(2*a^n*sqrt(-a*z^2))$
 385
 386 /* Problem 83: NEW 2 */
 387 integrate(z^(2*n-1)*%e^(a*z^2),z),factor;
 388 -(-1)^n*gamma_incomplete(n,-a*z^2)/(2*a^n);
 389
 390 /* Problem 84: OK */
 391 integrate(z*%e^(a*z^2),z);
 392 %e^(a*z^2)/(2*a);
 393
 394 /* Problem 86: OK */
 395 assume(a>0);
 396 [a>0];
 397 integrate(z^2*%e^(a*z^2),z),erf_representation:erfi;
 398 sqrt(%pi)*%i*erfi(%i*sqrt(-a)*z)/(4*sqrt(-a)*a)+z*%e^(a*z^2)/(2*a)$
 399 forget(a>0);
 400 [a>0];
 401
 402 /* Problem 88: OK */
 403 integrate(z^3*%e^(a*z^2),z);
 404 (a*z^2-1)*%e^(a*z^2)/(2*a^2);
 405
 406 /* Problem 90: OK */
 407 assume(a>0);
 408 [a>0];
 409 integrate(z^4*%e^(a*z^2),z),erf_representation:erfi;
 410 (2*a*z^3-3*z)*%e^(a*z^2)/(4*a^2)-3*sqrt(%pi)*%i*erfi(%i*sqrt(-a)*z)
 411                                  /(8*sqrt(-a)*a^2)$
 412 forget(a>0);
 413 [a>0];
 414
 415 /* Problem 92: OK */
 416 integrate(z^5*%e^(a*z^2),z);
 417 (a^2*z^4-2*a*z^2+2)*%e^(a*z^2)/(2*a^3);
 418
 419 /* Problem 93: NEW 2 */
 420 integrate(%e^(a*z^2)/z,z),gamma_expand:true,logcontract;
 421 expintegral_ei(a*z^2)/2;
 422
 423 /* Problem 94: NEW 2 */
 424 multthru(integrate(%e^(a*z^2)/z^2,z)), gamma_expand:true;
 425 sqrt(%pi)*sqrt(-a*z^2)*erfc(sqrt(-a*z^2))/z-%e^(a*z^2)/z;
 426
 427 /* Problem 95: NEW 2 */
 428 integrate(%e^(a*z^2)/z^3,z),gamma_expand:true,logcontract,ratsimp;
 429 (a*z^2*expintegral_ei(a*z^2)-%e^(a*z^2))/(2*z^2);
 430
 431 /* Problem 96: NEW 2 */
 432 integrate(%e^(a*z^2)/z^4,z), gamma_expand:true,ratsimp;
 433 (2*sqrt(%pi)*a^2*z^4*erfc(sqrt(-a*z^2))+sqrt(-a*z^2)*(2*a*z^2+1)*%e^(a*z^2))
 434  /(3*z^3*sqrt(-a*z^2))/-1;
 435
 436 /* Problem 97: NEW 2 */
 437 integrate(%e^(a*z^2)/z^5,z),gamma_expand:true,logcontract;
 438 (2*a^2*z^4*expintegral_ei(a*z^2)+(-2*a*z^2-2)*%e^(a*z^2))/(8*z^4);
 439
 440 /* Problem 98: NEW 2 */
 441 integrate(z^n*%e^(a*sqrt(z)),z);
 442 -2*gamma_incomplete(2*(n+1),-a*sqrt(z))/a^(2*(n+1));
 443
 444 /* Problem 99: OK */
 445 integrate(z*%e^(a*sqrt(z)),z);
 446 2*(a^3*z^(3/2)-3*a^2*z+6*a*sqrt(z)-6)*%e^(a*sqrt(z))/a^4;
 447
 448 /* Problem 100: OK */
 449 integrate(z^2*%e^(a*sqrt(z)),z);
 450 2*(a^5*z^(5/2)-5*a^4*z^2+20*a^3*z^(3/2)-60*a^2*z+120*a*sqrt(z)-120)
 451         *%e^(a*sqrt(z))
 452         /a^6;
 453
 454 /* Problem 101: OK */
 455 integrate(z^3*%e^(a*sqrt(z)),z);
 456 2*(a^7*z^(7/2)-7*a^6*z^3+42*a^5*z^(5/2)-210*a^4*z^2+840*a^3*z^(3/2)
 457                      -2520*a^2*z+5040*a*sqrt(z)-5040)*%e^(a*sqrt(z))
 458         /a^8;
 459
 460 /* Problem 102: OK */
 461 integrate(z^4*%e^(a*sqrt(z)),z);
 462 2*(a^9*z^(9/2)-9*a^8*z^4+72*a^7*z^(7/2)-504*a^6*z^3+3024*a^5*z^(5/2)
 463                      -15120*a^4*z^2+60480*a^3*z^(3/2)-181440*a^2*z
 464                      +362880*a*sqrt(z)-362880)*%e^(a*sqrt(z))
 465         /a^10;
 466
 467 /* Problem 103: OK */
 468 integrate(z^5*%e^(a*sqrt(z)),z);
 469 2*(a^11*z^(11/2)-11*a^10*z^5+110*a^9*z^(9/2)-990*a^8*z^4
 470                        +7920*a^7*z^(7/2)-55440*a^6*z^3+332640*a^5*z^(5/2)
 471                        -1663200*a^4*z^2+6652800*a^3*z^(3/2)-19958400*a^2*z
 472                        +39916800*a*sqrt(z)-39916800)*%e^(a*sqrt(z))
 473         /a^12;
 474
 475 /* Problem 104: NEW 2 */
 476 integrate(%e^(a*sqrt(z))/z,z),gamma_expand:true,logcontract;
 477 2*expintegral_ei(a*sqrt(z));
 478
 479 /* Problem 105: NEW 2 */
 480 integrate(%e^(a*sqrt(z))/z^2,z),gamma_expand:true,logcontract;
 481 ((2*a*z+2*sqrt(z))*%e^(a*sqrt(z))-2*a^2*expintegral_ei(a*sqrt(z))*z^(3/2))
 482  /-(2*z^(3/2));
 483
 484 /* Problem 106: NEW 2 */
 485 integrate(%e^(a*sqrt(z))/z^3,z),gamma_expand:true,logcontract;
 486 ((2*a^3*z^3+2*a^2*z^(5/2)+4*a*z^2+12*z^(3/2))*%e^(a*sqrt(z))
 487  -2*a^4*expintegral_ei(a*sqrt(z))*z^(7/2))
 488  /-(24*z^(7/2));
 489
 490 /* Problem 107: NEW 2 */
 491 integrate(%e^(a*sqrt(z))/z^4,z),gamma_expand:true,logcontract;
 492 ((2*a^5*z^5+2*a^4*z^(9/2)+4*a^3*z^4+12*a^2*z^(7/2)+48*a*z^3+240*z^(5/2))
 493  *%e^(a*sqrt(z))
 494  -2*a^6*expintegral_ei(a*sqrt(z))*z^(11/2))
 495  /-(720*z^(11/2));
 496
 497 /* Problem 108: NEW 2 */
 498 integrate(%e^(a*sqrt(z))/z^5,z),gamma_expand:true,logcontract;
 499 ((2*a^7*z^7+2*a^6*z^(13/2)+4*a^5*z^6+12*a^4*z^(11/2)+48*a^3*z^5
 500             +240*a^2*z^(9/2)+1440*a*z^4+10080*z^(7/2))
 501  *%e^(a*sqrt(z))
 502  -2*a^8*expintegral_ei(a*sqrt(z))*z^(15/2))
 503  /-(40320*z^(15/2));
 504
 505 /* ----- Involving z^(v-1), arguments b*z^r and base a ---------------------- */
 506
 507 /* Problem 109: NEW 2 */
 508 diffcheck(integrate(z^(v-1)*a^(d+b*z^r),z),z,radcan);
 509 z^(v-1)*a^(d+b*z^r);
 510
 511 /* Problem 110: NEW 2 */
 512 integrate(a^(d+b*z^r)/z,z),gamma_expand:true,logcontract;
 513 a^d*expintegral_ei(log(a)*b*z^r)/r;
 514
 515 /* ----- Involving z^(v-1), arguments b*z^r and base %e --------------------- */
 516
 517 /* Problem 111: NEW 2 */
 518 diffcheck(integrate(z^(v-1)*%e^(b+a*z^r),z),z,factor);
 519 z^(v-1)*%e^(b+a*z^r);
 520
 521 /* Problem 112: NEW 2 */
 522 integrate(%e^(b+a*z^r)/z,z),gamma_expand:true,logcontract;
 523 %e^b*expintegral_ei(a*z^r)/r;
 524
 525 /* ----- Involving (a*z+b)^-n ----------------------------------------------- */
 526
 527 /* Problem 113: NEW 3 */
 528 integrate(%e^(c*z)/(b+a*z),z),expintexpand:true,logcontract;
 529 %e^-(b*c/a)*expintegral_ei((a*c*z+b*c)/a)/a;
 530
 531 /* Problem 114: NEW 3 */
 532 integrate(%e^(c*z)/(b+a*z)^2,z);
 533 -expintegral_e(2,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b));
 534
 535 /* Problem 115: NEW 3 */
 536 integrate(%e^(c*z)/(b+a*z)^3,z);
 537 -expintegral_e(3,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b)^2);
 538
 539 /* Problem 116: NEW 3 */
 540 integrate(%e^(c*z)/(b+a*z)^4,z);
 541 -expintegral_e(4,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b)^3);
 542
 543 /* Problem 117: NEW 3 */
 544 integrate(%e^(c*z)/(b+a*z)^5,z);
 545 -expintegral_e(5,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b)^4);
 546
 547 /* Problem 118: NEW 3 */
 548 integrate(%e^(c*z)/(b+a*z)^6,z);
 549 -expintegral_e(6,-c*(a*z+b)/a)*%e^-(b*c/a)/(a*(a*z+b)^5);
 550
 551 /* Problem 119: NOUN
 552  * This integral and the integrals 120, 121, 122, 123, 124 return an
 553  * unevaluated integral. This is caused by rischint. Some of the integrals
 554  * can be integrated in a second step. The algorithm can be improved.
 555  */
 556 integrate(z*%e^(c*z)/(b+a*z),z);
 557 z*%e^(c*z)/(a*c*z+b*c)-b*'integrate(%e^(c*z)/(a^2*c*z^2+2*a*b*c*z+b^2*c),z);
 558
 559 /* Problem 120: NOUN */
 560 integrate(z^2*%e^(c*z)/(b+a*z),z);
 561 (c*z^2-z)*%e^(c*z)/(a*c^2*z+b*c^2)-'integrate(
 562                                    (b*c*z-b)*%e^(c*z)
 563                                     /(a^2*c^2*z^2+2*a*b*c^2*z+b^2*c^2),z);
 564
 565 /* Problem 121: NOUN */
 566 integrate(z*%e^(c*z)/(b+a*z)^2,z);
 567 'integrate((a*z-b)*%e^(c*z)/(a^3*c*z^3+3*a^2*b*c*z^2+3*a*b^2*c*z+b^3*c),z)
 568  +z*%e^(c*z)/(a^2*c*z^2+2*a*b*c*z+b^2*c);
 569
 570 /* Problem 122: NOUN */
 571 integrate(z^2*%e^(c*z)/(b+a*z)^2,z);
 572 z^2*%e^(c*z)/(a^2*c*z^2+2*a*b*c*z+b^2*c)
 573  -2*b*'integrate(z*%e^(c*z)/(a^3*c*z^3+3*a^2*b*c*z^2+3*a*b^2*c*z+b^3*c),z);
 574
 575 /* Problem 123: NOUN */
 576 integrate(z^3*%e^(c*z)/(b+a*z)^2,z);
 577 'integrate((2*b^2*c*z+2*b^2)*%e^(c*z)/(a^4*c^2*z^3+3*a^3*b*c^2*z^2
 578                                        +3*a^2*b^2*c^2*z+a*b^3*c^2),z)
 579   +(a*c*z^3-a*z^2-2*b*z)*%e^(c*z)/(a^3*c^2*z^2+2*a^2*b*c^2*z+a*b^2*c^2);
 580
 581 /* Problem 124: NOUN */
 582 integrate(z^4*%e^(c*z)/(b+a*z)^2,z);
 583 'integrate(((2*a*b^2*c-2*b^3*c^2)*z-2*b^3*c-4*a*b^2)*%e^(c*z)
 584             /(a^5*c^3*z^3+3*a^4*b*c^3*z^2+3*a^3*b^2*c^3*z+a^2*b^3*c^3),z)
 585  +(a^2*c^2*z^4-2*a^2*c*z^3+(2*a^2-2*a*b*c)*z^2+(2*b^2*c+4*a*b)*z)*%e^(c*z)
 586   /(a^4*c^3*z^2+2*a^3*b*c^3*z+a^2*b^2*c^3);
 587
 588 /* ----- Involving (a*z^2+b)^-n and base %e --------------------------------- */
 589
 590 /* Problem 125: NOUN */
 591 integrate(%e^(c*z)/(b+a*z^2),z);
 592 'integrate(%e^(c*z)/(a*z^2+b),z);
 593
 594 /* Problem 126: NOUN */
 595 integrate(z*%e^(c*z)/(b+a*z^2),z);
 596 'integrate((a*z^2-b)*%e^(c*z)/(a^2*c*z^4+2*a*b*c*z^2+b^2*c),z)
 597  +z*%e^(c*z)/(a*c*z^2+b*c);
 598
 599 /* Problem 127: NOUN */
 600 integrate(%e^(c*z)/(b+a*z^2)^2,z);
 601 'integrate(%e^(c*z)/(a*z^2+b)^2,z);
 602
 603 /* Problem 128: NOUN */
 604 integrate(z*%e^(c*z)/(b+a*z^2)^2,z);
 605 'integrate((3*a*z^2-b)*%e^(c*z)/(a^3*c*z^6+3*a^2*b*c*z^4+3*a*b^2*c*z^2+b^3*c),z)
 606  +z*%e^(c*z)/(a^2*c*z^4+2*a*b*c*z^2+b^2*c);
 607
 608 /* ----- Involving (a*z^2+b*z+c)^-n ----------------------------------------- */
 609
 610 /* Problem 129: NOUN */
 611 integrate(%e^(d*z)/(c+b*z+a*z^2),z);
 612 'integrate(%e^(d*z)/(a*z^2+b*z+c),z);
 613
 614 /* Problem 130: NOUN */
 615 integrate(z*%e^(d*z)/(c+b*z+a*z^2),z);
 616 'integrate((a*z^2-c)*%e^(d*z)/(a^2*d*z^4+2*a*b*d*z^3+(2*a*c*d+b^2*d)*z^2
 617                                         +2*b*c*d*z+c^2*d),z)
 618  +z*%e^(d*z)/(a*d*z^2+b*d*z+c*d);
 619
 620 /* Problem 131: NOUN */
 621 integrate(%e^(d*z)/(c+b*z+a*z^2)^2,z);
 622 'integrate(%e^(d*z)/(a*z^2+b*z+c)^2,z);
 623
 624 /* Problem 132: NOUN */
 625 integrate(z*%e^(d*z)/(c+b*z+a*z^2)^2,z);
 626 'integrate((3*a*z^2+b*z-c)*%e^(d*z)/(a^3*d*z^6+3*a^2*b*d*z^5
 627                                               +(3*a^2*c*d+3*a*b^2*d)*z^4
 628                                               +(6*a*b*c*d+b^3*d)*z^3
 629                                               +(3*a*c^2*d+3*b^2*c*d)*z^2
 630                                               +3*b*c^2*d*z+c^3*d),z)
 631  +z*%e^(d*z)/(a^2*d*z^4+2*a*b*d*z^3+(2*a*c*d+b^2*d)*z^2+2*b*c*d*z+c^2*d);
 632
 633 /* ----- Involving (a*z*b)^w and base %e ------------------------------------ */
 634
 635 /* Problem 133: NEW 3 */
 636 integrate((a*z+b)^w*%e^(c*z+d),z);
 637 -%e^(d-b*c/a)*expintegral_e(-w,-c*(a*z+b)/a)*(a*z+b)^(w+1)/a;
 638
 639 /* Problem 134: NEW 3 */
 640 integrate((a*z+b)^w*%e^(c*z),z);
 641 -%e^-(b*c/a)*expintegral_e(-w,-c*(a*z+b)/a)*(a*z+b)^(w+1)/a;
 642
 643 /* Problem 135: OK */
 644 multthru(integrate((a*z+b)^(3/2)*%e^(c*z),z));
 645 3*sqrt(%pi)*a*%e^-(b*c/a)*erf(sqrt(-c/a)*sqrt(a*z+b))/(4*c^2*sqrt(-c/a))
 646  +(2*a*c*(a*z+b)^(3/2)-3*a^2*sqrt(a*z+b))*%e^(c*(a*z+b)/a-b*c/a)/(2*a*c^2);
 647
 648 /* Problem 136: OK */
 649 multthru(integrate(sqrt(a*z+b)*%e^(c*z),z));
 650 sqrt(a*z+b)*%e^(c*(a*z+b)/a-b*c/a)/c-sqrt(%pi)*%e^-(b*c/a)
 651                                               *erf(sqrt(-c/a)*sqrt(a*z+b))
 652                                      /(2*c*sqrt(-c/a));
 653
 654 /* Problem 137: OK */
 655 integrate(%e^(c*z)/sqrt(a*z+b),z);
 656 sqrt(%pi)*%e^-(b*c/a)*erf(sqrt(-c/a)*sqrt(a*z+b))/(a*sqrt(-c/a));
 657
 658 /* Problem 138: NEW 2
 659  * This example is first transformed to an example of type 2.
 660  */
 661 diffcheck(integrate(%e^(c*z)/(a*z+b)^(3/2),z),z,factor);
 662 %e^(c*z)/(a*z+b)^(3/2);
 663
 664 /* ----- Involving a*z^2+b*z+c ---------------------------------------------- */
 665
 666 /* Problem 139: OK */
 667 integrate(d^(c+b*z+a*z^2),z),erf_representation:erfi,radexpand:all,factor;
 668 sqrt(%pi)*d^c*%e^-(b^2*log(d)/(4*a))*erfi(sqrt(log(d))*(2*a*z+b)/(2*sqrt(a)))
 669  /(2*sqrt(a)*sqrt(log(d)));
 670
 671 /* Problem 140: OK */
 672 integrate(%e^(c+b*z+a*z^2),z),erf_representation:erfi,radexpand:all,factor;
 673 sqrt(%pi)*%e^(c-b^2/(4*a))*erfi((2*a*z+b)/(2*sqrt(a)))/(2*sqrt(a));
 674
 675 /* ----- Involving a*z^2+b -------------------------------------------------- */
 676
 677 /* Problem 141: OK */
 678 integrate(d^(b*z+a*z^2),z),erf_representation:erfi,radexpand:all,factor;
 679 sqrt(%pi)*%e^-(b^2*log(d)/(4*a))*erfi(sqrt(log(d))*(2*a*z+b)/(2*sqrt(a)))
 680  /(2*sqrt(a)*sqrt(log(d)));
 681
 682 /* Problem 142: OK */
 683 integrate(%e^(b*z+a*z^2),z),erf_representation:erfi,radexpand:all,factor;
 684 sqrt(%pi)*%e^-(b^2/(4*a))*erfi((2*a*z+b)/(2*sqrt(a)))/(2*sqrt(a))$
 685
 686 /* Involving a*z^2+c -------------------------------------------------------- */
 687
 688 /* Problem 143: OK */
 689 integrate(d^(c+a*z^2),z),erf_representation:erfi,radexpand:all;
 690 sqrt(%pi)*d^c*erfi(sqrt(a)*sqrt(log(d))*z)/(2*sqrt(a)*sqrt(log(d)))$
 691
 692 /* Problem 144: OK */
 693 integrate(%e^(c+a*z^2),z),erf_representation:erfi,radexpand:all;
 694 sqrt(%pi)*%e^c*erfi(sqrt(a)*z)/(2*sqrt(a));
 695
 696 /* Involving a*z^2+b/z^2 ---------------------------------------------------- */
 697
 698 /* Problem 145: NEW 4 */
 699 diffcheck(integrate(d^(b/z^2+a*z^2),z),z,factor_radcan);
 700 d^(b/z^2+a*z^2);
 701
 702 /* Problem 146: NEW 4 */
 703 diffcheck(integrate(%e^(b/z^2+a*z^2),z),z,factor);
 704 %e^(b/z^2+a*z^2);
 705
 706 /* ----- Involving az^2+b/z^2+c --------------------------------------------- */
 707
 708 /* Problem 147: NEW 4 */
 709 diffcheck(integrate(d^(c+b/z^2+a*z^2),z),z,factor_radcan);
 710 d^(c+b/z^2+a*z^2);
 711
 712 /* Problem 148: NEW 4 */
 713 diffcheck(integrate(%e^(c+b/z^2+a*z^2),z),z,factor);
 714 %e^(c+b/z^2+a*z^2);
 715
 716 /* ----- Involving a*z+b*sqrt(z)+c ------------------------------------------ */
 717
 718 /* Problem 149: NEW 5
 719  * This integral is first transformed to an integral of type 5.
 720  */
 721 diffcheck(integrate(d^(c+a*z+sqrt(z)*b),z),z,radcan);
 722 d^(c+a*z+sqrt(z)*b);
 723
 724 /* Problem 150: NEW 5
 725  * This integral is first transformed to an integral of type 5.
 726 */
 727 diffcheck(integrate(%e^(c+a*z+sqrt(z)*b),z),z,factor), domain:real;
 728 %e^(c+a*z+sqrt(z)*b);
 729
 730 /* ----- Involving a*z+b*sqrt(z) -------------------------------------------- */
 731
 732 /* Problem 151: NEW 5 */
 733 diffcheck(integrate(d^(a*z+sqrt(z)*b),z),z,radcan);
 734 d^(a*z+sqrt(z)*b);
 735
 736 /* Problem 152: NEW 5 */
 737 diffcheck(integrate(%e^(a*z+sqrt(z)*b),z),z,factor), domain:real;
 738 %e^(a*z+sqrt(z)*b);
 739
 740 /* ----- Involving a*z^r+c -------------------------------------------------- */
 741
 742 /* Problem 153: NEW 1 */
 743 diffcheck(integrate(d^(c+a*z^r),z),z,radcan);
 744 d^(c+a*z^r);
 745
 746 /* Problem 154: NEW 1 */
 747 diffcheck(integrate(%e^(c+a*z^r),z),z,factor);
 748 %e^(c+a*z^r);
 749
 750 /* Problem 155: OK */
 751 integrate(%e^(c+a*z^2),z),erf_representation:erfi,radexpand:all;
 752 sqrt(%pi)*%e^c*erfi(sqrt(a)*z)/(2*sqrt(a))$
 753
 754 /* Problem 156: OK */
 755 integrate(%e^(c+a*sqrt(z)),z);
 756 2*(a*%e^c*sqrt(z)-%e^c)*%e^(a*sqrt(z))/a^2;
 757
 758 /* ----- Arguments involving exponential functions -------------------------- */
 759
 760 /* Problem 157: NEW 2 */
 761 integrate(a^b^z,z),gamma_expand:true,logcontract;
 762 expintegral_ei(log(a)*b^z)/log(b);
 763
 764 /* Problem 158: NEW 2 */
 765 integrate(%e^a^z,z),gamma_expand:true,logcontract,domain:complex;
 766 (expintegral_ei(a^z)+log(-1))/log(a);
 767
 768 /* Problem 159: NEW 2 */
 769 integrate(%e^%e^z,z),gamma_expand:true,logexpand:all;
 770 expintegral_ei(%e^z)+log(-1);
 771
 772 /* ----- Involving trigonometric functions ---------------------------------- */
 773
 774 /* Problem 160: NOUN */
 775 integrate(%e^tan(z),z);
 776 'integrate(%e^tan(z),z);
 777
 778 /* Problem 161: NOUN */
 779 integrate(%e^(a*tan(z)),z);
 780 'integrate(%e^(a*tan(z)),z);
 781
 782 /* Problem 162: NOUN */
 783 integrate(%e^cot(z),z);
 784 'integrate(%e^cot(z),z);
 785
 786 /* Problem 163: NOUN */
 787 integrate(%e^(a*cot(z)),z);
 788 'integrate(%e^(a*cot(z)),z);
 789
 790 /* ----- Involving hyperbolic functions ------------------------------------- */
 791
 792 /* Problem 164: NOUN */
 793 integrate(%e^tanh(z),z);
 794 'integrate(%e^tanh(z),z);
 795
 796 /* Problem 165: NOUN */
 797 integrate(%e^(a*tanh(z)),z);
 798 'integrate(%e^(a*tanh(z)),z);
 799
 800 /* Problem 166: NOUN */
 801 integrate(%e^coth(z),z);
 802 'integrate(%e^coth(z),z);
 803
 804 /* Problem 167: NOUN */
 805 integrate(%e^(a*coth(z)),z);
 806 'integrate(%e^(a*coth(z)),z);
 807
 808 /* ----- Involving inverse trigonometric functions -------------------------- */
 809
 810 /* Problem 168: NOUN */
 811 integrate(%e^asin(z),z);
 812 'integrate(%e^asin(z),z);
 813
 814 /* Problem 169: NOUN */
 815 integrate(%e^(a*asin(z)),z);
 816 'integrate(%e^(a*asin(z)),z);
 817
 818 /* Problem 170: NOUN */
 819 integrate(%e^acos(z),z);
 820 'integrate(%e^acos(z),z);
 821
 822 /* Problem 171: NOUN */
 823 integrate(%e^(a*acos(z)),z);
 824 'integrate(%e^(a*acos(z)),z);
 825
 826 /* Problem 172: NOUN */
 827 integrate(%e^atan(z),z);
 828 'integrate(%e^atan(z),z);
 829
 830 /* Problem 173: NOUN */
 831 integrate(%e^(a*atan(z)),z);
 832 'integrate(%e^(a*atan(z)),z);
 833
 834 /* Problem 174: NOUN */
 835 integrate(%e^acot(z),z);
 836 'integrate(%e^acot(z),z);
 837
 838 /* Problem 175: NOUN */
 839 integrate(%e^(a*acot(z)),z);
 840 'integrate(%e^(a*acot(z)),z);
 841
 842 /* Problem 176: NOUN */
 843 integrate(%e^acsc(z),z);
 844 'integrate(%e^acsc(z),z);
 845
 846 /* Problem 177: NOUN */
 847 integrate(%e^(a*acsc(z)),z);
 848 'integrate(%e^(a*acsc(z)),z);
 849
 850 /* Problem 178: NOUN */
 851 integrate(%e^asec(z),z);
 852 'integrate(%e^asec(z),z);
 853
 854 /* Problem 179: NOUN */
 855 integrate(%e^(a*asec(z)),z);
 856 'integrate(%e^(a*asec(z)),z);
 857
 858 /* Arguments invovling inverse hyperbolic functions ------------------------- */
 859
 860 /* Problem 180: NEW 12/2009 */
 861 integrate(%e^asinh(z),z);
 862 log(sqrt(z^2+1)+z)/2+z*sqrt(z^2+1)/2+z^2/2;
 863
 864 /* Problem 181: NOUN */
 865 integrate(%e^(a*asinh(z)),z);
 866 'integrate(%e^(a*asinh(z)),z);
 867
 868 /* Problem 182: NEW 12/2009 */
 869 integrate(%e^acosh(z),z);
 870 -log(2*sqrt(z^2-1)+2*z)/2+z*sqrt(z^2-1)/2+z^2/2;
 871
 872 /* Problem 183: NOUN */
 873 integrate(%e^(a*acosh(z)),z);
 874 'integrate(%e^(a*acosh(z)),z);
 875
 876 /* Problem 184: NOUN */
 877 integrate(%e^atan(z),z);
 878 'integrate(%e^atan(z),z);
 879
 880 /* Problem 185: NOUN */
 881 integrate(%e^(a*atan(z)),z);
 882 'integrate(%e^(a*atan(z)),z);
 883
 884 /* Problem 186: NOUN */
 885 integrate(%e^acot(z),z);
 886 'integrate(%e^acot(z),z);
 887
 888 /* Problem 187: NOUN */
 889 integrate(%e^(a*acot(z)),z);
 890 'integrate(%e^(a*acot(z)),z);
 891
 892 /* Problem 189: NEW 08/2010
 893  * This example works nicely for x>0. For z complex we get abs(z) expressions.
 894  */
 895 assume(x>0);
 896 [x>0];
 897 integrate(%e^acsch(x),x),radcan;
 898 -log(sqrt(x^2+1)+1)+2*log(x)+sqrt(x^2+1);
 899 forget(x>0);
 900 [x>0];
 901
 902 /* Problem 191: NOUN */
 903 integrate(%e^(a*acsch(z)),z);
 904 'integrate(%e^(a*acsch(z)),z);
 905
 906 /* Problem 193: NEW 12/2009 */
 907 assume(x>0);
 908 [x>0];
 909 integrate(%e^asech(x),x),ratsimp;
 910 -log((2*sqrt(1-x^2)+2)/x)+log(x)+sqrt(1-x^2)$
 911 forget(x>0);
 912 [x>0];
 913
 914 /* Problem 195: NOUN */
 915 integrate(%e^(a*asech(z)),z);
 916 'integrate(%e^(a*asech(z)),z);
 917
 918 /* ----- Involving z^n*d^(a*z^r+b*z) ---------------------------------------- */
 919
 920 /* Problem 196: NEW 5 */
 921 niceindices(integrate(z^n*d^(b*z+a*z^2),z));
 922 -a^(-n-1)*('sum(b^(n-i)*gamma_incomplete((i+1)/2,-log(d)*(2*a*z+b)^2/(4*a))
 923                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
 924                  /(-log(d)*(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
 925  /(2*d^(b^2/(4*a)));
 926
 927 /* ----- Prove algorithm type 5 for some special case ----- */
 928
 929 diffcheck(integrate(z*d^(b*z+a*z^2),z),z,radcan);
 930 z*d^(b*z+a*z^2);
 931
 932 diffcheck(integrate(z^2*d^(b*z+a*z^2),z),z,radcan);
 933 z^2*d^(b*z+a*z^2);
 934
 935 diffcheck(integrate(z^3*d^(b*z+a*z^2),z),z,radcan);
 936 z^3*d^(b*z+a*z^2);
 937
 938 /* Problem 200: NEW 5 */
 939 niceindices(integrate(z^n*%e^(b*z+a*z^2),z));
 940 -a^(-n-1)*%e^-(b^2/(4*a))
 941          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-(2*a*z+b)^2/(4*a))
 942                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
 943                  /(-(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
 944  /2;
 945
 946 /* ----- Prove algorithm type 5 for some special case ----- */
 947
 948 diffcheck(integrate(z*%e^(b*z+a*z^2),z),z,factor), domain:real;
 949 z*%e^(a*z^2+b*z)$
 950
 951 diffcheck(integrate(z^2*%e^(b*z+a*z^2),z),z,factor), domain:real;
 952 z^2*%e^(a*z^2+b*z)$
 953
 954 diffcheck(integrate(z^3*%e^(b*z+a*z^2),z),z,factor), domain:real;
 955 z^3*%e^(a*z^2+b*z)$
 956
 957 /* Problem 204: NEW 6 */
 958 niceindices(niceindices(integrate(z^n*d^(b*z+a*sqrt(z)),z)));
 959 log(d)^(-2*(n+1)+2*n+1)*2^(-n-1)
 960                        *('sum(4^j*binomial(n,j)
 961                                  *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
 962                                                   *(2*b*sqrt(z)+a)^(j+i)
 963                                                   *(a*log(d)
 964                                                      *gamma_incomplete(
 965                                                       (j+i+1)/2,
 966                                                       -log(d)
 967                                                        *(2*b*sqrt(z)+a)^2
 968                                                        /(4*b))*(2*b*sqrt(z)+a)
 969                                                    +2*b
 970                                                      *gamma_incomplete(
 971                                                       (j+i+2)/2,
 972                                                       -log(d)
 973                                                        *(2*b*sqrt(z)+a)^2
 974                                                        /(4*b))
 975                                                      *sqrt(
 976                                                       -log(d)
 977                                                        *(2*b*sqrt(z)+a)^2
 978                                                        /b))
 979                                         /(-log(d)*(2*b*sqrt(z)+a)^2/b)
 980                                          ^((j+i+1)/2),i,0,j),j,0,n))
 981  /(b^(2*(n+1))*d^(a^2/(4*b)));
 982
 983 /* --- For special cases n the integral is transformed to type 5 ------------ */
 984
 985 diffcheck(integrate(z*d^(b*z+a*sqrt(z)),z),z,radcan);
 986 z*d^(b*z+a*sqrt(z));
 987
 988 diffcheck(integrate(z^2*d^(b*z+a*sqrt(z)),z),z,radcan);
 989 z^2*d^(b*z+a*sqrt(z));
 990
 991 diffcheck(integrate(z^3*d^(b*z+a*sqrt(z)),z),z,radcan);
 992 z^3*d^(b*z+a*sqrt(z));
 993
 994 /* Problem 208: NEW 6 */
 995 niceindices(niceindices(integrate(z^n*%e^(b*z+a*sqrt(z)),z)));
 996 %e^-(a^2/(4*b))*2^(-n-1)
 997                *('sum(4^j*binomial(n,j)
 998                          *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
 999                                           *(2*b*sqrt(z)+a)^(j+i)
1000                                           *(a
1001                                            *gamma_incomplete(
1002                                             (j+i+1)/2,
1003                                             -(2*b*sqrt(z)+a)^2/(4*b))
1004                                            *(2*b*sqrt(z)+a)
1005                                            +2*b
1006                                              *gamma_incomplete(
1007                                               (j+i+2)/2,
1008                                               -(2*b*sqrt(z)+a)^2/(4*b))
1009                                              *sqrt(-(2*b*sqrt(z)+a)^2/b))
1010                                 /(-(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,0,j),j,
1011                       0,n))
1012  /b^(2*(n+1));
1013
1014 /* --- Again the problem is integrated with type 5 --- */
1015
1016 diffcheck(integrate(z*%e^(b*z+a*sqrt(z)),z),z,factor), domain:real;
1017 z*%e^(b*z+a*sqrt(z));
1018
1019 diffcheck(integrate(z^2*%e^(b*z+a*sqrt(z)),z),z,factor), domain:real;
1020 z^2*%e^(b*z+a*sqrt(z));
1021
1022 diffcheck(integrate(z^3*%e^(b*z+a*sqrt(z)),z),z,factor), domain:real;
1023 z^3*%e^(b*z+a*sqrt(z));
1024
1025 /* ----- Involving z^n*d^(a*z^r+b*z+c) -------------------------------------- */
1026
1027 /* Problem 212: NEW 5 */
1028 niceindices(integrate(z^n*d^(c+b*z+a*z^2),z));
1029 -a^(-n-1)*d^(c-b^2/(4*a))
1030          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-log(d)*(2*a*z+b)^2/(4*a))
1031                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
1032                  /(-log(d)*(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
1033  /2;
1034
1035 /* Problem 213: NEW 5 */
1036 niceindices(integrate(z^n*%e^(c+b*z+a*z^2),z));
1037 -a^(-n-1)*%e^(c-b^2/(4*a))
1038          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-(2*a*z+b)^2/(4*a))
1039                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
1040                  /(-(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
1041  /2;
1042
1043 /* Problem 214: NEW 6 */
1044 niceindices(niceindices(integrate(z^n*d^(c+b*z+a*sqrt(z)),z)));
1045 d^(c-a^2/(4*b))*log(d)^(-2*(n+1)+2*n+1)*2^(-n-1)
1046                *('sum(4^j*binomial(n,j)
1047                          *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
1048                                           *(2*b*sqrt(z)+a)^(j+i)
1049                                           *(a*log(d)
1050                                              *gamma_incomplete(
1051                                               (j+i+1)/2,
1052                                               -log(d)*(2*b*sqrt(z)+a)^2/(4*b))
1053                                              *(2*b*sqrt(z)+a)
1054                                            +2*b
1055                                              *gamma_incomplete(
1056                                               (j+i+2)/2,
1057                                               -log(d)*(2*b*sqrt(z)+a)^2/(4*b))
1058                                              *sqrt(
1059                                               -log(d)*(2*b*sqrt(z)+a)^2/b))
1060                                 /(-log(d)*(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,
1061                                0,j),j,0,n))
1062  /b^(2*(n+1));
1063
1064 /* Problem 215: NEW 6 */
1065 niceindices(niceindices(integrate(z^n*%e^(c+b*z+a*sqrt(z)),z)));
1066 %e^(c-a^2/(4*b))*2^(-n-1)
1067                 *('sum(4^j*binomial(n,j)
1068                           *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
1069                                            *(2*b*sqrt(z)+a)^(j+i)
1070                                            *(a
1071                                             *gamma_incomplete(
1072                                              (j+i+1)/2,
1073                                              -(2*b*sqrt(z)+a)^2/(4*b))
1074                                             *(2*b*sqrt(z)+a)
1075                                             +2*b
1076                                               *gamma_incomplete(
1077                                                (j+i+2)/2,
1078                                                -(2*b*sqrt(z)+a)^2/(4*b))
1079                                               *sqrt(-(2*b*sqrt(z)+a)^2/b))
1080                                  /(-(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,0,j),j,
1081                        0,n))
1082  /b^(2*(n+1));
1083
1084 /* ----- Involving z^(v-1)*d^(c+a*z^r) -------------------------------------- */
1085
1086 /* Problem 216: NEW 2 */
1087 integrate(z^(v-1)*d^(c+a*z^r),z);
1088 -d^c*gamma_incomplete(v/r,-a*log(d)*z^r)*z^v/(r*(-a*log(d)*z^r)^(v/r));
1089
1090 /* Problem 217: NEW 2 */
1091 integrate(z^(v-1)*%e^(c+a*z^r),z);
1092 -%e^c*gamma_incomplete(v/r,-a*z^r)*z^v/(r*(-a*z^r)^(v/r));
1093
1094 /* Problem 218: NEW 2 */
1095 integrate(z^(v-1)*d^(c+a*z^2),z);
1096 -d^c*gamma_incomplete(v/2,-a*log(d)*z^2)*z^v/(2*(-a*log(d)*z^2)^(v/2));
1097
1098 /* Problem 219: NEW 2 */
1099 integrate(z^(v-1)*%e^(c+a*z^2),z);
1100 -%e^c*gamma_incomplete(v/2,-a*z^2)*z^v/(2*(-a*z^2)^(v/2));
1101
1102 /* Problem 220: NEW 2 */
1103 integrate(z^(v-1)*d^(c+a*sqrt(z)),z);
1104 -2*d^c*gamma_incomplete(2*v,-a*log(d)*sqrt(z))*z^v/(-a*log(d)*sqrt(z))^(2*v);
1105
1106 /* Problem 221: NEW 2 */
1107 integrate(z^(v-1)*%e^(c+a*sqrt(z)),z);
1108 -2*%e^c*gamma_incomplete(2*v,-a*sqrt(z))*z^v/(-a*sqrt(z))^(2*v);
1109
1110 /* ----- Involving z^(2*n)*d^(a*z^2+b/Z^2) ---------------------------------- */
1111
1112 /* Problem 222: NOUN */
1113 integrate(z^(2*n)*d^(b/z^2+a*z^2),z);
1114 'integrate(d^(a*z^2+b/z^2)*z^(2*n),z);
1115
1116 /* Problem 223: NOUN */
1117 integrate(z^(2*n)*%e^(b/z^2+a*z^2),z);
1118 'integrate(z^(2*n)*%e^(a*z^2+b/z^2),z);
1119
1120 /* ----- Involving z^(2*n)*d^(a*z^2+b/Z^2+c) -------------------------------- */
1121
1122 /* Problem 224: NOUN */
1123 integrate(z^(2*n)*d^(c+b/z^2+a*z^2),z);
1124 'integrate(d^(a*z^2+b/z^2+c)*z^(2*n),z);
1125
1126 /* Problem 225: NOUN */
1127 integrate(z^(2*n)*%e^(c+b/z^2+a*z^2),z);
1128 'integrate(z^(2*n)*%e^(a*z^2+b/z^2+c),z);
1129
1130 /* ----- Involving powers of exp with arguments c*z and base a -------------- */
1131
1132 /* Problem 226: OK */
1133 integrate((a^(c*z))^v,z);
1134 (a^(c*z))^v/(c*v*log(a));
1135
1136 /* Problem 227: OK */
1137 integrate((a^z)^v,z);
1138 (a^z)^v/(log(a)*v);
1139
1140 /* ----- with arguments c*z and base %e ------------------------------------- */
1141
1142 /* The following examples 217 - 224 are not really correct, because Maxima
1143  * simplifies (%e^(c*z))^v -> %e^(v*c*z), which is not correct in general.
1144  */
1145
1146 /* Problem 228: OK */
1147 integrate((%e^(c*z))^v,z);
1148 (%e^(c*z))^v/(c*v);
1149
1150 /* Problem 229: OK */
1151 integrate((%e^z)^v,z);
1152 (%e^z)^v/v;
1153
1154 /* Problem 230: OK */
1155 integrate(sqrt(%e^(c*z)),z);
1156 2*sqrt(%e^(c*z))/c;
1157
1158 /* Problem 231: OK */
1159 integrate((%e^(c*z))^(3/2),z);
1160 2*(%e^(c*z))^(3/2)/(3*c);
1161
1162 /* Problem 232: OK */
1163 integrate((%e^(c*z))^(5/2),z);
1164 2*(%e^(c*z))^(5/2)/(5*c);
1165
1166 /* Problem 233: OK */
1167 integrate(1/sqrt(%e^(c*z)),z);
1168 -2/(c*sqrt(%e^(c*z)));
1169
1170 /* Problem 234: OK */
1171 integrate(1/(%e^(c*z))^(3/2),z);
1172 -2*(%e^(c*z))^(-3/2)/(3*c);
1173
1174 /* Problem 235: OK */
1175 integrate(1/(%e^(c*z))^(5/2),z);
1176 -2*(%e^(c*z))^(-5/2)/(5*c);
1177
1178 /* ----- with arguments c*z+b and base a ------------------------------------ */
1179
1180 /* Problem 236: OK */
1181 integrate((a^(c*z+b))^v,z);
1182 (a^(c*z+b))^v/(log(a)*c*v);
1183
1184 /* -----  with arguments c*z+b and base %e ---------------------------------- */
1185
1186 /* Problem 237: (OK) wrong simplification */
1187 integrate((%e^(c*z+b))^v,z);
1188 (%e^(c*z+b))^v/(c*v);
1189
1190 /* ----- with arguments c*z^r and base a ------------------------------------ */
1191
1192 /* Problem 238: NEW 1a */
1193 integrate((a^(c*z^r))^v,z);
1194 -gamma_incomplete(1/r,-log(a)*c*v*z^r)*(a^(c*z^r))^v*z
1195  /(a^(c*v*z^r)*r*(-log(a)*c*v*z^r)^(1/r));
1196
1197 /* Problem 239: (OK) wrong simplification
1198  * The examples 229 and 230 are not really correct.
1199  * e.g. (a^(c*z^2))^v is wrongly simplified to a^(v*c*z^2) and integrated.
1200  */
1201 integrate((a^(c*z^2))^v,z), domain:real;
1202 sqrt(%pi)*erf(sqrt(-log(a)*c*v)*z)/(2*sqrt(-log(a)*c*v))$
1203
1204 /* Problem 240: (OK) wrong simplification */
1205 integrate((a^(c*sqrt(z)))^v,z), domain:real;
1206 2*(log(a)*c*v*sqrt(z)-1)*%e^(log(a)*c*v*sqrt(z))/(log(a)^2*c^2*v^2)$
1207
1208 /* ----- with arguments c*z^r ----------------------------------------------- */
1209
1210 /* Problem 241: NEW 1a */
1211 integrate((%e^(c*z^r))^v,z);
1212 -gamma_incomplete(1/r,-c*v*z^r)*z*(%e^(c*z^r))^v*%e^-(c*v*z^r)
1213  /(r*(-c*v*z^r)^(1/r));
1214
1215 /* Problem 242: (OK) wrong simplification*/
1216 integrate((%e^(c*z^2))^v,z), domain:real;
1217 sqrt(%pi)*erf(sqrt(-c*v)*z)/(2*sqrt(-c*v))$
1218
1219 /* Problem 243: (OK) wrong simplification*/
1220 integrate((%e^(c*sqrt(z)))^v,z), domain:real;
1221 2*(c*v*sqrt(z)-1)*%e^(c*v*sqrt(z))/(c^2*v^2)$
1222
1223 /* ----- with arguments c*z^r+d and base a ---------------------------------- */
1224
1225 /* Problem 244: NEW 1a */
1226 integrate((a^(d+c*z^r))^v,z);
1227 -gamma_incomplete(1/r,-log(a)*c*v*z^r)*(a^(c*z^r+d))^v*z
1228  /(a^(c*v*z^r)*r*(-log(a)*c*v*z^r)^(1/r));
1229
1230 /* Problem 245: (OK) wrong simplification */
1231 integrate((a^(d+c*z^2))^v,z), domain:real;
1232 sqrt(%pi)*a^(d*v)*erf(sqrt(-log(a)*c*v)*z)/(2*sqrt(-log(a)*c*v))$
1233
1234 /* Problem 246: (OK) wrong simplification */
1235 integrate((a^(d+c*sqrt(z)))^v,z), domain:real;
1236 2*(a^(d*v)*log(a)*c*v*sqrt(z)-a^(d*v))*%e^(log(a)*c*v*sqrt(z))
1237  /(log(a)^2*c^2*v^2)$
1238
1239 /* ----- with arguments c*z^r+d --------------------------------------------- */
1240
1241 /* Problem 247: New 1a */
1242 integrate((%e^(d+c*z^r))^v,z);
1243 -gamma_incomplete(1/r,-c*v*z^r)*z*%e^-(c*v*z^r)*(%e^(c*z^r+d))^v
1244  /(r*(-c*v*z^r)^(1/r));
1245
1246 /* Problem 248: (OK) wrong simplification */
1247 integrate((%e^(d+c*z^2))^v,z), domain:real;
1248 sqrt(%pi)*%e^(d*v)*erf(sqrt(-c*v)*z)/(2*sqrt(-c*v))$
1249
1250 /* Problem 249: (OK) wrong simplification */
1251 integrate((%e^(d+c*sqrt(z)))^v,z), domain:real;
1252 2*(c*v*%e^(d*v)*sqrt(z)-%e^(d*v))*%e^(c*v*sqrt(z))/(c^2*v^2)$
1253
1254 /* ----- with arguments c*(z^r)^p and base a -------------------------------- */
1255
1256 /* Problem 250: NEW 1a
1257  * The minus factor is a workaround to get a comparable answer.
1258  */
1259 -integrate((a^(c*(z^r)^p))^v,z);
1260 gamma_incomplete(1/(p*r),-log(a)*c*v*(z^r)^p)*(a^(c*(z^r)^p))^v*z
1261  /(a^(c*v*(z^r)^p)*p*r*(-log(a)*c*v*(z^r)^p)^(1/(p*r)));
1262
1263 /* Problem 251: (OK) wrong simplification */
1264 integrate((a^(c*(z^r)^(1/r)))^v,z), domain:real;
1265 %e^(log(a)*c*v*z)/(log(a)*c*v)$
1266
1267 /* Problem 252: (OK) wrong simplification */
1268 integrate((a^(c*sqrt(z^2)))^v,z), domain:real;
1269 %e^(log(a)*c*v*z)/(log(a)*c*v)$
1270
1271 /* Problem 253: NEW 1a */
1272 integrate((%e^(c*(z^r)^p))^v,z);
1273 -gamma_incomplete(1/(p*r),-c*v*(z^r)^p)*z*(%e^(c*(z^r)^p))^v*%e^-(c*v*(z^r)^p)
1274  /(p*r*(-c*v*(z^r)^p)^(1/(p*r)));
1275
1276 /* Problem 254: (OK) wrong simplification */
1277 integrate((%e^(c*(z^r)^(1/r)))^v,z), domain:real;
1278 %e^(c*v*z)/(c*v)$
1279
1280 /* Problem 255: (OK) wrong simplification */
1281 integrate((%e^(c*sqrt(z^2)))^v,z), domain:real;
1282 %e^(c*v*z)/(c*v)$
1283
1284 /* ----- with arguments c*(z^r)^p+d and base a ------------------------------ */
1285
1286 /* Problem 256: NEW 1a */
1287 -integrate((a^(d+c*(z^r)^p))^v,z);
1288 gamma_incomplete(1/(p*r),-log(a)*c*v*(z^r)^p)*(a^(c*(z^r)^p+d))^v*z
1289  /(a^(c*v*(z^r)^p)*p*r*(-log(a)*c*v*(z^r)^p)^(1/(p*r)))$
1290
1291 /* Problem 257: (OK) wrong simplification */
1292 integrate((a^(d+c*(z^r)^(1/r)))^v,z), domain:real;
1293 a^(d*v)*%e^(log(a)*c*v*z)/(log(a)*c*v);
1294
1295 /* Problem 258: (OK) wrong simplification */
1296 integrate((a^(d+c*sqrt(z^2)))^v,z), domain:real;
1297 a^(d*v)*%e^(log(a)*c*v*z)/(log(a)*c*v);
1298
1299 /* Problem 259: NEW 1a */
1300 integrate((%e^(d+c*(z^r)^p))^v,z);
1301 -gamma_incomplete(1/(p*r),-c*v*(z^r)^p)*z*%e^-(c*v*(z^r)^p)
1302                                        *(%e^(c*(z^r)^p+d))^v
1303  /(p*r*(-c*v*(z^r)^p)^(1/(p*r)));
1304
1305 /* Problem 260: (OK) wrong simplification */
1306 integrate((%e^(d+c*(z^r)^(1/r)))^v,z), domain:real;
1307 %e^(c*v*z+d*v)/(c*v);
1308
1309 /* Problem 261: (OK) wrong simplification */
1310 integrate((%e^(d+c*sqrt(z^2)))^v,z), domain:real;
1311 %e^(c*v*z+d*v)/(c*v);
1312
1313 /* ----- with arguments a*z^2+b/z^2 ----------------------------------------- */
1314
1315 /* Problem 262: Noun */
1316 integrate((%e^(b/z^2+a*z^2))^v,z);
1317 'integrate((%e^(b/z^2+a*z^2))^v,z);
1318
1319 /* ----- with arguments a*z^2+b/z^2+c --------------------------------------- */
1320
1321 /* Problem 263: Noun */
1322 integrate((%e^(c+b/z^2+a*z^2))^v,z);
1323 'integrate((%e^(c+b/z^2+a*z^2))^v,z);
1324
1325 /* ----- Involving products of power functions ------------------------------ */
1326
1327 /* ----- a^(d*z)*h^(c*z) ---------------------------------------------------- */
1328
1329 /* Problem 265: OK
1330  * In this example we have a substitution of a^(d*z).
1331  * We get a question about the sign of an expression.
1332
1333   The expand(XXX,0,0) is due to a bug--the antiderivative is unsimplified.
1334  */
1335 (assume(notequal((c * log(h))/(d * log(a)),-1)),0);
1336 0$
1337
1338 expand(integrate(a^(d*z)*h^(c*z),z),0,0);
1339 (a^(d*z))^(c*log(h)/(log(a)*d)+1)/(log(a)*(c*log(h)/(log(a)*d)+1)*d)$
1340
1341 (forget(notequal((c * log(h))/(d * log(a)),-1)),0);
1342 0$
1343
1344 /* ----- a^(d*z)*h^(c*z+g) -------------------------------------------------- */
1345
1346 /* Problem 267: OK
1347  * But not for this example. We get no question about a sign.
1348  * With the help of radcan we get the expected answer.
1349  */
1350 integrate(a^(d*z)*h^(c*z+g),z),radcan;
1351 a^(d*z)*h^(c*z+g)/(c*log(h)+log(a)*d)$
1352
1353 /* ----- a^(d*z+e)*h^(c*z+g) ------------------------------------------------ */
1354
1355 /* Problem 268: OK */
1356 integrate(a^(d*z+e)*h^(c*z+g),z),radcan;
1357 a^(d*z+e)*h^(c*z+g)/(c*log(h)+log(a)*d)$
1358
1359 /* ----- a^(d*z)*h^(c*z^r) -------------------------------------------------- */
1360
1361 /* Problem 269: OK */
1362 -integrate(a^(d*z)*h^(c*z^2),z),factor;
1363 sqrt(%pi)*%e^-(log(a)^2*d^2/(4*c*log(h)))
1364           *erf((2*c*log(h)*z+log(a)*d)/(2*sqrt(-c*log(h))))
1365  /(2*sqrt(-c*log(h)));
1366
1367 /* Problem 270: NEW 8 */
1368 diffcheck(integrate(a^(d*z)*h^(c*sqrt(z)),z),z,radcan);
1369 a^(d*z)*h^(c*sqrt(z));
1370
1371 /* ----- a^(d*z+e)*h^(c*z^r) ------------------------------------------------ */
1372
1373 /* Problem 271: OK */
1374 -integrate(a^(d*z+e)*h^(c*z^2),z),factor;
1375 sqrt(%pi)*a^e*%e^-(log(a)^2*d^2/(4*c*log(h)))
1376           *erf((2*c*log(h)*z+log(a)*d)/(2*sqrt(-c*log(h))))
1377  /(2*sqrt(-c*log(h)));
1378
1379 /* Problem 272: NEW 8 */
1380 diffcheck(integrate(a^(d*z+e)*h^(c*sqrt(z)),z),z,radcan);
1381 a^(d*z+e)*h^(c*sqrt(z));
1382
1383 /* ----- a^(b*z^r)*h^(c*z^r) ------------------------------------------------ */
1384
1385 /* Problem 273: NEW 7 */
1386 diffcheck(integrate(a^(b*z^r)*h^(c*z^r),z),z,radcan);
1387 a^(b*z^r)*h^(c*z^r);
1388
1389 /* Problem 274: OK */
1390 integrate(a^(b*z^2)*h^(c*z^2),z);
1391 sqrt(%pi)*erf(sqrt(-c*log(h)-log(a)*b)*z)/(2*sqrt(-c*log(h)-log(a)*b));
1392
1393 /* Problem 275: OK */
1394 integrate(a^(b*sqrt(z))*h^(c*sqrt(z)),z),radcan, factor;
1395 2*a^(b*sqrt(z))*h^(c*sqrt(z))*(c*log(h)*sqrt(z)+log(a)*b*sqrt(z)-1)
1396  /(c*log(h)+log(a)*b)^2;
1397
1398 /* ----- a^(d*z)*h^(c*z^r+g) ------------------------------------------------ */
1399
1400 /* Problem 276: OK */
1401 integrate(a^(d*z)*h^(g+c*z^2),z),factor;
1402 -sqrt(%pi)*h^g*%e^-(log(a)^2*d^2/(4*c*log(h)))
1403           *erf((2*c*log(h)*z+log(a)*d)/(2*sqrt(-c*log(h))))
1404  /(2*sqrt(-c*log(h)));
1405
1406 /* Problem 277: NEW 8 */
1407 diffcheck(integrate(a^(d*z)*h^(g+c*sqrt(z)),z),z,radcan);
1408 a^(d*z)*h^(g+c*sqrt(z));
1409
1410 /* ----- a^(d*z+e)*h^(c*z^r+g) ---------------------------------------------- */
1411
1412 /* Problem 278: OK */
1413 integrate(a^(d*z+e)*h^(g+c*z^2),z);
1414 sqrt(%pi)*a^e*h^g*%e^-(log(a)^2*d^2/(4*c*log(h)))
1415                  *erf(sqrt(-c*log(h))*z-log(a)*d/(2*sqrt(-c*log(h))))
1416          /(2*sqrt(-c*log(h)));
1417
1418 /* Problem 279: NEW 8 */
1419 diffcheck(integrate(a^(d*z+e)*h^(g+c*sqrt(z)),z),z,radcan);
1420 a^(d*z+e)*h^(g+c*sqrt(z));
1421
1422 /* ----- a^(b*z^r)*h^(c*z^r+g) ---------------------------------------------- */
1423
1424 /* Problem 280: NEW 7 */
1425 diffcheck(integrate(a^(b*z^r)*h^(g+c*z^r),z),z,radcan);
1426 a^(b*z^r)*h^(g+c*z^r);
1427
1428 /* Problem 281: OK */
1429 integrate(a^(b*z^2)*h^(g+c*z^2),z);
1430 sqrt(%pi)*h^g*erf(sqrt(-c*log(h)-log(a)*b)*z)
1431          /(2*sqrt(-c*log(h)-log(a)*b));
1432
1433 /* Problem 282: OK */
1434 integrate(a^(b*sqrt(z))*h^(g+c*sqrt(z)),z),radcan,factor;
1435 2*a^(b*sqrt(z))*h^(c*sqrt(z)+g)*(c*log(h)*sqrt(z)+log(a)*b*sqrt(z)-1)
1436  /(c*log(h)+log(a)*b)^2;
1437
1438 /* ----- a^(b*z^r+e)*h^(c*z^r+g) -------------------------------------------- */
1439
1440 /* Problem 283: NEW 7 */
1441 expand(integrate(a^(e+b*z^r)*h^(g+c*z^r),z) -
1442 -a^e*h^g*gamma_incomplete(1/r,-(c*log(h)+log(a)*b)*z^r)*z
1443  /(r*(-(c*log(h)+log(a)*b)*z^r)^(1/r)));
1444 0;
1445
1446 /* Problem 284: OK */
1447 integrate(a^(e+b*z^2)*h^(g+c*z^2),z);
1448 sqrt(%pi)*a^e*h^g*erf(sqrt(-c*log(h)-log(a)*b)*z)
1449          /(2*sqrt(-c*log(h)-log(a)*b));
1450
1451 /* Problem 285: OK */
1452 integrate(a^(e+b*sqrt(z))*h^(g+c*sqrt(z)),z),radcan,factor;
1453 2*a^(b*sqrt(z)+e)*h^(c*sqrt(z)+g)*(c*log(h)*sqrt(z)+log(a)*b*sqrt(z)-1)
1454  /(c*log(h)+log(a)*b)^2;
1455
1456 /* ----- a^(d*z)*h^(c*z^r+f*z) ---------------------------------------------- */
1457
1458 /* Problem 286: OK */
1459 integrate(a^(d*z)*h^(f*z+c*z^2),z);
1460 sqrt(%pi)*%e^-((-f*log(h)-log(a)*d)^2/(4*c*log(h)))
1461                  *erf(sqrt(-c*log(h))*z+(-f*log(h)-log(a)*d)
1462                                         /(2*sqrt(-c*log(h))))
1463          /(2*sqrt(-c*log(h)));
1464
1465 /* Problem 287: NEW 8 */
1466 multthru(integrate(a^(d*z)*h^(f*z+c*sqrt(z)),z));
1467 a^(d*z)*h^(f*z+c*sqrt(z))/(f*log(h)+log(a)*d)
1468  -sqrt(%pi)*c*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*log(h)
1469            *erfi((2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
1470                   /(2*sqrt(f*log(h)+log(a)*d)))
1471   /(2*(f*log(h)+log(a)*d)^(3/2));
1472
1473 /* ----- a^(d*z+e)*h^(c*z^r+f*z) -------------------------------------------- */
1474
1475 /* Problem 288: OK */
1476 integrate(a^(d*z+e)*h^(f*z+c*z^2),z);
1477 sqrt(%pi)*a^e*%e^-((-f*log(h)-log(a)*d)^2/(4*c*log(h)))
1478                  *erf(sqrt(-c*log(h))*z+(-f*log(h)-log(a)*d)
1479                                         /(2*sqrt(-c*log(h))))
1480          /(2*sqrt(-c*log(h)));
1481
1482 /* Problem 289: NEW 8 */
1483 multthru(integrate(a^(d*z+e)*h^(f*z+c*sqrt(z)),z));
1484 a^(d*z+e)*h^(f*z+c*sqrt(z))/(f*log(h)+log(a)*d)
1485  -sqrt(%pi)*a^e*c*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*log(h)
1486            *erfi((2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
1487                   /(2*sqrt(f*log(h)+log(a)*d)))
1488   /(2*(f*log(h)+log(a)*d)^(3/2));
1489
1490 /* ----- a^(b*z^r)*h^(c*z^r+f*z) -------------------------------------------- */
1491
1492 /* Problem 290: OK */
1493 integrate(a^(b*z^2)*h^(f*z+c*z^2),z);
1494 sqrt(%pi)*%e^(f^2*log(h)^2/(4*(-c*log(h)-log(a)*b)))
1495                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1496                        -f*log(h)/(2*sqrt(-c*log(h)-log(a)*b)))
1497          /(2*sqrt(-c*log(h)-log(a)*b));
1498
1499 /* Problem 291: NEW 9
1500  * This problem does not simplify to a nice expression in terms of the erf
1501  * function and a term a^b*sqrt(z)*h^(sqrt(z)+f*z), but it is correct.
1502  */
1503 diffcheck(integrate(a^(b*sqrt(z))*h^(f*z+c*sqrt(z)),z),z,radcan);
1504 a^(b*sqrt(z))*h^(f*z+c*sqrt(z));
1505
1506 /* ----- a^(b*z^r+e)*h^(c*z^r+f*z) ------------------------------------------ */
1507
1508 /* Problem 292: OK */
1509 integrate(a^(e+b*z^2)*h^(f*z+c*z^2),z);
1510 sqrt(%pi)*a^e*%e^(f^2*log(h)^2/(4*(-c*log(h)-log(a)*b)))
1511                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1512                        -f*log(h)/(2*sqrt(-c*log(h)-log(a)*b)))
1513          /(2*sqrt(-c*log(h)-log(a)*b));
1514
1515 /* Problem 293: NEW 9 */
1516 diffcheck(integrate(a^(e+b*sqrt(z))*h^(f*z+c*sqrt(z)),z),z,radcan);
1517 a^(e+b*sqrt(z))*h^(f*z+c*sqrt(z));
1518
1519 /* ----- a^(b*z^r+d*z)*h^(c*z^r+f*z) ---------------------------------------- */
1520
1521 /* Problem 294: OK */
1522 integrate(a^(d*z+b*z^2)*h^(f*z+c*z^2),z);
1523 sqrt(%pi)*%e^((-f*log(h)-log(a)*d)^2/(4*(-c*log(h)-log(a)*b)))
1524                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1525                        +(-f*log(h)-log(a)*d)/(2*sqrt(-c*log(h)-log(a)*b)))
1526          /(2*sqrt(-c*log(h)-log(a)*b));
1527
1528 /* Problem 295: NEW 9
1529  * Is this example correct? Verify it again.
1530  * The problem is that Maxima first does some substitution, the integral
1531  * is solvable too, but the result becomes more complicated.
1532  */
1533 multthru(integrate(a^(d*z+b*sqrt(z))*h^(f*z+c*sqrt(z)),z));
1534 gamma_incomplete(1,
1535                  -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1536                   /(4*(f*log(h)+log(a)*d)))
1537  *%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1538  /(f*log(h)+log(a)*d)
1539  -gamma_incomplete(1/2,
1540                    -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1541                     /(4*(f*log(h)+log(a)*d)))
1542   *%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))*(-c*log(h)-log(a)*b)
1543   *(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))
1544   /(2*(f*log(h)+log(a)*d)^2
1545      *sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1546             /(f*log(h)+log(a)*d)))$
1547
1548 /* ----- a^(d*z)*h^(c*z^r+f*z+g) -------------------------------------------- */
1549
1550 /* Problem 296: OK */
1551 integrate(a^(d*z)*h^(g+f*z+c*z^2),z);
1552 sqrt(%pi)*h^g*%e^-((-f*log(h)-log(a)*d)^2/(4*c*log(h)))
1553                  *erf(sqrt(-c*log(h))*z+(-f*log(h)-log(a)*d)
1554                                         /(2*sqrt(-c*log(h))))
1555          /(2*sqrt(-c*log(h)));
1556
1557 /* Problem 297: NEW 8 */
1558 multthru(integrate(a^(d*z)*h^(g+f*z+c*sqrt(z)),z));
1559 a^(d*z)*h^(f*z+c*sqrt(z)+g)/(f*log(h)+log(a)*d)
1560  -sqrt(%pi)*c*h^g*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*log(h)
1561            *erfi((2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
1562                   /(2*sqrt(f*log(h)+log(a)*d)))
1563   /(2*(f*log(h)+log(a)*d)^(3/2));
1564
1565 /* ----- a^(d*z+e)*h^(c*z^r+f*z+g) ------------------------------------------ */
1566
1567 /* Problem 298: OK */
1568 integrate(a^(d*z+e)*h^(g+f*z+c*z^2),z);
1569 sqrt(%pi)*a^e*h^g*%e^-((-f*log(h)-log(a)*d)^2/(4*c*log(h)))
1570                  *erf(sqrt(-c*log(h))*z+(-f*log(h)-log(a)*d)
1571                                         /(2*sqrt(-c*log(h))))
1572          /(2*sqrt(-c*log(h)));
1573
1574 /* Problem 299: NEW 8 */
1575 multthru(integrate(a^(d*z+e)*h^(g+f*z+c*sqrt(z)),z));
1576 a^(d*z+e)*h^(f*z+c*sqrt(z)+g)/(f*log(h)+log(a)*d)
1577  -sqrt(%pi)*a^e*c*h^g*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*log(h)
1578            *erfi((2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
1579                   /(2*sqrt(f*log(h)+log(a)*d)))
1580   /(2*(f*log(h)+log(a)*d)^(3/2));
1581
1582 /* ----- a^(b*z^r)*h^(c*z^r+f*z+g) ------------------------------------------ */
1583
1584 /* Problem 300: OK */
1585 integrate(a^(b*z^2)*h^(g+f*z+c*z^2),z);
1586 sqrt(%pi)*h^g*%e^(f^2*log(h)^2/(4*(-c*log(h)-log(a)*b)))
1587                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1588                        -f*log(h)/(2*sqrt(-c*log(h)-log(a)*b)))
1589          /(2*sqrt(-c*log(h)-log(a)*b));
1590
1591 /* Problem 301: NEW 9 */
1592 multthru(integrate(a^(b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z));
1593 gamma_incomplete(1,-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(4*f*log(h)))
1594  *h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))
1595  /(f*log(h))
1596  -gamma_incomplete(1/2,-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(4*f*log(h)))
1597   *h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*(-c*log(h)-log(a)*b)
1598   *(log(h)*(2*f*sqrt(z)+c)+log(a)*b)
1599   /(2*f^2*log(h)^2*sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(f*log(h))));
1600
1601 /* ----- a^(b*z^r+e)*h^(c*z^r+f*z+g) ---------------------------------------- */
1602
1603 /* Problem 302: OK */
1604 integrate(a^(e+b*z^2)*h^(g+f*z+c*z^2),z);
1605 sqrt(%pi)*a^e*h^g*%e^(f^2*log(h)^2/(4*(-c*log(h)-log(a)*b)))
1606                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1607                        -f*log(h)/(2*sqrt(-c*log(h)-log(a)*b)))
1608          /(2*sqrt(-c*log(h)-log(a)*b));
1609
1610 /* Problem 303: NEW 9 */
1611 multthru(integrate(a^(e+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z));
1612 gamma_incomplete(1,-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(4*f*log(h)))
1613  *a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))
1614  /(f*log(h))
1615  -gamma_incomplete(1/2,-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(4*f*log(h)))
1616   *a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*(-c*log(h)-log(a)*b)
1617   *(log(h)*(2*f*sqrt(z)+c)+log(a)*b)
1618   /(2*f^2*log(h)^2*sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*b)^2/(f*log(h))));
1619
1620 /* ----- a^(b*z^r+d*z)*h^(c*z^r+f*z+g) -------------------------------------- */
1621
1622 /* Problem 304: OK */
1623 integrate(a^(d*z+b*z^2)*h^(g+f*z+c*z^2),z);
1624 sqrt(%pi)*h^g*%e^((-f*log(h)-log(a)*d)^2/(4*(-c*log(h)-log(a)*b)))
1625                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1626                        +(-f*log(h)-log(a)*d)/(2*sqrt(-c*log(h)-log(a)*b)))
1627          /(2*sqrt(-c*log(h)-log(a)*b));
1628
1629 /* Problem 305: NEW 9 */
1630 multthru(integrate(a^(d*z+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z));
1631 gamma_incomplete(1,
1632                  -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1633                   /(4*(f*log(h)+log(a)*d)))
1634  *h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1635  /(f*log(h)+log(a)*d)
1636  -gamma_incomplete(1/2,
1637                    -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1638                     /(4*(f*log(h)+log(a)*d)))
1639   *h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1640   *(-c*log(h)-log(a)*b)*(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))
1641   /(2*(f*log(h)+log(a)*d)^2
1642      *sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1643             /(f*log(h)+log(a)*d)));
1644
1645 /* ----- a^(b*z^r+d*z+e)*h^(c*z^r+f*z+g) ------------------------------------ */
1646
1647 /* Problem 306: OK */
1648 integrate(a^(e+d*z+b*z^2)*h^(g+f*z+c*z^2),z);
1649 sqrt(%pi)*a^e*h^g*%e^((-f*log(h)-log(a)*d)^2/(4*(-c*log(h)-log(a)*b)))
1650                  *erf(sqrt(-c*log(h)-log(a)*b)*z
1651                        +(-f*log(h)-log(a)*d)/(2*sqrt(-c*log(h)-log(a)*b)))
1652          /(2*sqrt(-c*log(h)-log(a)*b));
1653
1654 /* Problem 307: NEW 9 */
1655 multthru(integrate(a^(e+d*z+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z));
1656 gamma_incomplete(1,
1657                  -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1658                   /(4*(f*log(h)+log(a)*d)))
1659  *a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1660  /(f*log(h)+log(a)*d)
1661  -gamma_incomplete(1/2,
1662                    -(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1663                     /(4*(f*log(h)+log(a)*d)))
1664   *a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
1665   *(-c*log(h)-log(a)*b)*(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))
1666   /(2*(f*log(h)+log(a)*d)^2
1667      *sqrt(-(log(h)*(2*f*sqrt(z)+c)+log(a)*(2*d*sqrt(z)+b))^2
1668             /(f*log(h)+log(a)*d)));
1669
1670 /* ----- a^(d*z)*b^(e*z)*c^(f*z) -------------------------------------------- */
1671
1672 /* Problem 309: OK
1673  * This example does not simplify in a product of three power functions.
1674  */
1675
1676 (assume(notequal(ratsimp((log(c)*f+log(b)*e)/(log(a)*d)),-1)),0);
1677 0$
1678
1679 integrate(a^(d*z)*b^(e*z)*c^(f*z),z);
1680 (a^(d*z))^(log(c)*f/(log(a)*d)+log(b)*e/(log(a)*d)+1)/(log(a)*d*(log(c)*f/(log(a)*d)+log(b)*e/(log(a)*d)+1))$
1681
1682 (forget(notequal(log(c)*f/(log(a)*d)+log(b)*e/(log(a)*d),-1)),0);
1683 0$
1684
1685 /* ----- %e^(c*z)*(%e^(a*z))^v ---------------------------------------------- */
1686
1687 /* Problem 311: (OK) wrong simplification for complex integration variable
1688  * Change example to a real variable x.
1689  */
1690 integrate(%e^(c*x)*(%e^(a*x))^v,x);
1691 %e^(a*v*x+c*x)/(a*v+c)$
1692
1693 /* ----- %e^(c*z+d)*(%e^(a*z))^v -------------------------------------------- */
1694
1695 /* Problem 312: (OK) wrong simplification
1696  * Change example to a real variable x.
1697  */
1698 integrate(%e^(c*x+d)*(%e^(a*x))^v,x);
1699 %e^(a*v*x+c*x+d)/(a*v+c)$
1700
1701 /* ----- %e^(c*z)*(%e^(a*z+b))^v -------------------------------------------- */
1702
1703 /* Problem 313: (OK) wrong simplification
1704  * Change example to a real variable x.
1705  */
1706 integrate(%e^(c*x)*(%e^(a*x+b))^v,x);
1707 %e^(v*(a*x+b)+c*x)/(a*v+c)$
1708
1709 /* ----- %e^(c*z+d)*(%e^(a*z+b))^v ------------------------------------------ */
1710
1711 /* Problem 314: (OK) wrong simplifcation
1712  * Change example to a real variable x.
1713  */
1714 integrate(%e^(c*x+d)*(%e^(a*x+b))^v,x);
1715 %e^(v*(a*x+b)+c*x+d)/(a*v+c)$
1716
1717 /* ----- %e^(b*z^r)*(%e^(c*z))^v -------------------------------------------- */
1718
1719 /* Problem 315: (OK) wrong simplification */
1720 integrate(%e^(b*z^2)*(%e^(c*z))^v,z), domain:real;
1721 sqrt(%pi)*%e^-(c^2*v^2/(4*b))*erf(sqrt(-b)*z-c*v/(2*sqrt(-b)))/(2*sqrt(-b));
1722
1723 /* Problem 316: NEW 9-1 */
1724 diffcheck(integrate(%e^(b*sqrt(z))*(%e^(c*z))^v,z),z,factor_radcan),
1725    domain:complex;
1726 %e^(b*sqrt(z))*(%e^(c*z))^v;
1727
1728 /* ----- %e^(b*z^r+e)*(%e^(c*z))^v ------------------------------------------ */
1729
1730 /* Problem 317: (OK) wrong simplification */
1731 integrate(%e^(e+b*z^2)*(%e^(c*z))^v,z), domain:real;
1732 sqrt(%pi)*%e^(e-c^2*v^2/(4*b))*erf(sqrt(-b)*z-c*v/(2*sqrt(-b)))/(2*sqrt(-b));
1733
1734 /* Problem 318: NEW 9-1 */
1735 diffcheck(integrate(%e^(e+b*sqrt(z))*(%e^(c*z))^v,z),z,factor_radcan),
1736    domain:complex;
1737 %e^(e+b*sqrt(z))*(%e^(c*z))^v;
1738
1739 /* ----- %e^(b*z^r+d*z)*(%e^(c*z))^v ---------------------------------------- */
1740
1741 /* Problem 319: (OK) wrong simplification */
1742 integrate(%e^(d*z+b*z^2)*(%e^(c*z))^v,z), domain:real;
1743 sqrt(%pi)*%e^-((-c*v-d)^2/(4*b))*erf(sqrt(-b)*z+(-c*v-d)/(2*sqrt(-b)))
1744  /(2*sqrt(-b));
1745
1746 /* Problem 320: NEW 8-1 */
1747 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(c*z))^v,z),z,factor);
1748 %e^(d*z+b*sqrt(z))*(%e^(c*z))^v;
1749
1750 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z))^v -------------------------------------- */
1751
1752 /* Problem 321: OK */
1753 integrate(%e^(e+d*z+b*z^2)*(%e^(c*z))^v,z), domain:real;
1754 sqrt(%pi)*%e^(e-(-c*v-d)^2/(4*b))*erf(sqrt(-b)*z+(-c*v-d)/(2*sqrt(-b)))
1755  /(2*sqrt(-b));
1756
1757 /* Problem 322: NEW 8-1 */
1758 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(c*z))^v,z),z,factor);
1759 %e^(e+d*z+b*sqrt(z))*(%e^(c*z))^v;
1760
1761 /* ----- %e^(b*z^r)*(%e^(f*z+g))^v ------------------------------------------ */
1762
1763 /* Problem 323: OK */
1764 integrate(%e^(b*z^2)*(%e^(g+f*z))^v,z), domain:real;
1765 sqrt(%pi)*%e^(g*v-f^2*v^2/(4*b))*erf(sqrt(-b)*z-f*v/(2*sqrt(-b)))/(2*sqrt(-b));
1766
1767 /* Problem 324: NEW 9-1 */
1768 diffcheck(integrate(%e^(b*sqrt(z))*(%e^(g+f*z))^v,z),z,factor), domain:real;
1769 %e^(f*v*z+b*sqrt(z)+g*v)$
1770
1771 /* ----- %e^(b*z^r+e)*(%e^(f*z+g))^v ---------------------------------------- */
1772
1773 /* Problem 325: OK */
1774 integrate(%e^(e+b*z^2)*(%e^(g+f*z))^v,z), domain:real;
1775 sqrt(%pi)*%e^(-f^2*v^2/(4*b)+g*v+e)*erf(sqrt(-b)*z-f*v/(2*sqrt(-b)))
1776  /(2*sqrt(-b));
1777
1778 /* Problem 326: NEW 9-1 */
1779 diffcheck(integrate(%e^(e+b*sqrt(z))*(%e^(g+f*z))^v,z),z,factor), domain:real;
1780 %e^(f*v*z+b*sqrt(z)+g*v+e)$
1781
1782 /* ----- %e^(b*z^r+d*z)*(%e^(f*z+g))^v -------------------------------------- */
1783
1784 /* Problem 327: OK */
1785 integrate(%e^(d*z+b*z^2)*(%e^(g+f*z))^v,z), domain:real;
1786 sqrt(%pi)*%e^(g*v-(-f*v-d)^2/(4*b))*erf(sqrt(-b)*z+(-f*v-d)/(2*sqrt(-b)))
1787  /(2*sqrt(-b));
1788
1789 /* Problem 328: NEW 9-1
1790  * This example is not correct simplified.
1791  */
1792 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(g+f*z))^v,z),z,radcan),
1793    domain:complex;
1794 (%e^(f*z))^v*%e^(d*z+b*sqrt(z)+g*v);
1795
1796 /* ----- %e^(b*z^r+d*z+e)*(%e^(f*z+g))^v ------------------------------------ */
1797
1798 /* Problem 329: OK */
1799 integrate(%e^(e+d*z+b*z^2)*(%e^(g+f*z))^v,z), domain:real;
1800 sqrt(%pi)*%e^(-(-f*v-d)^2/(4*b)+g*v+e)*erf(sqrt(-b)*z+(-f*v-d)/(2*sqrt(-b)))
1801  /(2*sqrt(-b));
1802
1803 /* Problem 330: NEW 9-1
1804  * This example is not correct simplified.
1805  */
1806 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(g+f*z))^v,z),z,radcan),
1807    domain:complex;
1808 (%e^(f*z))^v*%e^(d*z+b*sqrt(z)+g*v+e);
1809
1810 /* ----- %e^(b*z)*(%e^(c*z^r))^v -------------------------------------------- */
1811
1812 /* Problem 331: OK */
1813 integrate(%e^(b*z)*(%e^(c*z^2))^v,z), domain:real;
1814 sqrt(%pi)*%e^-(b^2/(4*c*v))*erf(sqrt(-c*v)*z-b/(2*sqrt(-c*v)))/(2*sqrt(-c*v));
1815
1816 /* Problem 332: NEW 9-1 */
1817 diffcheck(integrate(%e^(b*z)*(%e^(c*sqrt(z)))^v,z),z,radcan),domain:complex;
1818 %e^(b*z)*(%e^(c*sqrt(z)))^v;
1819
1820 /* ----- %e^(d*z+e)*(%e^(c*z^r))^v ------------------------------------------ */
1821
1822 /* Problem 333: OK */
1823 integrate(%e^(d*z+e)*(%e^(c*z^2))^v,z), domain:real;
1824 sqrt(%pi)*%e^(e-d^2/(4*c*v))*erf(sqrt(-c*v)*z-d/(2*sqrt(-c*v)))
1825          /(2*sqrt(-c*v));
1826
1827 /* Problem 334: NEW 9-1 */
1828 diffcheck(integrate(%e^(d*z+e)*(%e^(c*sqrt(z)))^v,z),z,factor), domain:real;
1829 %e^(d*z+c*v*sqrt(z)+e)$
1830
1831 /* ----- %e^(b*z^r)*(%e^(c*z^r))^v ------------------------------------------ */
1832
1833 /* Problem 335: NEW 7-1 */
1834 diffcheck(integrate(%e^(b*z^r)*(%e^(c*z^r))^v,z),z,factor);
1835 %e^(b*z^r)*(%e^(c*z^r))^v;
1836
1837 /* Problem 336: OK */
1838 integrate(%e^(b*z^2)*(%e^(c*z^2))^v,z), domain:real;
1839 sqrt(%pi)*erf(sqrt(-c*v-b)*z)/(2*sqrt(-c*v-b));
1840
1841 /* Problem 337: OK */
1842 integrate(%e^(b*sqrt(z))*(%e^(c*sqrt(z)))^v,z), domain:real;
1843 2*((c*v+b)*sqrt(z)-1)*%e^(c*v*sqrt(z)+b*sqrt(z))/(c^2*v^2+2*b*c*v+b^2);
1844
1845 /* ----- %e^(b*z^r+e)*(%e^(c*z^r))^v ---------------------------------------- */
1846
1847 /* Problem 338: NEW 7-1 */
1848 diffcheck(integrate(%e^(e+b*z^r)*(%e^(c*z^r))^v,z),z,factor);
1849 %e^(e+b*z^r)*(%e^(c*z^r))^v;
1850
1851 /* Problem 339: OK */
1852 integrate(%e^(e+b*z^2)*(%e^(c*z^2))^v,z), domain:real;
1853 sqrt(%pi)*%e^e*erf(sqrt(-c*v-b)*z)/(2*sqrt(-c*v-b));
1854
1855 /* Problem 340: OK */
1856 integrate(%e^(e+b*sqrt(z))*(%e^(c*sqrt(z)))^v,z), domain:real;
1857 2*((c*%e^e*v+b*%e^e)*sqrt(z)-%e^e)*%e^(c*v*sqrt(z)+b*sqrt(z))
1858          /(c^2*v^2+2*b*c*v+b^2);
1859
1860 /* ----- %e^(b*z^r+d*z)*(%e^(c*z^r))^v -------------------------------------- */
1861
1862 /* Problem 341: OK */
1863 integrate(%e^(d*z+b*z^2)*(%e^(c*z^2))^v,z), domain:real;
1864 sqrt(%pi)*%e^(d^2/(4*(-c*v-b)))*erf(sqrt(-c*v-b)*z-d/(2*sqrt(-c*v-b)))
1865          /(2*sqrt(-c*v-b));
1866
1867 /* Problem 342: NEW 9-1 */
1868 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^v,z),z,radcan),
1869    domain:complex;
1870 %e^(d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^v;
1871
1872 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z^r))^v ------------------------------------ */
1873
1874 /* Problem 343: OK */
1875 integrate(%e^(e+d*z+b*z^2)*(%e^(c*z^2))^v,z), domain:real;
1876 sqrt(%pi)*%e^(d^2/(4*(-c*v-b))+e)
1877                  *erf(sqrt(-c*v-b)*z-d/(2*sqrt(-c*v-b)))
1878          /(2*sqrt(-c*v-b));
1879
1880 /* Problem 344: NEW 9-1 */
1881 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^v,z),z,radcan),
1882    domain:complex;
1883 %e^(e+d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^v;
1884
1885 /* ----- %e^(d*z)*(%e^(c*z^r+g))^v ------------------------------------------ */
1886
1887 /* Problem 345: OK */
1888 integrate(%e^(d*z)*(%e^(g+c*z^2))^v,z), domain:real;
1889 sqrt(%pi)*%e^(g*v-d^2/(4*c*v))*erf(sqrt(-c*v)*z-d/(2*sqrt(-c*v)))
1890          /(2*sqrt(-c*v));
1891
1892 /* Problem 346: NEW 9-1 */
1893 expand(integrate(%e^(d*z)*(%e^(g+c*sqrt(z)))^v,z)-
1894 (-(-gamma_incomplete(1/2,-(2*d*sqrt(z)+c*v)^2/(4*d))*c*v*(2*d*sqrt(z)+c*v)
1895  /(2*d^(3/2)*sqrt(-(2*d*sqrt(z)+c*v)^2/d))
1896  -gamma_incomplete(1,-(2*d*sqrt(z)+c*v)^2/(4*d))/sqrt(d))
1897  *(%e^(c*sqrt(z)+g))^v*%e^(d*z-(d*sqrt(z)+c*v)*sqrt(z)-c^2*v^2/(4*d))
1898  /sqrt(d)));
1899 0;
1900
1901 /* ----- %e^(d*z+e)*(%e^(c*z^r+g))^v ---------------------------------------- */
1902
1903 /* Problem 347: OK */
1904 integrate(%e^(d*z+e)*(%e^(g+c*z^2))^v,z), domain:real;
1905 sqrt(%pi)*%e^(g*v-d^2/(4*c*v)+e)*erf(sqrt(-c*v)*z-d/(2*sqrt(-c*v)))
1906          /(2*sqrt(-c*v));
1907
1908 /* Problem 348: NEW 9-1 */
1909 expand(integrate(%e^(d*z+e)*(%e^(g+c*sqrt(z)))^v,z)-
1910 (-(-gamma_incomplete(1/2,-(2*d*sqrt(z)+c*v)^2/(4*d))*c*v*(2*d*sqrt(z)+c*v)
1911  /(2*d^(3/2)*sqrt(-(2*d*sqrt(z)+c*v)^2/d))
1912  -gamma_incomplete(1,-(2*d*sqrt(z)+c*v)^2/(4*d))/sqrt(d))
1913  *(%e^(c*sqrt(z)+g))^v*%e^(d*z-(d*sqrt(z)+c*v)*sqrt(z)-c^2*v^2/(4*d)+e)
1914  /sqrt(d)));
1915 0;
1916
1917 /* ----- %e^(b*z^r)*(%e^(c*z^r+g))^v ---------------------------------------- */
1918
1919 /* Problem 349: NEW 7-1
1920  * The result is not correct simplified.
1921  */
1922 diffcheck(integrate(%e^(b*z^r)*(%e^(g+c*z^r))^v,z),z,radcan), domain:complex;
1923 (%e^(c*z^r))^v*%e^(b*z^r+g*v);
1924
1925 /* Problem 350: OK */
1926 integrate(%e^(b*z^2)*(%e^(g+c*z^2))^v,z), domain:real;
1927 sqrt(%pi)*%e^(g*v)*erf(sqrt(-c*v-b)*z)/(2*sqrt(-c*v-b));
1928
1929 /* Problem 351: OK */
1930 multthru(integrate(%e^(b*sqrt(z))*(%e^(g+c*sqrt(z)))^v,z)), domain:real;
1931 2*(c*v*%e^(g*v)+b*%e^(g*v))*sqrt(z)*%e^(c*v*sqrt(z)+b*sqrt(z))
1932  /(c^2*v^2+2*b*c*v+b^2)
1933  -2*%e^(c*v*sqrt(z)+b*sqrt(z)+g*v)/(c^2*v^2+2*b*c*v+b^2);
1934
1935 /* ----- %e^(b*z^r+e)*(%e^(c*z^r+g))^v -------------------------------------- */
1936
1937 /* Problem 352: NEW 7-1 */
1938 diffcheck(integrate(%e^(e+b*z^r)*(%e^(g+c*z^r))^v,z),z,factor);
1939 %e^(e+b*z^r)*(%e^(g+c*z^r))^v;
1940
1941 /* Problem 353: OK */
1942 integrate(%e^(e+b*z^2)*(%e^(g+c*z^2))^v,z), domain:real;
1943 sqrt(%pi)*%e^(g*v+e)*erf(sqrt(-c*v-b)*z)/(2*sqrt(-c*v-b));
1944
1945 /* Problem 354: OK */
1946 multthru(integrate(%e^(e+b*sqrt(z))*(%e^(g+c*sqrt(z)))^v,z)), domain:real;
1947 2*(c*v*%e^(g*v+e)+b*%e^(g*v+e))*sqrt(z)*%e^(c*v*sqrt(z)+b*sqrt(z))
1948  /(c^2*v^2+2*b*c*v+b^2)
1949  -2*%e^(c*v*sqrt(z)+b*sqrt(z)+g*v+e)/(c^2*v^2+2*b*c*v+b^2);
1950
1951 /* ----- %e^(b*z^r+d*z)*(%e^(c*z^r+g))^v ------------------------------------ */
1952
1953 /* Problem 355: OK */
1954 integrate(%e^(d*z+b*z^2)*(%e^(g+c*z^2))^v,z), domain:real;
1955 sqrt(%pi)*%e^(d^2/(4*(-c*v-b))+g*v)
1956                  *erf(sqrt(-c*v-b)*z-d/(2*sqrt(-c*v-b)))
1957          /(2*sqrt(-c*v-b));
1958
1959 /* Problem 356: NEW 9-1
1960  * Wrong simplified.
1961  */
1962 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(g+c*sqrt(z)))^v,z),z,radcan),
1963    domain:complex;
1964 (%e^(c*sqrt(z)))^v*%e^(d*z+b*sqrt(z)+g*v);
1965
1966 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z^r+g))^v ---------------------------------- */
1967
1968 /* Problem 357: OK */
1969 integrate(%e^(e+d*z+b*z^2)*(%e^(g+c*z^2))^v,z), domain:real;
1970 sqrt(%pi)*%e^(d^2/(4*(-c*v-b))+g*v+e)
1971                  *erf(sqrt(-c*v-b)*z-d/(2*sqrt(-c*v-b)))
1972          /(2*sqrt(-c*v-b));
1973
1974 /* Problem 358: NEW 9-1 */
1975 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(g+c*sqrt(z)))^v,z),z,radcan),
1976    domain:complex;
1977 (%e^(c*sqrt(z)))^v*%e^(d*z+b*sqrt(z)+g*v+e);
1978
1979 /* ----- %e^(d*z)*(%e^(c*z^r+f*z))^v ---------------------------------------- */
1980
1981 /* Problem 359: OK */
1982 integrate(%e^(d*z)*(%e^(f*z+c*z^2))^v,z), domain:real;
1983 sqrt(%pi)*%e^-((-f*v-d)^2/(4*c*v))
1984                  *erf(sqrt(-c*v)*z+(-f*v-d)/(2*sqrt(-c*v)))
1985          /(2*sqrt(-c*v));
1986
1987 /* Problem 360: NEW 8-1 */
1988 diffcheck(integrate(%e^(d*z)*(%e^(f*z+c*sqrt(z)))^v,z),z,factor);
1989 %e^(d*z)*(%e^(f*z+c*sqrt(z)))^v$
1990
1991 /* ----- %e^(d*z+e)*(%e^(c*z^r+f*z))^v -------------------------------------- */
1992
1993 /* Problem 361: OK */
1994 integrate(%e^(d*z+e)*(%e^(f*z+c*z^2))^v,z), domain:real;
1995 sqrt(%pi)*%e^(e-(-f*v-d)^2/(4*c*v))
1996                  *erf(sqrt(-c*v)*z+(-f*v-d)/(2*sqrt(-c*v)))
1997          /(2*sqrt(-c*v));
1998
1999 /* Problem 362: NEW 8-1 */
2000 integrate(%e^(d*z+e)*(%e^(f*z+c*sqrt(z)))^v,z);
2001 (2*sqrt(f*v+d)*%e^((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d)))
2002  -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)/(2*sqrt(f*v+d))))
2003  *%e^(d*z-(2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d))+e)
2004  *(%e^(f*z+c*sqrt(z)))^v
2005  /(2*(f*v+d)^(3/2));
2006
2007 /* ----- %e^(b*z^r)*(%e^(c*z^r+f*z))^v -------------------------------------- */
2008
2009 /* Problem 363: OK */
2010 integrate(%e^(b*z^2)*(%e^(f*z+c*z^2))^v,z), domain:real;
2011 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b)))
2012                  *erf(sqrt(-c*v-b)*z-f*v/(2*sqrt(-c*v-b)))
2013          /(2*sqrt(-c*v-b));
2014
2015 /* Problem 364: NEW 9-1 */
2016 diffcheck(integrate(%e^(b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^v,z),z,factor),domain:real;
2017 %e^(f*v*z+c*v*sqrt(z)+b*sqrt(z))$
2018
2019 /* ----- %e^(b*z^r+e)*(%e^(c*z^r+f*z))^v ------------------------------------ */
2020
2021 /* Problem 365: OK */
2022 integrate(%e^(e+b*z^2)*(%e^(f*z+c*z^2))^v,z), domain:real;
2023 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b))+e)
2024                  *erf(sqrt(-c*v-b)*z-f*v/(2*sqrt(-c*v-b)))
2025          /(2*sqrt(-c*v-b));
2026
2027 /* Problem 366: NEW 9-1 */
2028 diffcheck(integrate(%e^(e+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^v,z),z,factor), domain:real;
2029 %e^(f*v*z+c*v*sqrt(z)+b*sqrt(z)+e)$
2030
2031 /* ----- %e^(b*z^r+d*z)*(%e^(c*z^r+f*z))^v ---------------------------------- */
2032
2033 /* Problem 367: OK */
2034 integrate(%e^(d*z+b*z^2)*(%e^(f*z+c*z^2))^v,z), domain:real;
2035 sqrt(%pi)*%e^((-f*v-d)^2/(4*(-c*v-b)))
2036                  *erf(sqrt(-c*v-b)*z+(-f*v-d)/(2*sqrt(-c*v-b)))
2037          /(2*sqrt(-c*v-b));
2038
2039 /* Problem 368: NEW 9-1 */
2040 diffcheck(integrate(%e^(d*x+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^v,z),z,factor), domain:real;
2041 %e^(f*v*z+c*v*sqrt(z)+b*sqrt(z)+d*x)$
2042
2043 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z^r+f*z))^v -------------------------------- */
2044
2045 /* Problem 369: OK */
2046 integrate(%e^(e+d*z+b*z^2)*(%e^(f*z+c*z^2))^v,z), domain:real;
2047 sqrt(%pi)*%e^((-f*v-d)^2/(4*(-c*v-b))+e)
2048                  *erf(sqrt(-c*v-b)*z+(-f*v-d)/(2*sqrt(-c*v-b)))
2049          /(2*sqrt(-c*v-b));
2050
2051 /* Problem 370: NEW 9-1 */
2052 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^v,z),z,radcan),
2053    domain:complex;
2054 (%e^(c*sqrt(z)))^v*(%e^(f*z))^v*%e^(d*z+b*sqrt(z)+e);
2055
2056 /* ----- %e^(d*z)*(%e^(c*z^r+f*z+g))^v -------------------------------------- */
2057
2058 /* Problem 371: OK */
2059 integrate(%e^(d*z)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2060 sqrt(%pi)*%e^(g*v-(-f*v-d)^2/(4*c*v))
2061                  *erf(sqrt(-c*v)*z+(-f*v-d)/(2*sqrt(-c*v)))
2062          /(2*sqrt(-c*v));
2063
2064 /* Problem 372: NEW 8-1 */
2065 integrate(%e^(d*z)*(%e^(g+f*z+c*sqrt(z)))^v,z);
2066 (2*sqrt(f*v+d)*%e^((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d)))
2067  -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)/(2*sqrt(f*v+d))))
2068  *%e^(d*z-(2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d)))
2069  *(%e^(f*z+c*sqrt(z)+g))^v
2070  /(2*(f*v+d)^(3/2));
2071
2072 /* ----- %e^(d*z+e)*(%e^(c*z^r+f*z+g))^v ------------------------------------ */
2073
2074 /* Problem 373: OK */
2075 integrate(%e^(d*z+e)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2076 sqrt(%pi)*%e^(-(-f*v-d)^2/(4*c*v)+g*v+e)
2077                  *erf(sqrt(-c*v)*z+(-f*v-d)/(2*sqrt(-c*v)))
2078          /(2*sqrt(-c*v));
2079
2080 /* Problem 374: NEW 8-1 */
2081 integrate(%e^(d*z+e)*(%e^(g+f*z+c*sqrt(z)))^v,z);
2082 (2*sqrt(f*v+d)*%e^((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d)))
2083  -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)/(2*sqrt(f*v+d))))
2084  *%e^(d*z-(2*f*v*sqrt(z)+2*d*sqrt(z)+c*v)^2/(4*(f*v+d))+e)
2085  *(%e^(f*z+c*sqrt(z)+g))^v
2086  /(2*(f*v+d)^(3/2));
2087
2088 /* ----- %e^(b*z^r)*(%e^(c*z^r+f*z+g))^v ------------------------------------ */
2089
2090 /* Problem 375: OK */
2091 integrate(%e^(b*z^2)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2092 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b))+g*v)
2093                  *erf(sqrt(-c*v-b)*z-f*v/(2*sqrt(-c*v-b)))
2094          /(2*sqrt(-c*v-b));
2095
2096 /* Problem 376: NEW 9-1 */
2097 diffcheck(integrate(%e^(b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2098    domain:complex;
2099 (%e^(c*sqrt(z)))^v*%e^(b*sqrt(z)+g*v)*(%e^(f*z))^v;
2100
2101 /* ----- %e^(b*z^r+e)*(%e^(c*z^r+f*z+g))^v ---------------------------------- */
2102
2103 /* Problem 377: OK */
2104 integrate(%e^(e+b*z^2)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2105 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b))+g*v+e)
2106                  *erf(sqrt(-c*v-b)*z-f*v/(2*sqrt(-c*v-b)))
2107          /(2*sqrt(-c*v-b));
2108
2109 /* Problem 378: NEW 9-1 */
2110 diffcheck(integrate(%e^(e+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2111    domain:complex;
2112 (%e^(c*sqrt(z)))^v*%e^(b*sqrt(z)+g*v+e)*(%e^(f*z))^v;
2113
2114 /* ----- %e^(b*z^r+d*z)*(%e^(c*z^r+f*z+g))^v -------------------------------- */
2115
2116 /* Problem 379: OK */
2117 integrate(%e^(d*z+b*z^2)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2118 sqrt(%pi)*%e^((-f*v-d)^2/(4*(-c*v-b))+g*v)
2119                  *erf(sqrt(-c*v-b)*z+(-f*v-d)/(2*sqrt(-c*v-b)))
2120          /(2*sqrt(-c*v-b));
2121
2122 /* Problem 380: NEW 9-1 */
2123 diffcheck(integrate(%e^(d*z+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2124    domain:complex;
2125 (%e^(c*sqrt(z)))^v*(%e^(f*z))^v*%e^(d*z+b*sqrt(z)+g*v);
2126
2127 /* ----- %e^(b*z^r+d*z+e)*(%e^(c*z^r+f*z+g))^v ------------------------------ */
2128
2129 /* Problem 381: OK */
2130 integrate(%e^(e+d*z+b*z^2)*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2131 sqrt(%pi)*%e^((-f*v-d)^2/(4*(-c*v-b))+g*v+e)
2132                  *erf(sqrt(-c*v-b)*z+(-f*v-d)/(2*sqrt(-c*v-b)))
2133          /(2*sqrt(-c*v-b));
2134
2135 /* Problem 382: NEW 9-1 */
2136 diffcheck(integrate(%e^(e+d*z+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2137    domain:complex;
2138 (%e^(c*sqrt(z)))^v*(%e^(f*z))^v*%e^(d*z+b*sqrt(z)+g*v+e);
2139
2140 /* ----- (%e^(c*z))^u*(%e^(a*z)^v ------------------------------------------- */
2141
2142 /* Problem 383: OK */
2143 integrate((%e^(c*x))^u*(%e^(a*x))^v,x);
2144 %e^(a*v*x+c*u*x)/(a*v+c*u)$
2145
2146 /* ----- (%e^(c*z))^u*(%e^(a*z+b)^v ----------------------------------------- */
2147
2148 /* Problem 384: OK */
2149 integrate((%e^(c*x))^u*(%e^(a*x+b))^v,x);
2150 %e^(v*(a*x+b)+c*u*x)/(a*v+c*u)$
2151
2152 /* ----- (%e^(c*z+d))^u*(%e^(a*z+b)^v --------------------------------------- */
2153
2154 /* Problem 385: OK */
2155 integrate((%e^(c*x+d))^u*(%e^(a*x+b))^v,x);
2156 %e^(u*(c*x+d)+v*(a*x+b))/(a*v+c*u)$
2157
2158 /* ----- (%e^(b*z))^u*(%e^(c*z^r)^v ----------------------------------------- */
2159
2160 /* Problem 386: OK */
2161 integrate((%e^(b*z))^u*(%e^(c*z^2))^v,z), domain:real;
2162 sqrt(%pi)*%e^-(b^2*u^2/(4*c*v))*erf(sqrt(-c*v)*z-b*u/(2*sqrt(-c*v)))
2163          /(2*sqrt(-c*v));
2164
2165 /* Problem 387: NEW 9-1 */
2166 diffcheck(integrate((%e^(b*z))^u*(%e^(c*sqrt(z)))^v,z),z,factor), domain:real;
2167 %e^(b*u*z+c*v*sqrt(z))$
2168
2169 /* ----- (%e^(d*z+e))^u*(%e^(c*z^r)^v --------------------------------------- */
2170
2171 /* Problem 388: OK */
2172 integrate((%e^(d*z+e))^u*(%e^(c*z^2))^v,z), domain:real;
2173 sqrt(%pi)*%e^(e*u-d^2*u^2/(4*c*v))
2174                  *erf(sqrt(-c*v)*z-d*u/(2*sqrt(-c*v)))
2175          /(2*sqrt(-c*v));
2176
2177 /* Problem 389: NEW 9-1 */
2178 diffcheck(integrate((%e^(d*z+e))^u*(%e^(c*sqrt(z)))^v,z),z,factor), domain:real;
2179 %e^(d*u*z+c*v*sqrt(z)+e*u)$
2180
2181 /* ----- (%e^(b*z^r))^u*(%e^(c*z^r+g)^v ------------------------------------- */
2182
2183 /* Problem 390: NEW 7-1 */
2184 diffcheck(integrate((%e^(b*z^r))^u*(%e^(c*z^r))^v,z),z,factor);
2185 (%e^(b*z^r))^u*(%e^(c*z^r))^v;
2186
2187 /* Problem 391: OK */
2188 integrate((%e^(b*z^2))^u*(%e^(c*z^2))^v,z), domain:real;
2189 sqrt(%pi)*erf(sqrt(-c*v-b*u)*z)/(2*sqrt(-c*v-b*u));
2190
2191 /* Problem 392: OK */
2192 integrate((%e^(b*sqrt(z)))^u*(%e^(c*sqrt(z)))^v,z), domain:real;
2193 2*((c*v+b*u)*sqrt(z)-1)*%e^(c*v*sqrt(z)+b*u*sqrt(z))
2194  /(c^2*v^2+2*b*c*u*v+b^2*u^2);
2195
2196 /* ----- (%e^(d*z))^u*(%e^(c*z^r+g)^v --------------------------------------- */
2197
2198 /* Problem 393: OK */
2199 integrate((%e^(d*z))^u*(%e^(g+c*z^2))^v,z), domain:real;
2200 sqrt(%pi)*%e^(g*v-d^2*u^2/(4*c*v))
2201                  *erf(sqrt(-c*v)*z-d*u/(2*sqrt(-c*v)))
2202          /(2*sqrt(-c*v));
2203
2204 /* Problem 394: NEW 9-1 */
2205 diffcheck(integrate((%e^(d*z))^u*(%e^(g+c*sqrt(z)))^v,z),z,factor), domain:real;
2206 %e^(d*u*z+c*v*sqrt(z)+g*v)$
2207
2208 /* ----- (%e^(d*z+e))^u*(%e^(c*z^r+g)^v ------------------------------------- */
2209
2210 /* Problem 395: OK */
2211 integrate((%e^(d*z+e))^u*(%e^(g+c*z^2))^v,z), domain:real;
2212 sqrt(%pi)*%e^(g*v-d^2*u^2/(4*c*v)+e*u)
2213                  *erf(sqrt(-c*v)*z-d*u/(2*sqrt(-c*v)))
2214          /(2*sqrt(-c*v));
2215
2216 /* Problem 396: NEW 9-1 */
2217 diffcheck(integrate((%e^(d*z+e))^u*(%e^(g+c*sqrt(z)))^v,z),z,factor), domain:real;
2218 %e^(d*u*z+c*v*sqrt(z)+g*v+e*u)$
2219
2220 /* ----- (%e^(b*z^r))^u*(%e^(c*z^r+g)^v ------------------------------------- */
2221
2222 /* Problem 397: NEW 7-1 */
2223 diffcheck(integrate((%e^(b*z^r))^u*(%e^(g+c*z^r))^v,z),z,factor);
2224 (%e^(b*z^r))^u*(%e^(g+c*z^r))^v;
2225
2226 /* Problem 398: OK */
2227 integrate((%e^(b*z^2))^u*(%e^(g+c*z^2))^v,z), domain:real;
2228 sqrt(%pi)*%e^(g*v)*erf(sqrt(-c*v-b*u)*z)/(2*sqrt(-c*v-b*u));
2229
2230 /* Problem 399: OK */
2231 integrate((%e^(b*sqrt(z)))^u*(%e^(g+c*sqrt(z)))^v,z), domain:real;
2232 2*((c*v*%e^(g*v)+b*u*%e^(g*v))*sqrt(z)-%e^(g*v))*%e^(c*v*sqrt(z)+b*u*sqrt(z))
2233  /(c^2*v^2+2*b*c*u*v+b^2*u^2);
2234
2235 /* ----- (%e^(b*z^r+e))^u*(%e^(c*z^r+g)^v ----------------------------------- */
2236
2237 /* Problem 400: NEW 7-1 */
2238 diffcheck(integrate((%e^(e+b*z^r))^u*(%e^(g+c*z^r))^v,z),z,factor);
2239 (%e^(e+b*z^r))^u*(%e^(g+c*z^r))^v;
2240
2241 /* Problem 401: OK */
2242 integrate((%e^(e+b*z^2))^u*(%e^(g+c*z^2))^v,z), domain:real;
2243 sqrt(%pi)*%e^(g*v+e*u)*erf(sqrt(-c*v-b*u)*z)/(2*sqrt(-c*v-b*u));
2244
2245 /* Problem 402: OK */
2246 integrate((%e^(e+b*sqrt(z)))^u*(%e^(g+c*sqrt(z)))^v,z), domain:real;
2247 2*((c*v*%e^(g*v+e*u)+b*u*%e^(g*v+e*u))*sqrt(z)-%e^(g*v+e*u))
2248  *%e^(c*v*sqrt(z)+b*u*sqrt(z))
2249  /(c^2*v^2+2*b*c*u*v+b^2*u^2);
2250
2251 /* ----- (%e^(d*z))^u*(%e^(c*z^r+f*z)^v ------------------------------------- */
2252
2253 /* Problem 403: OK */
2254 integrate((%e^(d*z))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2255 sqrt(%pi)*%e^-((-f*v-d*u)^2/(4*c*v))
2256                  *erf(sqrt(-c*v)*z+(-f*v-d*u)/(2*sqrt(-c*v)))
2257          /(2*sqrt(-c*v));
2258
2259 /* Problem 404: NEW 8-1 */
2260 integrate((%e^(d*z))^u*(%e^(f*z+c*sqrt(z)))^v,z);
2261 %e^-((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2262  *(2*sqrt(f*v+d*u)*%e^((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2263   -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)/(2*sqrt(f*v+d*u))))
2264  *(%e^(d*z))^u*(%e^(f*z+c*sqrt(z)))^v
2265  /(2*(f*v+d*u)^(3/2));
2266
2267 /* ----- (%e^(d*z+e))^u*(%e^(c*z^r+f*z)^v ----------------------------------- */
2268
2269 /* Problem 405: OK */
2270 integrate((%e^(e+d*z))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2271 sqrt(%pi)*%e^(e*u-(-f*v-d*u)^2/(4*c*v))
2272                  *erf(sqrt(-c*v)*z+(-f*v-d*u)/(2*sqrt(-c*v)))
2273          /(2*sqrt(-c*v));
2274
2275 /* Problem 406: NEW 8-1 */
2276 diffcheck(integrate((%e^(e+d*z))^u*(%e^(f*z+c*sqrt(z)))^v,z),z,factor);
2277 (%e^(e+d*z))^u*(%e^(f*z+c*sqrt(z)))^v;
2278
2279 /* ----- (%e^(b*z^r))^u*(%e^(c*z^r+f*z)^v ----------------------------------- */
2280
2281 /* Problem 407: OK */
2282 integrate((%e^(b*z^2))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2283 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b*u)))
2284                  *erf(sqrt(-c*v-b*u)*z-f*v/(2*sqrt(-c*v-b*u)))
2285          /(2*sqrt(-c*v-b*u));
2286
2287 /* Problem 408: NEW 9-1 */
2288 diffcheck(integrate((%e^(b*sqrt(z)))^u*(%e^(f*z+c*sqrt(z)))^v,z),z,factor), domain:real;
2289 %e^(f*v*z+c*v*sqrt(z)+b*u*sqrt(z))$
2290
2291 /* ----- (%e^(b*z^r+e))^u*(%e^(c*z^r+f*z)^v --------------------------------- */
2292
2293 /* Problem 409: OK */
2294 integrate((%e^(e+b*z^2))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2295 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b*u))+e*u)
2296                  *erf(sqrt(-c*v-b*u)*z-f*v/(2*sqrt(-c*v-b*u)))
2297          /(2*sqrt(-c*v-b*u));
2298
2299 /* Problem 410: NEW 9-1 */
2300 diffcheck(integrate((%e^(e+b*sqrt(z)))^u*(%e^(f*z+c*sqrt(z)))^v,z),z,factor), domain:real;
2301 %e^(f*v*z+c*v*sqrt(z)+b*u*sqrt(z)+e*u)$
2302
2303 /* ----- (%e^(b*z^r+d*z))^u*(%e^(c*z^r+f*z)^v ------------------------------- */
2304
2305 /* Problem 411: OK */
2306 integrate((%e^(d*z+b*z^2))^u*(%e^(f*z+c*z^2))^v,z), domain:real;
2307 sqrt(%pi)*%e^((-f*v-d*u)^2/(4*(-c*v-b*u)))
2308                  *erf(sqrt(-c*v-b*u)*z+(-f*v-d*u)/(2*sqrt(-c*v-b*u)))
2309          /(2*sqrt(-c*v-b*u));
2310
2311 /* Problem 412: NEW 9-1 */
2312 diffcheck(integrate((%e^(d*z+b*sqrt(z)))^u*(%e^(f*z+c*sqrt(z)))^v,z),z,radcan),
2313    domain:complex;
2314 (%e^(b*sqrt(z)))^u*(%e^(c*sqrt(z)))^v*(%e^(d*z))^u*(%e^(f*z))^v$
2315
2316 /* ----- (%e^(d*z))^u*(%e^(c*z^r+f*z+g)^v ----------------------------------- */
2317
2318 /* Problem 413: OK */
2319 integrate((%e^(d*z))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2320 sqrt(%pi)*%e^(g*v-(-f*v-d*u)^2/(4*c*v))
2321                  *erf(sqrt(-c*v)*z+(-f*v-d*u)/(2*sqrt(-c*v)))
2322          /(2*sqrt(-c*v));
2323
2324 /* Problem 414: NEW 8-1 */
2325 integrate((%e^(d*z))^u*(%e^(g+f*z+c*sqrt(z)))^v,z);
2326 %e^-((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2327  *(2*sqrt(f*v+d*u)*%e^((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2328   -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)/(2*sqrt(f*v+d*u))))
2329  *(%e^(d*z))^u*(%e^(f*z+c*sqrt(z)+g))^v
2330  /(2*(f*v+d*u)^(3/2));
2331
2332 /* ----- (%e^(d*z+e))^u*(%e^(c*z^r+f*z+g)^v --------------------------------- */
2333
2334 /* Problem 415: OK */
2335 integrate((%e^(e+d*z))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2336 sqrt(%pi)*%e^(-(-f*v-d*u)^2/(4*c*v)+g*v+e*u)
2337                  *erf(sqrt(-c*v)*z+(-f*v-d*u)/(2*sqrt(-c*v)))
2338          /(2*sqrt(-c*v));
2339
2340 /* Problem 416: NEW 8-1 */
2341 integrate((%e^(e+d*z))^u*(%e^(g+f*z+c*sqrt(z)))^v,z);
2342 %e^-((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2343  *(2*sqrt(f*v+d*u)*%e^((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)^2/(4*(f*v+d*u)))
2344   -sqrt(%pi)*c*v*erfi((2*f*v*sqrt(z)+2*d*u*sqrt(z)+c*v)/(2*sqrt(f*v+d*u))))
2345  *(%e^(d*z+e))^u*(%e^(f*z+c*sqrt(z)+g))^v
2346  /(2*(f*v+d*u)^(3/2));
2347
2348 /* ----- (%e^(b*z^r))^u*(%e^(c*z^r+f*z+g)^v --------------------------------- */
2349
2350 /* Problem 417: OK */
2351 integrate((%e^(b*z^2))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2352 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b*u))+g*v)
2353                  *erf(sqrt(-c*v-b*u)*z-f*v/(2*sqrt(-c*v-b*u)))
2354          /(2*sqrt(-c*v-b*u));
2355
2356 /* Problem 418: NEW 9-1 */
2357 diffcheck(integrate((%e^(b*sqrt(z)))^u*(%e^(g+f*z+c*sqrt(z)))^v,z),z,factor),domain:real;
2358 %e^(f*v*z+c*v*sqrt(z)+b*u*sqrt(z)+g*v)$
2359
2360 /* ----- (%e^(b*z^r+e))^u*(%e^(c*z^r+f*z+g)^v ------------------------------- */
2361
2362 /* Problem 419: OK */
2363 integrate((%e^(e+b*z^2))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2364 sqrt(%pi)*%e^(f^2*v^2/(4*(-c*v-b*u))+g*v+e*u)
2365                  *erf(sqrt(-c*v-b*u)*z-f*v/(2*sqrt(-c*v-b*u)))
2366          /(2*sqrt(-c*v-b*u));
2367
2368 /* Problem 420: NEW 9-1 */
2369 diffcheck(integrate((%e^(e+b*sqrt(z)))^u*(%e^(g+f*z+c*sqrt(z)))^v,z),z,factor),domain:real;
2370 %e^(f*v*z+c*v*sqrt(z)+b*u*sqrt(z)+g*v+e*u)$
2371
2372 /* ----- (%e^(b*z^r+d*z))^u*(%e^(c*z^r+f*z+g)^v ----------------------------- */
2373
2374 /* Problem 421: OK */
2375 integrate((%e^(d*z+b*z^2))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2376 sqrt(%pi)*%e^((-f*v-d*u)^2/(4*(-c*v-b*u))+g*v)
2377                  *erf(sqrt(-c*v-b*u)*z+(-f*v-d*u)/(2*sqrt(-c*v-b*u)))
2378          /(2*sqrt(-c*v-b*u));
2379
2380 /* Problem 422: NEW 9-1 */
2381 diffcheck(integrate((%e^(d*z+b*sqrt(z)))^u*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2382    domain:complex;
2383 %e^(g*v)*(%e^(b*sqrt(z)))^u*(%e^(c*sqrt(z)))^v*(%e^(d*z))^u*(%e^(f*z))^v;
2384
2385 /* ----- (%e^(b*z^r+d*z+e))^u*(%e^(c*z^r+f*z+g)^v --------------------------- */
2386
2387 /* Problem 423: OK */
2388 integrate((%e^(e+d*z+b*z^2))^u*(%e^(g+f*z+c*z^2))^v,z), domain:real;
2389 sqrt(%pi)*%e^((-f*v-d*u)^2/(4*(-c*v-b*u))+g*v+e*u)
2390                  *erf(sqrt(-c*v-b*u)*z+(-f*v-d*u)/(2*sqrt(-c*v-b*u)))
2391          /(2*sqrt(-c*v-b*u));
2392
2393 /* Problem 424: NEW 9-1 */
2394 diffcheck(integrate((%e^(e+d*z+b*sqrt(z)))^u*(%e^(g+f*z+c*sqrt(z)))^v,z),z,radcan),
2395    domain:complex;
2396 %e^(g*v+e*u)*(%e^(b*sqrt(z)))^u*(%e^(c*sqrt(z)))^v*(%e^(d*z))^u*(%e^(f*z))^v;
2397
2398 /* ----- Involving rational functions of the direct function ---------------- */
2399
2400 /* ----- Involving 1/(a+b*%e^(c*z)) ----------------------------------------- */
2401
2402 /* Problem 425: OK */
2403 integrate(1/(b*%e^(c*z)+a),z), domain:real;
2404 z/a-log(b*%e^(c*z)+a)/(a*c);
2405
2406 /* Problem 426: OK */
2407 integrate(1/(%e^(c*z)+1),z), domain:real;
2408 z-log(%e^(c*z)+1)/c;
2409
2410 /* Problem 427: OK */
2411 integrate(1/(1-%e^(c*z)),z), domain:real;
2412 z-log(%e^(c*z)-1)/c;
2413
2414 /* ----- Involving (a+b*%e^(c*z))^(-n)---------------------------------------- */
2415
2416 /* Problem 428: OK */
2417 integrate(1/(b*%e^(c*z)+a)^2,z), domain:real;
2418 -log(b*%e^(c*z)+a)/(a^2*c)+1/(c*(a*b*%e^(c*z)+a^2))+z/a^2;
2419
2420 /* Problem 429: OK */
2421 integrate(1/(%e^(c*z)+1)^2,z), domain:real;
2422 -log(%e^(c*z)+1)/c+1/(c*(%e^(c*z)+1))+z;
2423
2424 /* Problem 430: OK */
2425 integrate(1/(1-%e^(c*z))^2,z), domain:real;
2426 -log(%e^(c*z)-1)/c-1/(c*(%e^(c*z)-1))+z;
2427
2428 /* Problem 431: OK */
2429 integrate(1/(b*%e^(c*z)+a)^3,z), domain:real;
2430 -log(b*%e^(c*z)+a)/(a^3*c)+(2*b*%e^(c*z)+3*a)
2431                            /(c*(2*a^2*b^2*%e^(2*c*z)+4*a^3*b*%e^(c*z)+2*a^4))
2432                           +z/a^3;
2433
2434 /* Problem 432: OK */
2435 integrate(1/(b*%e^(c*z)+a)^4,z), domain:real;
2436 -log(b*%e^(c*z)+a)/(a^4*c)+(6*b^2*%e^(2*c*z)+15*a*b*%e^(c*z)+11*a^2)
2437                            /(c*(6*a^3*b^3*%e^(3*c*z)+18*a^4*b^2*%e^(2*c*z)
2438                                                     +18*a^5*b*%e^(c*z)+6*a^6))
2439                           +z/a^4;
2440
2441 /* ----- Involving %e^(d*z)/(a+b*%e^(c*z)) ---------------------------------- */
2442
2443 /* Problem 433: NOUN */
2444 integrate(%e^(d*z)/(b*%e^(c*z)+a),z);
2445 a*c
2446  *'integrate(%e^(d*z)/(b^2*(c-d)*%e^(2*c*z)+a*b*(2*c-2*d)*%e^(c*z)+a^2*(c-d)),
2447              z)
2448  -%e^(d*z)/(b*(c-d)*%e^(c*z)+a*(c-d));
2449
2450 /* Problem 435: OK */
2451 assume(a>0,b>0);
2452 [a>0,b>0];
2453
2454 integrate(%e^z/(a+b*%e^(2*z)),z), domain:real;
2455 atan(sqrt(b)*%e^z/sqrt(a))/(sqrt(a)*sqrt(b));
2456
2457 forget(a>0,b>0);
2458 [a>0,b>0];
2459
2460 /* Problem 437: OK */
2461 integrate(%e^(c*z)/(b*%e^(c*z)+a),z);
2462 log(b*%e^(c*z)+a)/(b*c);
2463
2464 /* Problem 438: OK */
2465 integrate((B*%e^(c*z)+A)/(b*%e^(c*z)+a),z), domain:real;
2466 (A*z)/a-((A*b-B*a)*log(b*%e^(c*z)+a))/(a*b*c);
2467
2468 /* Problem 439: OK */
2469 integrate(%e^(2*c*z)/(b*%e^(c*z)+a),z);
2470 %e^(c*z)/(b*c)-a*log(b*%e^(c*z)+a)/(b^2*c);
2471
2472 /* Problem 441: OK */
2473 assume(a>0,b>0);
2474 [a>0,b>0];
2475
2476 integrate(%e^(c*z)/(b*%e^(2*c*z)+a),z);
2477 atan(b*%e^(c*z)/sqrt(a*b))/(sqrt(a*b)*c);
2478
2479 forget(a>0,b>0);
2480 [a>0,b>0];
2481
2482 /* Problem 444: OK */
2483 assume(a>0,b>0);
2484 [a>0,b>0];
2485
2486 integrate(%e^(c*z)/(b*%e^(3*c*z)+a),z), domain:real;
2487 -log(b^(2/3)*%e^(2*c*z)-a^(1/3)*b^(1/3)*%e^(c*z)+a^(2/3))
2488  /(6*a^(2/3)*b^(1/3)*c)
2489  +atan((2*b^(2/3)*%e^(c*z)-a^(1/3)*b^(1/3))/(sqrt(3)*a^(1/3)*b^(1/3)))
2490   /(sqrt(3)*a^(2/3)*b^(1/3)*c)
2491  +log((b^(1/3)*%e^(c*z)+a^(1/3))/b^(1/3))/(3*a^(2/3)*b^(1/3)*c);
2492
2493 forget(a>0,b>0);
2494 [a>0,b>0];
2495
2496 /* ----- Involving %e^(f*z)/(a+b*%e^(c*z))^-n ------------------------------- */
2497
2498 /* Problem 446: NOUN */
2499 integrate(%e^(f*z)/(b*c^(d*z)+a),z);
2500 'integrate(%e^(f*z)/(b*c^(d*z)+a),z);
2501 /* a*log(c)*d
2502    *'integrate(%e^(f*z)/(b^2*(log(c)*d-f)*%e^(2*log(c)*d*z)
2503                       +a*b*(2*log(c)*d-2*f)*%e^(log(c)*d*z)+a^2*(log(c)*d-f)),
2504              z)
2505  -%e^(f*z)/(b*(log(c)*d-f)*%e^(log(c)*d*z)+a*(log(c)*d-f));
2506 */
2507
2508 /* Problem 447: NOUN */
2509 integrate(%e^(d*z)/(b*%e^(c*z)+a)^2,z);
2510 2*a*c
2511  *'integrate(%e^(d*z)/(b^3*(2*c-d)*%e^(3*c*z)+a*b^2*(6*c-3*d)*%e^(2*c*z)
2512                                              +a^2*b*(6*c-3*d)*%e^(c*z)
2513                                              +a^3*(2*c-d)),z)
2514  -%e^(d*z)/(b^2*(2*c-d)*%e^(2*c*z)+a*b*(4*c-2*d)*%e^(c*z)+a^2*(2*c-d));
2515
2516 /* Problem 448: OK */
2517 integrate((B*%e^(c*z)+A)/(b*%e^(c*z)+a)^2,z), domain:real;
2518 (-(A*log(b*%e^(c*z)+a))/(a^2*c))+(A*b-B*a)/(c*(a^2*b+a*b^2*%e^(c*z)))
2519                                 +(A*z)/a^2;
2520
2521 /* Problem 449: OK */
2522 integrate((B*%e^(c*z)+A)/(b*%e^(c*z)+a)^3,z), domain:real;
2523 (-a^2*B+2*b^2*%e^(c*z)*A+3*a*b*A)/(c*(2*a^2*b^3*%e^(2*c*z)
2524                                      +4*a^3*b^2*%e^(c*z)+2*a^4*b))
2525  -log(b*%e^(c*z)+a)*A/(a^3*c)+z*A/a^3$
2526
2527 /* Problem 450: OK */
2528 integrate((C*%e^(2*c*z)+B*%e^(c*z)+A)/(b*%e^(c*z)+a)^3,z), domain:real;
2529 (-(A*log(b*%e^(c*z)+a))/(a^3*c))+((2*A*b^3-2*C*a^2*b)*%e^(c*z)
2530                                  +3*A*a*b^2-B*a^2*b-C*a^3)
2531                                  /(c*(2*a^4*b^2+4*a^3*b^3*%e^(c*z)
2532                                                +2*a^2*b^4*%e^(2*c*z)))
2533                                 +(A*z)/a^3;
2534
2535 /* ----- Involving 1/(a*%e^(2*d*z)+b*%e^(d*z)+c)----------------------------- */
2536
2537 /* Problem 452: OK */
2538 assume(4*a*c-b^2>0);
2539 [4*a*c > b^2];
2540
2541 integrate(1/(c+b*%e^(d*z)+a*%e^(2*d*z)),z), domain:real;
2542 -log(a*%e^(2*d*z)+b*%e^(d*z)+c)/(2*c*d)-b
2543                                         *atan(
2544                                          (2*a*%e^(d*z)+b)/sqrt(4*a*c-b^2))
2545                                         /(c*sqrt(4*a*c-b^2)*d)+z/c$
2546
2547 forget(4*a*c-b^2>0);
2548 [4*a*c > b^2];
2549
2550 /* ----- Involving %e^(e*z)/(a*%e^(2*d*z)+b*%e^(d*z)+c)---------------------- */
2551
2552 /* Problem 454: NOUN */
2553 integrate(%e^(e*z)/(c+b*%e^(d*z)+a*%e^(2*d*z)),z);
2554 'integrate((b*d*%e^(d*z)+2*c*d)*%e^(e*z)
2555             /(a^2*(2*d-e)*%e^(4*d*z)+a*b*(4*d-2*e)*%e^(3*d*z)
2556                                     +(b^2*(2*d-e)+a*c*(4*d-2*e))*%e^(2*d*z)
2557                                     +b*c*(4*d-2*e)*%e^(d*z)+c^2*(2*d-e)),z)
2558  -%e^(e*z)/(a*(2*d-e)*%e^(2*d*z)+b*(2*d-e)*%e^(d*z)+c*(2*d-e));
2559
2560 /* Problem 456: OK */
2561 assume(4*a*c-b^2>0);
2562 [4*a*c > b^2];
2563
2564 integrate(%e^(2*d*z)/(c+b*%e^(d*z)+a*%e^(2*d*z)),z),logexpand;
2565 log(b*sqrt(%e^(2*d*z))+a*%e^(2*d*z)+c)/(2*a*d)
2566  -b*atan((2*a*sqrt(%e^(2*d*z))+b)/sqrt(4*a*c-b^2))/(a*sqrt(4*a*c-b^2)*d);
2567
2568 forget(4*a*c-b^2>0);
2569 [4*a*c > b^2];
2570
2571 /* ----- Other integrals ---------------------------------------------------- */
2572
2573 /* Problem 458: NOUN */
2574 integrate(6^z/(9^z*b+4^z*a),z);
2575 'integrate(6^z/(b*9^z+a*4^z),z);
2576
2577 /* Problem 459: OK */
2578 integrate((%e^(5*z)+%e^z)/(%e^(3*z)-%e^(2*z)+%e^z-1),z);
2579 -log(%e^(2*z)+1)/2-atan(%e^z)+log(%e^z-1)+(%e^(2*z)+2*%e^z)/2;
2580
2581 /* Problem 460: OK */
2582 integrate(1/(%e^(z/2)+%e^(z/3)+%e^(z/6)+1),z), domain:real;
2583 -3*log(%e^(z/3)+1)/2-3*log(%e^(z/6)+1)-3*atan(%e^(z/6))+z$
2584
2585 /* ----- Involving algebraic functions of the direct function --------------- */
2586
2587 /* ----- Involving (a+b*c^(d*z))^v ------------------------------------------ */
2588
2589 /* Problem 461: NOUN */
2590 integrate((b*c^(d*z)+a)^v,z);
2591 'integrate((b*c^(d*z)+a)^v,z);
2592
2593 /* Problem 463: OK */
2594 assume(a>0);
2595 [a>0];
2596
2597 integrate((b*c^(d*z)+a)^(1/2),z);
2598 2*sqrt(b*c^(d*z)+a)/(log(c)*d)+sqrt(a)*log(
2599                                        (2*sqrt(b*c^(d*z)+a)-2*sqrt(a))
2600                                         /(2*sqrt(b*c^(d*z)+a)+2*sqrt(a)))
2601                                /(log(c)*d);
2602 forget(a>0);
2603 [a>0];
2604
2605 /* Problem 465: NOUN */
2606 integrate((b*%e^(c*z)+a)^v,z);
2607 'integrate((b*%e^(c*z)+a)^v,z);
2608
2609 /* Problem 466: NOUN */
2610 integrate((a*%e^(c*z)+a)^v,z);
2611 'integrate((a*%e^(c*z)+a)^v,z);
2612
2613 /* Problem 467: NOUN */
2614 integrate((a-a*%e^(c*z))^v,z);
2615 'integrate((a-a*%e^(c*z))^v,z);
2616
2617 /* This assumptions is for the problems 457 - 468 */
2618 assume(a>0);
2619 [a>0];
2620
2621 /* Problem 469: OK */
2622 integrate((b*%e^(c*z)+a)^(5/2),z);
2623 a^(5/2)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2624  /c
2625  +(6*(b*%e^(c*z)+a)^(5/2)+10*a*(b*%e^(c*z)+a)^(3/2)+30*a^2*sqrt(b*%e^(c*z)+a))
2626   /(15*c);
2627
2628 /* Problem 470: OK */
2629 integrate((b*%e^(c*z)+a)^(3/2),z);
2630 a^(3/2)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))
2631                      /(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2632          /c
2633          +(2*(b*%e^(c*z)+a)^(3/2)+6*a*sqrt(b*%e^(c*z)+a))/(3*c);
2634
2635 /* Problem 471: OK */
2636 integrate((b*%e^(c*z)+a)^(1/2),z);
2637 sqrt(a)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))
2638                      /(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2639          /c
2640          +2*sqrt(b*%e^(c*z)+a)/c;
2641
2642 /* Problem 472: OK */
2643 integrate((a*%e^(c*z)+a)^(1/2),z);
2644 sqrt(a)*log((2*sqrt(a*%e^(c*z)+a)-2*sqrt(a))
2645                      /(2*sqrt(a*%e^(c*z)+a)+2*sqrt(a)))
2646          /c
2647          +2*sqrt(a*%e^(c*z)+a)/c;
2648
2649 /* Problem 473: OK */
2650 integrate((a-a*%e^(c*z))^(1/2),z);
2651 sqrt(a)*log((2*sqrt(a-a*%e^(c*z))-2*sqrt(a))
2652                      /(2*sqrt(a-a*%e^(c*z))+2*sqrt(a)))
2653          /c
2654          +2*sqrt(a-a*%e^(c*z))/c;
2655
2656 /* Problem 474: OK */
2657 integrate((b*%e^(c*z)+a)^((-1)/2),z);
2658 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2659          /(sqrt(a)*c);
2660
2661 /* Problem 475: OK */
2662 integrate((a*%e^(c*z)+a)^((-1)/2),z);
2663 log((2*sqrt(a*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(a*%e^(c*z)+a)+2*sqrt(a)))
2664          /(sqrt(a)*c);
2665
2666 /* Problem 476: OK */
2667 integrate((a-a*%e^(c*z))^((-1)/2),z);
2668 log((2*sqrt(a-a*%e^(c*z))-2*sqrt(a))/(2*sqrt(a-a*%e^(c*z))+2*sqrt(a)))
2669          /(sqrt(a)*c);
2670
2671 /* Problem 477: OK */
2672 integrate((b*%e^(c*z)+a)^((-3)/2),z);
2673 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2674          /(a^(3/2)*c)
2675          +2/(a*c*sqrt(b*%e^(c*z)+a));
2676
2677 /* Problem 478: OK */
2678 integrate((a*%e^(c*z)+a)^((-3)/2),z);
2679 log((2*sqrt(a*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(a*%e^(c*z)+a)+2*sqrt(a)))
2680          /(a^(3/2)*c)
2681          +2/(a*c*sqrt(a*%e^(c*z)+a));
2682
2683 /* Problem 479: OK */
2684 integrate((a-a*%e^(c*z))^((-3)/2),z);
2685 log((2*sqrt(a-a*%e^(c*z))-2*sqrt(a))/(2*sqrt(a-a*%e^(c*z))+2*sqrt(a)))
2686          /(a^(3/2)*c)
2687          +2/(a*c*sqrt(a-a*%e^(c*z)));
2688
2689 /* Problem 480: OK */
2690 integrate((b*%e^(c*z)+a)^((-5)/2),z);
2691 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2692          /(a^(5/2)*c)
2693          +(6*(b*%e^(c*z)+a)+2*a)/(3*a^2*c*(b*%e^(c*z)+a)^(3/2));
2694
2695 /* Forget assumption for Problems 457 - 468 */
2696 forget(a>0);
2697 [a>0];
2698
2699 /* ----- Involving ((a+b*%e^(c*z))^v)^p ------------------------------------- */
2700
2701 /* Problem 482: NOUN */
2702 integrate(((b*%e^(c*z)+a)^v)^p,z);
2703 'integrate(((b*%e^(c*z)+a)^v)^p,z);
2704
2705 /* Assumption for Problems 472 - 475 */
2706 assume(a>0);
2707 [a>0];
2708
2709 /* Problem 484: OK */
2710 integrate(((b*%e^(c*z)+a)^5)^(1/2),z),radexpand:all;
2711 a^(5/2)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))
2712                      /(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2713          /c
2714          +(6*(b*%e^(c*z)+a)^(5/2)+10*a*(b*%e^(c*z)+a)^(3/2)
2715                                  +30*a^2*sqrt(b*%e^(c*z)+a))
2716           /(15*c);
2717
2718 /* Problem 485: OK */
2719 integrate(((b*%e^(c*z)+a)^3)^(1/2),z),radexpand:all;
2720 a^(3/2)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))
2721                      /(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2722          /c
2723          +(2*(b*%e^(c*z)+a)^(3/2)+6*a*sqrt(b*%e^(c*z)+a))/(3*c);
2724
2725 /* Problem 486: OK */
2726 integrate((b*%e^(c*z)+a)^(-3/2),z);
2727 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2728          /(a^(3/2)*c)
2729          +2/(a*c*sqrt(b*%e^(c*z)+a));
2730
2731 /* Problem 487: OK */
2732 integrate((b*%e^(c*z)+a)^(-5/2),z);
2733 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2734          /(a^(5/2)*c)
2735          +(6*(b*%e^(c*z)+a)+2*a)/(3*a^2*c*(b*%e^(c*z)+a)^(3/2));
2736
2737 /* Forget assumption for Problems 472 - 475 */
2738 forget(a>0);
2739 [a>0];
2740
2741 /* ----- Involving (a+b*c*%e^(d*z))^p*%e^(f*z) ------------------------------ */
2742
2743 /* Problem 489: NOUN */
2744 integrate((b*c^(d*z)+a)^p*%e^(f*z),z);
2745 'integrate((b*c^(d*z)+a)^p*%e^(f*z),z);
2746
2747 /* Problem 490: NOUN */
2748 integrate((b*%e^(c*z)+a)^p*%e^(f*z),z);
2749 'integrate((b*%e^(c*z)+a)^p*%e^(f*z),z);
2750
2751 /* Assumption for problems 480 - 490 */
2752 assume(notequal(p+1,0));
2753 [notequal(p,-1)];
2754
2755 /* Problem 492: OK */
2756 integrate((b*%e^(c*z)+a)^p*%e^(c*z),z);
2757 (b*%e^(c*z)+a)^(p+1)/(b*c*(p+1));
2758
2759 /* Problem 493: OK */
2760 integrate((a*%e^(c*z)+a)^p*%e^(c*z),z);
2761 (a*%e^(c*z)+a)^(p+1)/(a*c*(p+1));
2762
2763 /* Problem 494: OK */
2764 integrate((a-a*%e^(c*z))^p*%e^(c*z),z);
2765 -(a-a*%e^(c*z))^(p+1)/(a*c*(p+1));
2766
2767 /* Problem 495: OK */
2768 integrate((b*%e^(c*z)+a)^(1/2)*%e^(c*z),z);
2769 2*(b*%e^(c*z)+a)^(3/2)/(3*b*c);
2770
2771 /* Problem 496: OK */
2772 integrate((a*%e^(c*z)+a)^(1/2)*%e^(c*z),z);
2773 2*(a*%e^(c*z)+a)^(3/2)/(3*a*c);
2774
2775 /* Problem 497: OK */
2776 integrate((a-a*%e^(c*z))^(1/2)*%e^(c*z),z);
2777 -2*(a-a*%e^(c*z))^(3/2)/(3*a*c);
2778
2779 /* Problem 498: OK */
2780 integrate((b*%e^(c*z)+a)^((-1)/2)*%e^(c*z),z);
2781 2*sqrt(b*%e^(c*z)+a)/(b*c);
2782
2783 /* Problem 499: OK */
2784 integrate((a*%e^(c*z)+a)^((-1)/2)*%e^(c*z),z);
2785 2*sqrt(a*%e^(c*z)+a)/(a*c);
2786
2787 /* Problem 500: OK */
2788 integrate((a-a*%e^(c*z))^((-1)/2)*%e^(c*z),z);
2789 -2*sqrt(a-a*%e^(c*z))/(a*c);
2790
2791 /* Problem 501: OK */
2792 integrate((b*%e^(c*z)+a)^((-3)/2)*%e^(c*z),z);
2793 -2/(b*c*sqrt(b*%e^(c*z)+a));
2794
2795 /* Problem 502: OK */
2796 integrate((b*%e^(c*z)+a)^((-5)/2)*%e^(c*z),z);
2797 -2/(3*b*c*(b*%e^(c*z)+a)^(3/2));
2798
2799 /* Forget assumption for problems 480 - 490 */
2800 forget(notequal(p+1,0));
2801 [notequal(p,-1)];
2802
2803 /* ----- Involving ((a+b*c*%e^(c*z))^v)^p*%e^(d*z) -------------------------- */
2804
2805 /* Problem 504: NOUN */
2806 integrate(((b*%e^(c*z)+a)^v)^p*%e^(d*z),z);
2807 'integrate(((b*%e^(c*z)+a)^v)^p*%e^(d*z),z);
2808
2809 /* Problem 505: OK */
2810 integrate(((b*%e^(c*z)+a)^5)^(1/2)*%e^(c*z),z),domain:real;
2811 2*(b*%e^(c*z)+a)^(7/2)/(7*b*c)$
2812
2813 /* Problem 506: OK */
2814 integrate(((b*%e^(c*z)+a)^3)^(1/2)*%e^(c*z),z),domain:real;
2815 2*(b*%e^(c*z)+a)^(5/2)/(5*b*c)$
2816
2817 /* Problem 507: OK */
2818 integrate((b*%e^(c*z)+a)^(-3/2)*%e^(c*z),z);
2819 -2/(b*c*sqrt(b*%e^(c*z)+a));
2820
2821 /* Problem 508: OK */
2822 integrate((a*%e^(c*z)+a)^(-3/2)*%e^(c*z),z);
2823 -2/(a*c*sqrt(a*%e^(c*z)+a));
2824
2825 /* Problem 509: OK */
2826 integrate((a-a*%e^(c*z))^(-3/2)*%e^(c*z),z);
2827 2/(a*c*sqrt(a-a*%e^(c*z)));
2828
2829 /* Problem 510: OK */
2830 integrate((b*%e^(c*z)+a)^(-5/2)*%e^(c*z),z);
2831 -2/(3*b*c*(b*%e^(c*z)+a)^(3/2));
2832
2833 /* ----- Involving (a+b*%e^(c*z))^p*(%e^(d*z))^v ---------------------------- */
2834
2835 /* Problem 511: NOUN */
2836 integrate((b*%e^(c*z)+a)^p*(%e^(d*z))^v,z);
2837 'integrate((b*%e^(c*z)+a)^p*(%e^(d*z))^v,z);
2838
2839 /* Problem 512: NOUN */
2840 integrate((b*%e^(c*z)+a)^p*(%e^(c*z))^v,z);
2841 'integrate((%e^(c*z))^v*(b*%e^(c*z)+a)^p,z);
2842
2843 /* Problem 514: OK */
2844 assume(a>0,b>0);
2845 [a>0,b>0];
2846
2847 integrate((%e^(c*z))^(1/2)/(b*%e^(c*z)+a),z);
2848 2*atan(b*sqrt(%e^(c*z))/sqrt(a*b))/(sqrt(a*b)*c);
2849
2850 forget(a>0,b>0);
2851 [a>0,b>0];
2852
2853 /* ----- Involving (a+b*%e^(c*z))^p and rational function of %e^(c*z) ------- */
2854
2855 /* Problem 516: NOUN */
2856 integrate(e^(q*z)*(b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2857 'integrate(e^(q*z)*(b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2858
2859 /* Problem 517: NOUN */
2860 integrate((b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2861 'integrate((b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2862
2863 assume(a>0,e>0,(a*e-b*d)>0);
2864 [a > 0,e>0,a*e>b*d];
2865
2866 /* Problem 519: NEW 08-2010 */
2867 integrate((b*%e^(c*z)+a)^(1/2)/(e*%e^(c*z)+d),z);
2868 sqrt(a)*log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2869  /(c*d)
2870  -(a*e-b*d)*log((2*e*sqrt(b*%e^(c*z)+a)-2*sqrt(e*(a*e-b*d)))
2871                  /(2*e*sqrt(b*%e^(c*z)+a)+2*sqrt(e*(a*e-b*d))))
2872   /(c*d*sqrt(e*(a*e-b*d)))$
2873
2874 /* Problem 520: NEW 08-2010 */
2875 integrate((b*%e^(c*z)+a)^((-1)/2)/(e*%e^(c*z)+d),z);
2876 log((2*sqrt(b*%e^(c*z)+a)-2*sqrt(a))/(2*sqrt(b*%e^(c*z)+a)+2*sqrt(a)))
2877  /(sqrt(a)*c*d)
2878  -e*log((2*e*sqrt(b*%e^(c*z)+a)-2*sqrt(e*(a*e-b*d)))
2879          /(2*e*sqrt(b*%e^(c*z)+a)+2*sqrt(e*(a*e-b*d))))
2880   /(c*d*sqrt(e*(a*e-b*d)))$
2881
2882 /* Problem 521: NEW 08-2010 */
2883 integrate(%e^(c*z)*(b*%e^(c*z)+a)^((-1)/2)/(e*%e^(c*z)+d),z);
2884 log((2*e*sqrt(b*%e^(c*z)+a)-2*sqrt(e*(a*e-b*d)))
2885      /(2*e*sqrt(b*%e^(c*z)+a)+2*sqrt(e*(a*e-b*d))))
2886  /(c*sqrt(e*(a*e-b*d)))$
2887
2888 forget(a>0,e>0,(a*e-b*d)>0);
2889 [a > 0,e>0,a*e>b*d];
2890
2891 /* Problem 523: NOUN */
2892 integrate(e^(d*z)*(b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2893 'integrate(e^(d*z)*(b*%e^(c*z)+a)^p/(e*%e^(c*z)+d),z);
2894
2895 /* ----- Involving (a+b*%e^(2*c*z))^p*%e^(c*z) ------------------------------ */
2896
2897 assume(a>0,b>0);
2898 [a>0,b>0];
2899
2900 /* Problem 525: NEW 08-2010 */
2901 integrate((b*%e^(2*c*z)+a)^(5/2)*%e^(c*z),z);
2902 5*a^3*asinh(2*b*%e^(c*z)/sqrt(4*a*b))/(16*sqrt(b)*c)
2903  +%e^(c*z)*(b*%e^(2*c*z)+a)^(5/2)/(6*c)
2904  +5*a*%e^(c*z)*(b*%e^(2*c*z)+a)^(3/2)/(24*c)
2905  +5*a^2*%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(16*c)$
2906
2907 /* Problem 526: NEW 08-2010 */
2908 integrate((b*%e^(2*c*z)+a)^(3/2)*%e^(c*z),z);
2909 3*a^2*asinh(2*b*%e^(c*z)/sqrt(4*a*b))/(8*sqrt(b)*c)
2910  +%e^(c*z)*(b*%e^(2*c*z)+a)^(3/2)/(4*c)
2911  +3*a*%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(8*c)$
2912
2913 /* Problem 527: NEW 08-2010 */
2914 integrate((b*%e^(2*c*z)+a)^(1/2)*%e^(c*z),z);
2915 a*asinh(2*b*%e^(c*z)/sqrt(4*a*b))/(2*sqrt(b)*c)
2916  +%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(2*c)$
2917
2918 /* Problem 528: NEW 08-2010 */
2919 integrate((b*%e^(2*c*z)+a)^((-1)/2)*%e^(c*z),z);
2920 asinh(2*b*%e^(c*z)/sqrt(4*a*b))/(sqrt(b)*c)$
2921
2922 /* Problem 529: NEW 08-2010 */
2923 integrate((b*%e^(2*c*z)+a)^((-3)/2)*%e^(c*z),z);
2924 %e^(c*z)/(a*c*sqrt(b*%e^(2*c*z)+a));
2925
2926 /* Problem 530: NEW 08-2010 */
2927 integrate((b*%e^(2*c*z)+a)^((-5)/2)*%e^(c*z),z);
2928 2*%e^(c*z)/(3*a^2*c*sqrt(b*%e^(2*c*z)+a))
2929  +%e^(c*z)/(3*a*c*(b*%e^(2*c*z)+a)^(3/2));
2930
2931 forget(a>0,b>0);
2932 [a>0,b>0];
2933
2934 /* ----- Involving ((a+b*%e^(2*c*z))^v)^p*%e^(c*z) -------------------------- */
2935
2936 /* Problem 532: NOUN */
2937 integrate(((b*%e^(2*c*z)+a)^v)^p*%e^(c*z),z);
2938 'integrate(%e^(c*z)*((b*%e^(2*c*z)+a)^v)^p,z);
2939
2940 assume(a>0,b>0);
2941 [a>0,b>0];
2942
2943 /* Problem 534: NEW 08-2010 */
2944 integrate(((b*%e^(2*c*z)+a)^5)^(1/2)*%e^(c*z),z),domain:real;
2945 5*a^3*asinh(sqrt(b)*%e^(c*z)/sqrt(a))/(16*sqrt(b)*c)
2946  +%e^(c*z)*(b*%e^(2*c*z)+a)^(5/2)/(6*c)
2947  +5*a*%e^(c*z)*(b*%e^(2*c*z)+a)^(3/2)/(24*c)
2948  +5*a^2*%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(16*c)$
2949
2950 /* Problem 535: NEW 08-2010 */
2951 integrate(((b*%e^(2*c*z)+a)^3)^(1/2)*%e^(c*z),z),domain:real;
2952 3*a^2*asinh(sqrt(b)*%e^(c*z)/sqrt(a))/(8*sqrt(b)*c)
2953  +%e^(c*z)*(b*%e^(2*c*z)+a)^(3/2)/(4*c)
2954  +3*a*%e^(c*z)*sqrt(b*%e^(2*c*z)+a)/(8*c)$
2955
2956 forget(a>0,b>0);
2957 [a>0,b>0];
2958
2959 /* Problem 537: NEW 08-2010 */
2960 integrate((b*%e^(2*c*z)+a)^(-3/2)*%e^(c*z),z);
2961 %e^(c*z)/(a*c*sqrt(b*%e^(2*c*z)+a));
2962
2963 /* Problem 538: NEW 08-2010 */
2964 integrate((b*%e^(2*c*z)+a)^(-5/2)*%e^(c*z),z);
2965 2*%e^(c*z)/(3*a^2*c*sqrt(b*%e^(2*c*z)+a))
2966  +%e^(c*z)/(3*a*c*(b*%e^(2*c*z)+a)^(3/2));
2967
2968 /* ----- Involving (a+b*%e^(2*c*z))^p*(%e^(c*z))^v -------------------------- */
2969
2970 /* Problem 539: NOUN */
2971 integrate((b*%e^(2*c*z)+a)^p*(%e^(c*z))^v,z);
2972 'integrate((b*%e^(2*c*z)+a)^p*(%e^(c*z))^v,z);
2973
2974 /* Problem 540: NOUN */
2975 integrate((b*%e^(2*c*z)+a)^(5/2)*(%e^(c*z))^v,z);
2976 'integrate((b*%e^(2*c*z)+a)^(5/2)*(%e^(c*z))^v,z);
2977
2978 /* Problem 541: NOUN */
2979 integrate((b*%e^(2*c*z)+a)^(3/2)*(%e^(c*z))^v,z);
2980 'integrate((b*%e^(2*c*z)+a)^(3/2)*(%e^(c*z))^v,z);
2981
2982 /* Problem 542: NOUN */
2983 integrate((b*%e^(2*c*z)+a)^(1/2)*(%e^(c*z))^v,z);
2984 'integrate((b*%e^(2*c*z)+a)^(1/2)*(%e^(c*z))^v,z);
2985
2986 /* Problem 543: NOUN */
2987 integrate((b*%e^(2*c*z)+a)^((-1)/2)*(%e^(c*z))^v,z);
2988 'integrate((b*%e^(2*c*z)+a)^((-1)/2)*(%e^(c*z))^v,z);
2989
2990 /* Problem 544: NOUN */
2991 integrate((b*%e^(2*c*z)+a)^((-3)/2)*(%e^(c*z))^v,z);
2992 'integrate((b*%e^(2*c*z)+a)^((-3)/2)*(%e^(c*z))^v,z);
2993
2994 /* Problem 545: NOUN */
2995 integrate((b*%e^(2*c*z)+a)^((-5)/2)*(%e^(c*z))^v,z);
2996 'integrate((b*%e^(2*c*z)+a)^((-5)/2)*(%e^(c*z))^v,z);
2997
2998 /* ----- Involving %e^(q*z)*(b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v --------------- */
2999
3000 /* Problem 546: NOUN */
3001 integrate(%e^(q*z)*(b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v,z);
3002 'integrate((b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v*%e^(q*z),z);
3003
3004 /* Problem 547: NOUN */
3005 integrate((b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v,z);
3006 'integrate((b*%e^(c*z)+a)^p*(e*%e^(c*z)+d)^v,z);
3007
3008 /* ----- Involvoving (a*%e^(2*d*z)+b*%e^(d*z)+c)^p -------------------------- */
3009
3010 /* Problem 548: NOUN */
3011 integrate((c+b*%e^(d*z)+a*%e^(2*d*z))^p,z);
3012 'integrate((a*%e^(2*d*z)+b*%e^(d*z)+c)^p,z);
3013
3014 /* Problem 550: NEW 08-2010
3015  * We get a correct result for x a real variable.
3016  */
3017 assume(a>0,b>0,c>0,4*a*c>b^2);
3018 [a > 0,b > 0,c > 0,4*a*c > b^2];
3019
3020 integrate((c+b*%e^(d*x)+a*%e^(2*d*x))^(1/2),x);
3021 b*asinh((2*a*%e^(d*x)+b)/sqrt(4*a*c-b^2))/(2*sqrt(a)*d)
3022  -sqrt(c)*asinh(2*c*%e^-(d*x)/sqrt(4*a*c-b^2)+b/sqrt(4*a*c-b^2))/d
3023  +sqrt(a*%e^(2*d*x)+b*%e^(d*x)+c)/d;
3024
3025 forget(a>0,b>0,c>0,4*a*c>b^2);
3026 [a > 0,b > 0,c > 0,4*a*c > b^2];
3027
3028 /* ----- Involvoving %e^(e*z)*(a*%e^(2*d*z)+b*%e^(d*z)+c)^p ----------------- */
3029
3030 /* Problem 552: NOUN */
3031 integrate(%e^(e*z)*(c+b*%e^(d*z)+a*%e^(2*d*z))^p,z);
3032 'integrate((a*%e^(2*d*z)+b*%e^(d*z)+c)^p*%e^(e*z),z);
3033
3034 /* ----- Other integrals ---------------------------------------------------- */
3035
3036 assume(a>0,b>0,c>0,d>0);
3037 [a>0,b>0,c>0,d>0];
3038
3039 /* Problem 554: NEW 08-2010 */
3040
3041 integrate(sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c)),z);
3042 a*log((2*c*sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c))-2*sqrt(a*c))
3043        /(2*c*sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c))+2*sqrt(a*c)))
3044  /(sqrt(a*c)*e)
3045  -b*log((2*d*sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c))-2*sqrt(b*d))
3046          /(2*d*sqrt((b*%e^(e*z)+a)/(d*%e^(e*z)+c))+2*sqrt(b*d)))
3047   /(sqrt(b*d)*e)$
3048
3049 assume(a*d>b*c);
3050 [a*d>b*c];
3051
3052 /* Problem 556: NEW 08-2010 */
3053 integrate(sqrt((%e^(c*z)-1)/(%e^(c*z)+1)),z);
3054 log(sqrt((%e^(c*z)-1)/(%e^(c*z)+1))+1)/c
3055  -2*atan(sqrt((%e^(c*z)-1)/(%e^(c*z)+1)))/c
3056  -log(sqrt((%e^(c*z)-1)/(%e^(c*z)+1))-1)/c$
3057
3058 forget(a>0,b>0,c>0,d>0,a*d>b*c);
3059 [a>0,b>0,c>0,d>0,a*d>b*c];
3060
3061 /* Problem 558: OK */
3062 integrate(sqrt((%e^(c*z)-1)/(%e^(c*z)+1)),z);
3063 log(sqrt((%e^(c*z)-1)/(%e^(c*z)+1))+1)/c
3064  -2*atan(sqrt((%e^(c*z)-1)/(%e^(c*z)+1)))/c
3065  -log(sqrt((%e^(c*z)-1)/(%e^(c*z)+1))-1)/c;
3066
3067 /* Problem 559: NOUN */
3068 integrate(1/(sqrt(1-%e^z)+sqrt(1+%e^z)),z);
3069 'integrate(1/(sqrt(1-%e^z)+sqrt(1+%e^z)),z);
3070
3071 /* ----- Involving powers of the dircect function and a power function ------ */
3072
3073 /* ----- Involving z^(v-1) and arguments a*z -------------------------------- */
3074
3075 /* Problem 560: NEW 2-1 */
3076 diffcheck(integrate(z^(v-1)*(%e^(a*z))^u,z),z,factor);
3077 z^(v-1)*(%e^(a*z))^u;
3078
3079 /* Problem 561: NEW 2
3080  * We get the most simple result for a real argument x.
3081  */
3082 integrate((%e^(a*x))^u/x,x),gamma_expand:true,logcontract;
3083 expintegral_ei(a*u*x);
3084
3085 /* Problem 562: NEW 2-1 */
3086 diffcheck(integrate(z^n*(%e^(a*z))^u,z),z,factor);
3087 z^n*(%e^(a*z))^u;
3088
3089 /* Problem 563: OK */
3090 integrate(z*(%e^(a*z))^u,z), domain:real;
3091 (a*u*z-1)*%e^(a*u*z)/(a^2*u^2);
3092
3093 /* Problem 564: NEW 2-1*/
3094 integrate(z^(1/2+n)*(%e^(a*z))^u,z);
3095 -gamma_incomplete(n+3/2,-a*u*z)*z^(n+3/2)*(-a*u*z)^(-n-3/2)*(%e^(a*z))^u
3096                                *%e^-(a*u*z);
3097
3098 /* ----- Involving z^(v-1) and arguments a*z+b ------------------------------ */
3099
3100 /* Problem 565: NEW 2-1 */
3101 -integrate(z^(v-1)*(%e^(a*z+b))^u,z);
3102 gamma_incomplete(v,-a*u*z)*z^v*%e^-(a*u*z)*(%e^(a*z+b))^u/(-a*u*z)^v;
3103
3104 /* Problem 566: NEW Typ 2
3105  * We get the most simple result only for a real argument x.
3106  */
3107 integrate((%e^(a*x+b))^u/x,x),gamma_expand:true,logcontract;
3108 %e^(b*u)*expintegral_ei(a*u*x);
3109
3110 /* Problem 567: NEW 2-1 */
3111 integrate(z^n*(%e^(a*z+b))^u,z);
3112 -a^(-n-1)*(-1)^(n+1)*gamma_incomplete(n+1,-a*u*z)*u^(-n-1)*%e^-(a*u*z)
3113          *(%e^(a*z+b))^u;
3114
3115 /* Problem 568: OK */
3116 integrate(z*(%e^(a*z+b))^u,z), domain:real;
3117 (a*u*%e^(b*u)*z-%e^(b*u))*%e^(a*u*z)/(a^2*u^2);
3118
3119 /* Problem 569: NEW 2-1 */
3120 -integrate(z^(1/2+n)*(%e^(a*z+b))^u,z);
3121 gamma_incomplete(n+3/2,-a*u*z)*z^(n+3/2)*(-a*u*z)^(-n-3/2)*%e^-(a*u*z)
3122                               *(%e^(a*z+b))^u;
3123
3124 /* ----- Involving z^(v-1) and arguments a*z^r ------------------------------ */
3125
3126 /* Problem 570: NEW 2-1 */
3127 integrate(z^(v-1)*(%e^(a*z^r))^u,z);
3128 -gamma_incomplete(v/r,-a*u*z^r)*z^v*(%e^(a*z^r))^u*%e^-(a*u*z^r)
3129  /(r*(-a*u*z^r)^(v/r));
3130
3131 /* Problem 571: NEW 2
3132  * We get the most simple result only for a real argument x.
3133  */
3134 integrate((%e^(a*x^r))^u/x,x),gamma_expand:true,logcontract;
3135 expintegral_ei(a*u*x^r)/r;
3136
3137 /* Problem 572: NEW 2-1 */
3138 integrate(z^n*(%e^(a*z^2))^u,z);
3139 -gamma_incomplete((n+1)/2,-a*u*z^2)*z^(n+1)*(-a*u*z^2)^((-n-1)/2)
3140                                    *(%e^(a*z^2))^u*%e^-(a*u*z^2)
3141  /2;
3142
3143 /* Problem 573: NEW 2-1 */
3144 integrate(z^(2*n)*(%e^(a*z^2))^u,z);
3145 -gamma_incomplete((2*n+1)/2,-a*u*z^2)*z^(2*n+1)*(-a*u*z^2)^((-2*n-1)/2)
3146                                      *(%e^(a*z^2))^u*%e^-(a*u*z^2)
3147  /2;
3148
3149 /* Problem 574: NEW 2-1 */
3150 integrate(z^(1+2*n)*(%e^(a*z^2))^u,z),factor;
3151 a^(-n-1)*(-1)^n*gamma_incomplete(n+1,-a*u*z^2)*u^(-n-1)*(%e^(a*z^2))^u
3152         *%e^-(a*u*z^2)
3153  /2;
3154
3155 /* Problem 575: NEW 2-1 */
3156 integrate(z^n*(%e^(a*sqrt(z)))^u,z),factor;
3157 -2*a^(-2*n-2)*gamma_incomplete(2*(n+1),-a*u*sqrt(z))*u^(-2*n-2)
3158   *(%e^(a*sqrt(z)))^u*%e^-(a*u*sqrt(z));
3159
3160 /* ----- Involving z^(v-1) and arguments a*z^r+b ---------------------------- */
3161
3162 /* Problem 576: NEW 2-1*/
3163 integrate(z^(v-1)*(%e^(b+a*z^r))^u,z);
3164 -gamma_incomplete(v/r,-a*u*z^r)*z^v*%e^-(a*u*z^r)*(%e^(a*z^r+b))^u
3165  /(r*(-a*u*z^r)^(v/r));
3166
3167 /* Problem 577: NEW 2
3168  * We get the most simple result only for a real argument x.
3169  */
3170 integrate((%e^(b+a*x^r))^u/x,x),gamma_expand:true,logcontract;
3171 %e^(b*u)*expintegral_ei(a*u*x^r)/r;
3172
3173 /* Problem 578: NEW 2-1 */
3174 integrate(z^n*(%e^(b+a*z^2))^u,z),ratsimp;
3175 -gamma_incomplete((n+1)/2,-a*u*z^2)*z^(n+1)*(-a*u*z^2)^(-n/2-1/2)
3176                                    *%e^-(a*u*z^2)*(%e^(a*z^2+b))^u
3177  /2;
3178
3179 /* Problem 579: NEW 2-1 */
3180 integrate(z^(2*n)*(%e^(b+a*z^2))^u,z),ratsimp;
3181 -(-1)^n*gamma_incomplete((2*n+1)/2,-a*u*z^2)*z*%e^-(a*u*z^2)*(%e^(a*z^2+b))^u
3182  /(2*a^n*u^n*sqrt(-a*u*z^2));
3183
3184 /* Problem 580: NEW 2-1 */
3185 integrate(z^(1+2*n)*(%e^(b+a*z^2))^u,z),ratsimp;
3186 a^(-n-1)*(-1)^n*gamma_incomplete(n+1,-a*u*z^2)*u^(-n-1)*%e^-(a*u*z^2)
3187         *(%e^(a*z^2+b))^u
3188  /2;
3189
3190 /* Problem 581: NEW 2-1 */
3191 integrate(z^n*(%e^(b+a*sqrt(z)))^u,z),ratsimp;
3192 -2*a^(-2*n-2)*gamma_incomplete(2*n+2,-a*u*sqrt(z))*u^(-2*n-2)
3193   *%e^-(a*u*sqrt(z))*(%e^(a*sqrt(z)+b))^u;
3194
3195 /* ----- Involving z^(v-1) and arguments a*z^r+b*z -------------------------- */
3196
3197 /* Problem 582: NEW 5-1 */
3198 expand(niceindices(integrate(z^n*(%e^(b*z+a*z^2))^u,z))-
3199 (-a^(-n-1)*(%e^(a*z^2+b*z))^u*%e^(-u*(a*z^2+b*z)-b^2*u/(4*a))
3200          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-u*(2*a*z+b)^2/(4*a))
3201                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
3202                  /(-u*(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
3203  /2));
3204 0;
3205
3206 /* Problem 583: NEW 6-1 */
3207 niceindices(integrate(z^n*(%e^(b*z+a*sqrt(z)))^u,z));
3208 2^(-2*n-1)*('sum(4^j*binomial(n,j)
3209                     *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3210                                      *(2*b*sqrt(z)+a)^(j+i)
3211                                      *(a
3212                                       *gamma_incomplete((j+i+1)/2,
3213                                                         -u*(2*b*sqrt(z)+a)^2
3214                                                          /(4*b))
3215                                       *(2*b*sqrt(z)+a)
3216                                       +2*b
3217                                         *gamma_incomplete((j+i+2)/2,
3218                                                           -u*(2*b*sqrt(z)+a)^2
3219                                                            /(4*b))
3220                                         *sqrt(-u*(2*b*sqrt(z)+a)^2/b)
3221                                        /u)
3222                            /(-u*(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,0,j),j,0,
3223                  n))*(%e^(b*z+a*sqrt(z)))^u*%e^(u*(b*z+a*sqrt(z))-a^2*u/(4*b))
3224  /b^(2*(n+1));
3225
3226 /* ----- Involving z^(v-1) and arguments a*z^r+b*z+c ------------------------ */
3227
3228 /* Problem 584: NEW 5-1 */
3229 expand(niceindices(integrate(z^n*(%e^(c+b*z+a*z^2))^u,z))-
3230 (-a^(-n-1)*(%e^(a*z^2+b*z+c))^u*%e^(-u*(a*z^2+b*z)-b^2*u/(4*a))
3231          *('sum(b^(n-i)*gamma_incomplete((i+1)/2,-u*(2*a*z+b)^2/(4*a))
3232                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*a*z+b)^(i+1)
3233                  /(-u*(2*a*z+b)^2/a)^((i+1)/2),i,0,n))
3234  /2));
3235 0;
3236
3237 /* Problem 585: NEW 6-1 */
3238 niceindices(integrate(z^n*(%e^(c+b*z+a*sqrt(z)))^u,z));
3239 2^(-2*n-1)*('sum(4^j*binomial(n,j)
3240                     *'sum(a^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3241                                      *(2*b*sqrt(z)+a)^(j+i)
3242                                      *(a
3243                                       *gamma_incomplete((j+i+1)/2,
3244                                                         -u*(2*b*sqrt(z)+a)^2
3245                                                          /(4*b))
3246                                       *(2*b*sqrt(z)+a)
3247                                       +2*b
3248                                         *gamma_incomplete((j+i+2)/2,
3249                                                           -u*(2*b*sqrt(z)+a)^2
3250                                                            /(4*b))
3251                                         *sqrt(-u*(2*b*sqrt(z)+a)^2/b)
3252                                        /u)
3253                            /(-u*(2*b*sqrt(z)+a)^2/b)^((j+i+1)/2),i,0,j),j,0,
3254                  n))*(%e^(b*z+a*sqrt(z)))^u
3255           *%e^(u*(b*z+a*sqrt(z)+c)-a^2*u/(4*b))
3256  /b^(2*(n+1));
3257
3258 /* ----- Involving z^(v-1)*a^(d*z)*h^(c*z) ---------------------------------- */
3259
3260 /* Problem 586: NEW 7 */
3261 expand(integrate(z^(v-1)*a^(d*z)*h^(c*z),z)-
3262 (-gamma_incomplete(v,-(c*log(h)+log(a)*d)*z)*z^v/(-(c*log(h)+log(a)*d)*z)^v));
3263 0;
3264
3265 /* Problem 587: NEW 7 */
3266 expand(integrate(z^n*a^(d*z)*h^(c*z),z) -
3267 (-(c*log(h)+log(a)*d)^(-n-1)*(-1)^(n+1)
3268                            *gamma_incomplete(n+1,-(c*log(h)+log(a)*d)*z)));
3269 0;
3270
3271 /* Problem 588: NEW 7 */
3272 expand(integrate(z^(1/2+n)*a^(d*z)*h^(c*z),z)-
3273 (-gamma_incomplete(n+3/2,-(c*log(h)+log(a)*d)*z)
3274  *z^(n+3/2)*(-(c*log(h)+log(a)*d)*z)^(-n-3/2)));
3275 0;
3276
3277 /* ----- Involving z^(v-1)*a^(d*z)*h^(c*z+g) -------------------------------- */
3278
3279 /* Problem 589: NEW 7 */
3280 expand(integrate(z^(v-1)*a^(d*z)*h^(g+c*z),z)-
3281 -h^g*gamma_incomplete(v,-(c*log(h)+log(a)*d)*z)*z^v/(-(c*log(h)+log(a)*d)*z)^v);
3282 0;
3283
3284 /* Problem 590: NEW 7 */
3285 expand(integrate(z^n*a^(d*z)*h^(g+c*z),z)-
3286 -h^g*(c*log(h)+log(a)*d)^(-n-1)*(-1)^(n+1)
3287     *gamma_incomplete(n+1,-(c*log(h)+log(a)*d)*z));
3288 0;
3289
3290 /* Problem 591: NEW 7 */
3291 expand(integrate(z^(1/2+n)*a^(d*z)*h^(g+c*z),z)-
3292 -h^g*gamma_incomplete(n+3/2,-(c*log(h)+log(a)*d)*z)*z^(n+3/2)
3293     *(-(c*log(h)+log(a)*d)*z)^(-n-3/2));
3294 0;
3295
3296 /* ----- Involving z^(v-1)*a^(d*z+e)*h^(c*z+g) ------------------------------ */
3297
3298 /* Problem 592: NEW 7 */
3299 expand(integrate(z^(v-1)*a^(e+d*z)*h^(g+c*z),z)-
3300 -a^e*h^g*gamma_incomplete(v,-(c*log(h)+log(a)*d)*z)*z^v
3301  /(-(c*log(h)+log(a)*d)*z)^v);
3302 0;
3303
3304 /* Problem 593: NEW 7 */
3305 expand(integrate(z^n*a^(e+d*z)*h^(g+c*z),z)-
3306 -a^e*h^g*(c*log(h)+log(a)*d)^(-n-1)*(-1)^(n+1)
3307     *gamma_incomplete(n+1,-(c*log(h)+log(a)*d)*z));
3308 0;
3309
3310 /* Problem 594: NEW 7 */
3311 expand(integrate(z^(1/2+n)*a^(e+d*z)*h^(g+c*z),z)-
3312 -a^e*h^g*gamma_incomplete(n+3/2,-(c*log(h)+log(a)*d)*z)*z^(n+3/2)
3313     *(-(c*log(h)+log(a)*d)*z)^(-n-3/2));
3314 0;
3315
3316 /* ----- Involving z^n*a^(b*z)*h^(c*z^r) ------------------------------------ */
3317
3318 /* Problem 595: NEW 9 */
3319 expand(niceindices(integrate(z^n*a^(b*z)*h^(c*z^2),z))-
3320 (-c^(-n-1)*%e^-(log(a)^2*b^2/(4*c*log(h)))*log(h)^(-n-1)
3321          *('sum(log(a)^(n-i)*b^(n-i)
3322                             *gamma_incomplete((i+1)/2,
3323                                               -(2*c*log(h)*z+log(a)*b)^2
3324                                                /(4*c*log(h)))*(-1)^(i-n)
3325                             *2^(i-n)*binomial(n,i)
3326                             *(2*c*log(h)*z+log(a)*b)^(i+1)
3327                  /(-(2*c*log(h)*z+log(a)*b)^2/(c*log(h)))^((i+1)/2),i,0,n))
3328  /2));
3329 0;
3330
3331 /* Problem 596: NEW 10 */
3332 expand(niceindices(integrate(z^n*a^(b*z)*h^(c*sqrt(z)),z))-
3333 (%e^-(c^2*log(h)^2/(4*log(a)*b))*2^(-2*n-1)
3334                                *('sum(4^j*binomial(n,j)
3335                                          *'sum(
3336                                           c^(2*n-j-i)*log(h)^(2*n-j-i)
3337                                                      *(-1)^(i-j)*binomial(j,i)
3338                                                      *(2*log(a)*b*sqrt(z)
3339                                                       +c*log(h))
3340                                                       ^(j+i)
3341                                                      *(c*log(h)
3342                                                         *gamma_incomplete(
3343                                                          (j+i+1)/2,
3344                                                          -(2*log(a)*b*sqrt(z)
3345                                                           +c*log(h))
3346                                                           ^2
3347                                                           /(4*log(a)*b))
3348                                                         *(2*log(a)*b*sqrt(z)
3349                                                          +c*log(h))
3350                                                       +2*log(a)*b
3351                                                         *gamma_incomplete(
3352                                                          (j+i+2)/2,
3353                                                          -(2*log(a)*b*sqrt(z)
3354                                                           +c*log(h))
3355                                                           ^2
3356                                                           /(4*log(a)*b))
3357                                                         *sqrt(
3358                                                          -(2*log(a)*b*sqrt(z)
3359                                                           +c*log(h))
3360                                                           ^2
3361                                                           /(log(a)*b)))
3362                                            /(-(2*log(a)*b*sqrt(z)+c*log(h))^2
3363                                             /(log(a)*b))
3364                                             ^((j+i+1)/2),i,0,j),j,0,n))
3365  /(log(a)^(2*(n+1))*b^(2*(n+1)))));
3366 0;
3367
3368 /* ----- Involving z^n*a^(d*z+e)*h^(c*z^r) ---------------------------------- */
3369
3370 /* Problem 597: NEW 9 */
3371 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(c*z^2),z))-
3372 (-a^e*c^(-n-1)*%e^-(log(a)^2*d^2/(4*c*log(h)))*log(h)^(-n-1)
3373     *('sum(log(a)^(n-i)*d^(n-i)
3374                        *gamma_incomplete((i+1)/2,
3375                                          -(2*c*log(h)*z+log(a)*d)^2
3376                                           /(4*c*log(h)))*(-1)^(i-n)*2^(i-n)
3377                        *binomial(n,i)*(2*c*log(h)*z+log(a)*d)^(i+1)
3378             /(-(2*c*log(h)*z+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3379  /2));
3380 0;
3381
3382 /* Problem 598: NEW 10 */
3383 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(c*sqrt(z)),z))-
3384 (a^e*%e^-(c^2*log(h)^2/(4*log(a)*d))*2^(-2*n-1)
3385    *('sum(4^j*binomial(n,j)
3386              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3387                               *(2*log(a)*d*sqrt(z)+c*log(h))^(j+i)
3388                               *(c*log(h)
3389                                  *gamma_incomplete((j+i+1)/2,
3390                                                    -(2*log(a)*d*sqrt(z)
3391                                                     +c*log(h))
3392                                                     ^2
3393                                                     /(4*log(a)*d))
3394                                  *(2*log(a)*d*sqrt(z)+c*log(h))
3395                                +2*log(a)*d
3396                                  *gamma_incomplete((j+i+2)/2,
3397                                                    -(2*log(a)*d*sqrt(z)
3398                                                     +c*log(h))
3399                                                     ^2
3400                                                     /(4*log(a)*d))
3401                                  *sqrt(-(2*log(a)*d*sqrt(z)+c*log(h))^2
3402                                         /(log(a)*d)))
3403                     /(-(2*log(a)*d*sqrt(z)+c*log(h))^2/(log(a)*d))
3404                      ^((j+i+1)/2),i,0,j),j,0,n))
3405  /(log(a)^(2*(n+1))*d^(2*(n+1)))));
3406 0;
3407
3408 /* ----- Involving z^(v-1)*a^(b*z^r)*h^(c*z^r) ------------------------------ */
3409
3410 /* Problem 599: NEW 7 */
3411 expand(integrate(z^(v-1)*a^(b*z^r)*h^(c*z^r),z)-
3412 -gamma_incomplete(v/r,-(c*log(h)+log(a)*b)*z^r)*z^v
3413  /(r*(-(c*log(h)+log(a)*b)*z^r)^(v/r)));
3414 0;
3415
3416 /* Problem 600: NEW 7 */
3417 expand(integrate(z^n*a^(b*z^2)*h^(c*z^2),z)-
3418 (-gamma_incomplete((n+1)/2,-(c*log(h)+log(a)*b)*z^2)
3419  *z^(n+1)*(-(c*log(h)+log(a)*b)*z^2)^((-n-1)/2)
3420  /2));
3421 0;
3422
3423 /* Problem 601: NEW 7 */
3424 expand(integrate(z^(2*n)*a^(b*z^2)*h^(c*z^2),z)-
3425 (-gamma_incomplete((2*n+1)/2,-(c*log(h)+log(a)*b)*z^2)
3426  *z^(2*n+1)*(-(c*log(h)+log(a)*b)*z^2)^((-2*n-1)/2)
3427  /2));
3428 0;
3429
3430 /* Problem 602: NEW 7 */
3431 expand(integrate(z^(1+2*n)*a^(b*z^2)*h^(c*z^2),z)-
3432 -(c*log(h)+log(a)*b)^((-2*n-2)/2)*(-1)^((-2*n-2)/2)
3433                                  *gamma_incomplete((2*n+2)/2,
3434                                                    -(c*log(h)+log(a)*b)*z^2)
3435  /2);
3436 0;
3437
3438 /* Problem 603: NEW 7 */
3439 expand(integrate(z^n*a^(b*sqrt(z))*h^(c*sqrt(z)),z)-
3440 (-2*(c*log(h)+log(a)*b)^(2*(-n-1))
3441   *gamma_incomplete(2*(n+1),-(c*log(h)+log(a)*b)*sqrt(z))));
3442 0;
3443
3444 /* ----- Involving z^n*a^(d*z)*h^(c*z^r+g) ---------------------------------- */
3445
3446 /* Problem 604: NEW 9 */
3447 expand(niceindices(integrate(z^n*a^(d*z)*h^(g+c*z^2),z))-
3448 (-c^(-n-1)*h^g*%e^-(log(a)^2*d^2/(4*c*log(h)))*log(h)^(-n-1)
3449          *('sum(log(a)^(n-i)*d^(n-i)
3450                             *gamma_incomplete((i+1)/2,
3451                                               -(2*c*log(h)*z+log(a)*d)^2
3452                                                /(4*c*log(h)))*(-1)^(i-n)
3453                             *2^(i-n)*binomial(n,i)
3454                             *(2*c*log(h)*z+log(a)*d)^(i+1)
3455                  /(-(2*c*log(h)*z+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3456  /2));
3457 0;
3458
3459 /* Problem 605: NEW 10 */
3460 expand(niceindices(integrate(z^n*a^(d*z)*h^(g+c*sqrt(z)),z))-
3461 (h^g*%e^-(c^2*log(h)^2/(4*log(a)*d))*2^(-2*n-1)
3462    *('sum(4^j*binomial(n,j)
3463              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3464                               *(2*log(a)*d*sqrt(z)+c*log(h))^(j+i)
3465                               *(c*log(h)
3466                                  *gamma_incomplete((j+i+1)/2,
3467                                                    -(2*log(a)*d*sqrt(z)
3468                                                     +c*log(h))
3469                                                     ^2
3470                                                     /(4*log(a)*d))
3471                                  *(2*log(a)*d*sqrt(z)+c*log(h))
3472                                +2*log(a)*d
3473                                  *gamma_incomplete((j+i+2)/2,
3474                                                    -(2*log(a)*d*sqrt(z)
3475                                                     +c*log(h))
3476                                                     ^2
3477                                                     /(4*log(a)*d))
3478                                  *sqrt(-(2*log(a)*d*sqrt(z)+c*log(h))^2
3479                                         /(log(a)*d)))
3480                     /(-(2*log(a)*d*sqrt(z)+c*log(h))^2/(log(a)*d))
3481                      ^((j+i+1)/2),i,0,j),j,0,n))
3482  /(log(a)^(2*(n+1))*d^(2*(n+1)))));
3483 0;
3484
3485 /* ----- Involving z^n*a^(d*z+e)*h^(c*z^r+g) -------------------------------- */
3486
3487 /* Problem 606: NEW 9 */
3488 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(g+c*z^2),z))-
3489 (-a^e*c^(-n-1)*h^g*%e^-(log(a)^2*d^2/(4*c*log(h)))*log(h)^(-n-1)
3490     *('sum(log(a)^(n-i)*d^(n-i)
3491                        *gamma_incomplete((i+1)/2,
3492                                          -(2*c*log(h)*z+log(a)*d)^2
3493                                           /(4*c*log(h)))*(-1)^(i-n)*2^(i-n)
3494                        *binomial(n,i)*(2*c*log(h)*z+log(a)*d)^(i+1)
3495             /(-(2*c*log(h)*z+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3496  /2));
3497 0;
3498
3499 /* Problem 607: NEW 10 */
3500 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(g+c*sqrt(z)),z))-
3501 (a^e*h^g*%e^-(c^2*log(h)^2/(4*log(a)*d))*2^(-2*n-1)
3502    *('sum(4^j*binomial(n,j)
3503              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3504                               *(2*log(a)*d*sqrt(z)+c*log(h))^(j+i)
3505                               *(c*log(h)
3506                                  *gamma_incomplete((j+i+1)/2,
3507                                                    -(2*log(a)*d*sqrt(z)
3508                                                     +c*log(h))
3509                                                     ^2
3510                                                     /(4*log(a)*d))
3511                                  *(2*log(a)*d*sqrt(z)+c*log(h))
3512                                +2*log(a)*d
3513                                  *gamma_incomplete((j+i+2)/2,
3514                                                    -(2*log(a)*d*sqrt(z)
3515                                                     +c*log(h))
3516                                                     ^2
3517                                                     /(4*log(a)*d))
3518                                  *sqrt(-(2*log(a)*d*sqrt(z)+c*log(h))^2
3519                                         /(log(a)*d)))
3520                     /(-(2*log(a)*d*sqrt(z)+c*log(h))^2/(log(a)*d))
3521                      ^((j+i+1)/2),i,0,j),j,0,n))
3522  /(log(a)^(2*(n+1))*d^(2*(n+1)))));
3523 0;
3524
3525 /* ----- Involving z^(v-1)*a^(b*z^r)*h^(c*z^r+g) ---------------------------- */
3526
3527 /* Problem 608: NEW 7 */
3528 expand(integrate(z^(v-1)*a^(b*z^r)*h^(g+c*z^r),z)-
3529 -h^g*gamma_incomplete(v/r,-(c*log(h)+log(a)*b)*z^r)*z^v
3530  /(r*(-(c*log(h)+log(a)*b)*z^r)^(v/r)));
3531 0;
3532
3533 /* Problem 609: NEW 7 */
3534 expand(integrate(z^n*a^(b*z^2)*h^(g+c*z^2),z)-
3535 (-h^g*gamma_incomplete((n+1)/2,-(c*log(h)+log(a)*b)*z^2)*z^(n+1)
3536     *(-(c*log(h)+log(a)*b)*z^2)^((-n-1)/2)
3537  /2));
3538 0;
3539
3540 /* Problem 610: NEW 7 */
3541 expand(integrate(z^(2*n)*a^(b*z^2)*h^(g+c*z^2),z)-
3542 (-h^g*gamma_incomplete((2*n+1)/2,-(c*log(h)+log(a)*b)*z^2)*z^(2*n+1)
3543     *(-(c*log(h)+log(a)*b)*z^2)^((-2*n-1)/2)
3544  /2));
3545 0;
3546
3547 /* Problem 611: NEW 7 */
3548 expand(integrate(z^(1+2*n)*a^(b*z^2)*h^(g+c*z^2),z)-
3549 -h^g*(c*log(h)+log(a)*b)^((-2*n-2)/2)*(-1)^((-2*n-2)/2)
3550     *gamma_incomplete((2*n+2)/2,-(c*log(h)+log(a)*b)*z^2)
3551  /2);
3552 0;
3553
3554 /* Problem 612: NEW 7 */
3555 expand(integrate(z^(1+2*n)*a^(b*sqrt(z))*h^(g+c*sqrt(z)),z)-
3556 -2*h^g*(c*log(h)+log(a)*b)^(2*(-2*n-2))
3557   *gamma_incomplete(2*(2*n+2),-(c*log(h)+log(a)*b)*sqrt(z)));
3558 0;
3559
3560 /* ----- Involving z^(v-1)*a^(b*z^r+e)*h^(c*z^r+g) -------------------------- */
3561
3562 /* Problem 613: NEW 7 */
3563 expand(integrate(z^(v-1)*a^(e+b*z^r)*h^(g+c*z^r),z)-
3564 -a^e*h^g*gamma_incomplete(v/r,-(c*log(h)+log(a)*b)*z^r)*z^v
3565  /(r*(-(c*log(h)+log(a)*b)*z^r)^(v/r)));
3566 0;
3567
3568 /* Problem 614: NEW 7 */
3569 expand(integrate(z^n*a^(e+b*z^2)*h^(g+c*z^2),z)-
3570 (-a^e*h^g*gamma_incomplete((n+1)/2,-(c*log(h)+log(a)*b)*z^2)*z^(n+1)
3571     *(-(c*log(h)+log(a)*b)*z^2)^((-n-1)/2)
3572  /2));
3573 0;
3574
3575 /* Problem 615: NEW 7 */
3576 expand(integrate(z^(2*n)*a^(e+b*z^2)*h^(g+c*z^2),z)-
3577 (-a^e*h^g*gamma_incomplete((2*n+1)/2,-(c*log(h)+log(a)*b)*z^2)*z^(2*n+1)
3578     *(-(c*log(h)+log(a)*b)*z^2)^((-2*n-1)/2)
3579  /2));
3580 0;
3581
3582 /* Problem 616: NEW 7 */
3583 expand(integrate(z^(1+2*n)*a^(e+b*z^2)*h^(g+c*z^2),z)-
3584 -a^e*h^g*(c*log(h)+log(a)*b)^((-2*n-2)/2)*(-1)^((-2*n-2)/2)
3585     *gamma_incomplete((2*n+2)/2,-(c*log(h)+log(a)*b)*z^2)
3586  /2);
3587 0;
3588
3589 /* Problem 617: NEW 7 */
3590 expand(integrate(z^(1+2*n)*a^(e+b*sqrt(z))*h^(g+c*sqrt(z)),z)-
3591 -2*a^e*h^g*(c*log(h)+log(a)*b)^(2*(-2*n-2))
3592   *gamma_incomplete(2*(2*n+2),-(c*log(h)+log(a)*b)*sqrt(z)));
3593 0;
3594
3595 /* ----- Involving z^n*a^(d*z)*h^(c*z^r+f*z) -------------------------------- */
3596
3597 /* Problem 618: NEW 9 */
3598 expand(niceindices(integrate(z^n*a^(d*z)*h^(f*z+c*z^2),z))-
3599 (-c^(-n-1)*%e^-((f*log(h)+log(a)*d)^2/(4*c*log(h)))*log(h)^(-n-1)
3600          *('sum((-f*log(h)-log(a)*d)^(n-i)
3601                  *gamma_incomplete((i+1)/2,
3602                                    -(log(h)*(2*c*z+f)+log(a)*d)^2
3603                                     /(4*c*log(h)))*2^(i-n)*binomial(n,i)
3604                  *(log(h)*(2*c*z+f)+log(a)*d)^(i+1)
3605                  /(-(log(h)*(2*c*z+f)+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,
3606                 n))
3607  /2));
3608 0;
3609
3610 /* Problem 619: NEW 10 */
3611 expand(niceindices(integrate(z^n*a^(d*z)*h^(f*z+c*sqrt(z)),z)) -
3612 (%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))
3613  *2^(-2*n-1)
3614  *('sum(4^j*binomial(n,j)
3615            *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3616                             *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^(j+i)
3617                             *(c*log(h)
3618                                *gamma_incomplete((j+i+1)/2,
3619                                                  -(2*(f*log(h)+log(a)*d)
3620                                                     *sqrt(z)
3621                                                   +c*log(h))
3622                                                   ^2
3623                                                   /(4*(f*log(h)+log(a)*d)))
3624                                *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3625                              +2*(f*log(h)+log(a)*d)
3626                                *gamma_incomplete((j+i+2)/2,
3627                                                  -(2*(f*log(h)+log(a)*d)
3628                                                     *sqrt(z)
3629                                                   +c*log(h))
3630                                                   ^2
3631                                                   /(4*(f*log(h)+log(a)*d)))
3632                                *sqrt(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3633                                       ^2
3634                                       /(f*log(h)+log(a)*d)))
3635                   /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^2
3636                    /(f*log(h)+log(a)*d))
3637                    ^((j+i+1)/2),i,0,j),j,0,n))
3638  /(f*log(h)+log(a)*d)^(2*(n+1))));
3639 0;
3640
3641 /* ----- Involving z^n*a^(d*z+e)*h^(c*z^r+f*z) ------------------------------ */
3642
3643 /* Problem 620: NEW 9 */
3644 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(f*z+c*z^2),z))-
3645 (-a^e*c^(-n-1)*%e^-((f*log(h)+log(a)*d)^2/(4*c*log(h)))*log(h)^(-n-1)
3646     *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
3647                                                        -(log(h)*(2*c*z+f)
3648                                                         +log(a)*d)
3649                                                         ^2
3650                                                         /(4*c*log(h)))*2^(i-n)
3651                                      *binomial(n,i)
3652                                      *(log(h)*(2*c*z+f)+log(a)*d)^(i+1)
3653             /(-(log(h)*(2*c*z+f)+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3654  /2));
3655 0;
3656
3657 /* Problem 621: NEW 10 */
3658 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(f*z+c*sqrt(z)),z))-
3659 (a^e*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
3660    *('sum(4^j*binomial(n,j)
3661              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3662                               *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^(j+i)
3663                               *(c*log(h)
3664                                  *gamma_incomplete((j+i+1)/2,
3665                                                    -(2*(f*log(h)+log(a)*d)
3666                                                       *sqrt(z)
3667                                                     +c*log(h))
3668                                                     ^2
3669                                                     /(4*(f*log(h)+log(a)*d)))
3670                                  *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3671                                +2*(f*log(h)+log(a)*d)
3672                                  *gamma_incomplete((j+i+2)/2,
3673                                                    -(2*(f*log(h)+log(a)*d)
3674                                                       *sqrt(z)
3675                                                     +c*log(h))
3676                                                     ^2
3677                                                     /(4*(f*log(h)+log(a)*d)))
3678                                  *sqrt(-(2*(f*log(h)+log(a)*d)*sqrt(z)
3679                                         +c*log(h))
3680                                         ^2
3681                                         /(f*log(h)+log(a)*d)))
3682                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^2
3683                      /(f*log(h)+log(a)*d))
3684                      ^((j+i+1)/2),i,0,j),j,0,n))
3685  /(f*log(h)+log(a)*d)^(2*(n+1))));
3686 0;
3687
3688 /* ----- Involving z^n*a^(b*z^r)*h^(c*z^r+f*z) ------------------------------ */
3689
3690 /* Problem 622: NEW 9 */
3691 expand(niceindices(integrate(z^n*a^(b*z^2)*h^(f*z+c*z^2),z))-
3692 (-%e^-(f^2*log(h)^2/(4*(c*log(h)+log(a)*b)))
3693  *(c*log(h)+log(a)*b)^(-n-1)
3694  *('sum(f^(n-i)*log(h)^(n-i)
3695                *gamma_incomplete((i+1)/2,
3696                                  -(log(h)*(2*c*z+f)+2*log(a)*b*z)^2
3697                                   /(4*(c*log(h)+log(a)*b)))*(-1)^(i-n)*2^(i-n)
3698                *binomial(n,i)*(log(h)*(2*c*z+f)+2*log(a)*b*z)^(i+1)
3699          /(-(log(h)*(2*c*z+f)+2*log(a)*b*z)^2/(c*log(h)+log(a)*b))^((i+1)/2),
3700         i,0,n))
3701  /2));
3702 0;
3703
3704 /* Problem 623: NEW 10 */
3705 expand(niceindices(integrate(z^n*a^(b*sqrt(z))*h^(f*z+c*sqrt(z)),z))-
3706 (%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))
3707  *2^(-2*n-1)
3708  *('sum(4^j*binomial(n,j)
3709            *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3710                                               *(2*f*log(h)*sqrt(z)
3711                                                +c*log(h)+log(a)*b)
3712                                                ^(j+i)
3713                                               *((c*log(h)+log(a)*b)
3714                                                *gamma_incomplete(
3715                                                 (j+i+1)/2,
3716                                                 -(2*f*log(h)*sqrt(z)
3717                                                  +c*log(h)+log(a)*b)
3718                                                  ^2
3719                                                  /(4*f*log(h)))
3720                                                *(2*f*log(h)*sqrt(z)
3721                                                 +c*log(h)+log(a)*b)
3722                                                +2*f*log(h)
3723                                                  *gamma_incomplete(
3724                                                   (j+i+2)/2,
3725                                                   -(2*f*log(h)*sqrt(z)
3726                                                    +c*log(h)+log(a)*b)
3727                                                    ^2
3728                                                    /(4*f*log(h)))
3729                                                  *sqrt(
3730                                                   -(2*f*log(h)*sqrt(z)
3731                                                    +c*log(h)+log(a)*b)
3732                                                    ^2
3733                                                    /(f*log(h))))
3734                   /(-(2*f*log(h)*sqrt(z)+c*log(h)+log(a)*b)^2/(f*log(h)))
3735                    ^((j+i+1)/2),i,0,j),j,0,n))
3736  /(f^(2*(n+1))*log(h)^(2*(n+1)))));
3737 0;
3738
3739 /* ----- Involving z^n*a^(b*z^r+e)*h^(c*z^r+f*z) ---------------------------- */
3740
3741 /* Problem 624: NEW 9 */
3742 expand(niceindices(integrate(z^n*a^(e+b*z^2)*h^(f*z+c*z^2),z))-
3743 (-a^e*%e^-(f^2*log(h)^2/(4*(c*log(h)+log(a)*b)))*(c*log(h)+log(a)*b)^(-n-1)
3744     *('sum(f^(n-i)*log(h)^(n-i)
3745                   *gamma_incomplete((i+1)/2,
3746                                     -(log(h)*(2*c*z+f)+2*log(a)*b*z)^2
3747                                      /(4*(c*log(h)+log(a)*b)))*(-1)^(i-n)
3748                   *2^(i-n)*binomial(n,i)*(log(h)*(2*c*z+f)+2*log(a)*b*z)^(i+1)
3749             /(-(log(h)*(2*c*z+f)+2*log(a)*b*z)^2/(c*log(h)+log(a)*b))
3750              ^((i+1)/2),i,0,n))
3751  /2));
3752 0;
3753
3754 /* Problem 625: NEW 10 */
3755 expand(niceindices(integrate(z^n*a^(e+b*sqrt(z))*h^(f*z+c*sqrt(z)),z))-
3756 (a^e*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*2^(-2*n-1)
3757    *('sum(4^j*binomial(n,j)
3758              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3759                                                 *(2*f*log(h)*sqrt(z)
3760                                                  +c*log(h)+log(a)*b)
3761                                                  ^(j+i)
3762                                                 *((c*log(h)+log(a)*b)
3763                                                  *gamma_incomplete(
3764                                                   (j+i+1)/2,
3765                                                   -(2*f*log(h)*sqrt(z)
3766                                                    +c*log(h)+log(a)*b)
3767                                                    ^2
3768                                                    /(4*f*log(h)))
3769                                                  *(2*f*log(h)*sqrt(z)
3770                                                   +c*log(h)+log(a)*b)
3771                                                  +2*f*log(h)
3772                                                    *gamma_incomplete(
3773                                                     (j+i+2)/2,
3774                                                     -(2*f*log(h)*sqrt(z)
3775                                                      +c*log(h)+log(a)*b)
3776                                                      ^2
3777                                                      /(4*f*log(h)))
3778                                                    *sqrt(
3779                                                     -(2*f*log(h)*sqrt(z)
3780                                                      +c*log(h)+log(a)*b)
3781                                                      ^2
3782                                                      /(f*log(h))))
3783                     /(-(2*f*log(h)*sqrt(z)+c*log(h)+log(a)*b)^2/(f*log(h)))
3784                      ^((j+i+1)/2),i,0,j),j,0,n))
3785  /(f^(2*(n+1))*log(h)^(2*(n+1)))));
3786 0;
3787
3788 /* ----- Involving z^n*a^(b*z^r+d*z)*h^(c*z^r+f*z) -------------------------- */
3789
3790 /* Problem 626: NEW 9 */
3791 expand(niceindices(integrate(z^n*a^(d*z+b*z^2)*h^(f*z+c*z^2),z))-
3792 (-%e^-((f*log(h)+log(a)*d)^2/(4*(c*log(h)+log(a)*b)))
3793  *(c*log(h)+log(a)*b)^(-n-1)
3794  *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
3795                                                     -(log(h)*(2*c*z+f)
3796                                                      +log(a)*(2*b*z+d))
3797                                                      ^2
3798                                                      /(4*(c*log(h)+log(a)*b)))
3799                                   *2^(i-n)*binomial(n,i)
3800                                   *(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))^(i+1)
3801          /(-(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))^2/(c*log(h)+log(a)*b))
3802           ^((i+1)/2),i,0,n))
3803  /2));
3804 0;
3805
3806 /* Problem 627: NEW 10 */
3807 expand(niceindices(integrate(z^n*a^(d*z+b*sqrt(z))*h^(f*z+c*sqrt(z)),z))-
3808 (%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))
3809  *2^(-2*n-1)
3810  *('sum(4^j*binomial(n,j)
3811            *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3812                                               *(2*(f*log(h)+log(a)*d)*sqrt(z)
3813                                                +c*log(h)+log(a)*b)
3814                                                ^(j+i)
3815                                               *((c*log(h)+log(a)*b)
3816                                                *gamma_incomplete(
3817                                                 (j+i+1)/2,
3818                                                 -(2*(f*log(h)+log(a)*d)
3819                                                    *sqrt(z)
3820                                                  +c*log(h)+log(a)*b)
3821                                                  ^2
3822                                                  /(4*(f*log(h)+log(a)*d)))
3823                                                *(2*(f*log(h)+log(a)*d)*sqrt(z)
3824                                                 +c*log(h)+log(a)*b)
3825                                                +2*(f*log(h)+log(a)*d)
3826                                                  *gamma_incomplete(
3827                                                   (j+i+2)/2,
3828                                                   -(2*(f*log(h)+log(a)*d)
3829                                                      *sqrt(z)
3830                                                    +c*log(h)+log(a)*b)
3831                                                    ^2
3832                                                    /(4*(f*log(h)+log(a)*d)))
3833                                                  *sqrt(
3834                                                   -(2*(f*log(h)+log(a)*d)
3835                                                      *sqrt(z)
3836                                                    +c*log(h)+log(a)*b)
3837                                                    ^2
3838                                                    /(f*log(h)+log(a)*d)))
3839                   /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h)+log(a)*b)^2
3840                    /(f*log(h)+log(a)*d))
3841                    ^((j+i+1)/2),i,0,j),j,0,n))
3842  /(f*log(h)+log(a)*d)^(2*(n+1))));
3843 0;
3844
3845 /* ----- Involving z^n*a^(d*z)*h^(c*z^r+f*z+g) ------------------------------ */
3846
3847 /* Problem 628: NEW 9 */
3848 expand(niceindices(integrate(z^n*a^(d*z)*h^(g+f*z+c*z^2),z))-
3849 (-c^(-n-1)*h^g*%e^-((f*log(h)+log(a)*d)^2/(4*c*log(h)))*log(h)^(-n-1)
3850          *('sum((-f*log(h)-log(a)*d)^(n-i)
3851                  *gamma_incomplete((i+1)/2,
3852                                    -(log(h)*(2*c*z+f)+log(a)*d)^2
3853                                     /(4*c*log(h)))*2^(i-n)*binomial(n,i)
3854                  *(log(h)*(2*c*z+f)+log(a)*d)^(i+1)
3855                  /(-(log(h)*(2*c*z+f)+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,
3856                 n))
3857  /2));
3858 0;
3859
3860 /* Problem 629: NEW 10 */
3861 expand(niceindices(integrate(z^n*a^(d*z)*h^(g+f*z+c*sqrt(z)),z))-
3862 (h^g*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
3863    *('sum(4^j*binomial(n,j)
3864              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3865                               *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^(j+i)
3866                               *(c*log(h)
3867                                  *gamma_incomplete((j+i+1)/2,
3868                                                    -(2*(f*log(h)+log(a)*d)
3869                                                       *sqrt(z)
3870                                                     +c*log(h))
3871                                                     ^2
3872                                                     /(4*(f*log(h)+log(a)*d)))
3873                                  *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3874                                +2*(f*log(h)+log(a)*d)
3875                                  *gamma_incomplete((j+i+2)/2,
3876                                                    -(2*(f*log(h)+log(a)*d)
3877                                                       *sqrt(z)
3878                                                     +c*log(h))
3879                                                     ^2
3880                                                     /(4*(f*log(h)+log(a)*d)))
3881                                  *sqrt(-(2*(f*log(h)+log(a)*d)*sqrt(z)
3882                                         +c*log(h))
3883                                         ^2
3884                                         /(f*log(h)+log(a)*d)))
3885                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^2
3886                      /(f*log(h)+log(a)*d))
3887                      ^((j+i+1)/2),i,0,j),j,0,n))
3888  /(f*log(h)+log(a)*d)^(2*(n+1))));
3889 0;
3890 /* ----- Involving z^n*a^(d*z+e)*h^(c*z^r+f*z+g) ---------------------------- */
3891
3892 /* Problem 630: NEW 9 */
3893 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(g+f*z+c*z^2),z))-
3894 (-a^e*c^(-n-1)*h^g*%e^-((f*log(h)+log(a)*d)^2/(4*c*log(h)))*log(h)^(-n-1)
3895     *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
3896                                                        -(log(h)*(2*c*z+f)
3897                                                         +log(a)*d)
3898                                                         ^2
3899                                                         /(4*c*log(h)))*2^(i-n)
3900                                      *binomial(n,i)
3901                                      *(log(h)*(2*c*z+f)+log(a)*d)^(i+1)
3902             /(-(log(h)*(2*c*z+f)+log(a)*d)^2/(c*log(h)))^((i+1)/2),i,0,n))
3903  /2));
3904 0;
3905
3906 /* Problem 631: NEW 10 */
3907 expand(niceindices(integrate(z^n*a^(e+d*z)*h^(g+f*z+c*sqrt(z)),z))-
3908 (a^e*h^g*%e^-(c^2*log(h)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
3909    *('sum(4^j*binomial(n,j)
3910              *'sum(c^(2*n-j-i)*log(h)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3911                               *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^(j+i)
3912                               *(c*log(h)
3913                                  *gamma_incomplete((j+i+1)/2,
3914                                                    -(2*(f*log(h)+log(a)*d)
3915                                                       *sqrt(z)
3916                                                     +c*log(h))
3917                                                     ^2
3918                                                     /(4*(f*log(h)+log(a)*d)))
3919                                  *(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))
3920                                +2*(f*log(h)+log(a)*d)
3921                                  *gamma_incomplete((j+i+2)/2,
3922                                                    -(2*(f*log(h)+log(a)*d)
3923                                                       *sqrt(z)
3924                                                     +c*log(h))
3925                                                     ^2
3926                                                     /(4*(f*log(h)+log(a)*d)))
3927                                  *sqrt(-(2*(f*log(h)+log(a)*d)*sqrt(z)
3928                                         +c*log(h))
3929                                         ^2
3930                                         /(f*log(h)+log(a)*d)))
3931                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h))^2
3932                      /(f*log(h)+log(a)*d))
3933                      ^((j+i+1)/2),i,0,j),j,0,n))
3934  /(f*log(h)+log(a)*d)^(2*(n+1))));
3935 0;
3936
3937 /* ----- Involving z^n*a^(b*z^r)*h^(c*z^r+f*z+g) ---------------------------- */
3938
3939 /* Problem 632: NEW 9 */
3940 expand(niceindices(integrate(z^n*a^(b*z^2)*h^(g+f*z+c*z^2),z))-
3941 (-h^g*%e^-(f^2*log(h)^2/(4*(c*log(h)+log(a)*b)))*(c*log(h)+log(a)*b)^(-n-1)
3942     *('sum(f^(n-i)*log(h)^(n-i)
3943                   *gamma_incomplete((i+1)/2,
3944                                     -(log(h)*(2*c*z+f)+2*log(a)*b*z)^2
3945                                      /(4*(c*log(h)+log(a)*b)))*(-1)^(i-n)
3946                   *2^(i-n)*binomial(n,i)*(log(h)*(2*c*z+f)+2*log(a)*b*z)^(i+1)
3947             /(-(log(h)*(2*c*z+f)+2*log(a)*b*z)^2/(c*log(h)+log(a)*b))
3948              ^((i+1)/2),i,0,n))
3949  /2));
3950 0;
3951
3952 /* Problem 633: NEW 10 */
3953 expand(niceindices(integrate(z^n*a^(b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z))-
3954 (h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*2^(-2*n-1)
3955    *('sum(4^j*binomial(n,j)
3956              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
3957                                                 *(2*f*log(h)*sqrt(z)
3958                                                  +c*log(h)+log(a)*b)
3959                                                  ^(j+i)
3960                                                 *((c*log(h)+log(a)*b)
3961                                                  *gamma_incomplete(
3962                                                   (j+i+1)/2,
3963                                                   -(2*f*log(h)*sqrt(z)
3964                                                    +c*log(h)+log(a)*b)
3965                                                    ^2
3966                                                    /(4*f*log(h)))
3967                                                  *(2*f*log(h)*sqrt(z)
3968                                                   +c*log(h)+log(a)*b)
3969                                                  +2*f*log(h)
3970                                                    *gamma_incomplete(
3971                                                     (j+i+2)/2,
3972                                                     -(2*f*log(h)*sqrt(z)
3973                                                      +c*log(h)+log(a)*b)
3974                                                      ^2
3975                                                      /(4*f*log(h)))
3976                                                    *sqrt(
3977                                                     -(2*f*log(h)*sqrt(z)
3978                                                      +c*log(h)+log(a)*b)
3979                                                      ^2
3980                                                      /(f*log(h))))
3981                     /(-(2*f*log(h)*sqrt(z)+c*log(h)+log(a)*b)^2/(f*log(h)))
3982                      ^((j+i+1)/2),i,0,j),j,0,n))
3983  /(f^(2*(n+1))*log(h)^(2*(n+1)))));
3984 0;
3985
3986 /* ----- Involving z^n*a^(b*z^r+e)*h^(c*z^r+f*z+g) -------------------------- */
3987
3988 /* Problem 634: NEW 9 */
3989 expand(niceindices(integrate(z^n*a^(e+b*z^2)*h^(g+f*z+c*z^2),z))-
3990 (-a^e*h^g*%e^-(f^2*log(h)^2/(4*(c*log(h)+log(a)*b)))*(c*log(h)+log(a)*b)^(-n-1)
3991     *('sum(f^(n-i)*log(h)^(n-i)
3992                   *gamma_incomplete((i+1)/2,
3993                                     -(log(h)*(2*c*z+f)+2*log(a)*b*z)^2
3994                                      /(4*(c*log(h)+log(a)*b)))*(-1)^(i-n)
3995                   *2^(i-n)*binomial(n,i)*(log(h)*(2*c*z+f)+2*log(a)*b*z)^(i+1)
3996             /(-(log(h)*(2*c*z+f)+2*log(a)*b*z)^2/(c*log(h)+log(a)*b))
3997              ^((i+1)/2),i,0,n))
3998  /2));
3999 0;
4000
4001 /* Problem 635: NEW 10 */
4002 expand(niceindices(integrate(z^n*a^(e+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z))-
4003 (a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*f*log(h)))*2^(-2*n-1)
4004    *('sum(4^j*binomial(n,j)
4005              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4006                                                 *(2*f*log(h)*sqrt(z)
4007                                                  +c*log(h)+log(a)*b)
4008                                                  ^(j+i)
4009                                                 *((c*log(h)+log(a)*b)
4010                                                  *gamma_incomplete(
4011                                                   (j+i+1)/2,
4012                                                   -(2*f*log(h)*sqrt(z)
4013                                                    +c*log(h)+log(a)*b)
4014                                                    ^2
4015                                                    /(4*f*log(h)))
4016                                                  *(2*f*log(h)*sqrt(z)
4017                                                   +c*log(h)+log(a)*b)
4018                                                  +2*f*log(h)
4019                                                    *gamma_incomplete(
4020                                                     (j+i+2)/2,
4021                                                     -(2*f*log(h)*sqrt(z)
4022                                                      +c*log(h)+log(a)*b)
4023                                                      ^2
4024                                                      /(4*f*log(h)))
4025                                                    *sqrt(
4026                                                     -(2*f*log(h)*sqrt(z)
4027                                                      +c*log(h)+log(a)*b)
4028                                                      ^2
4029                                                      /(f*log(h))))
4030                     /(-(2*f*log(h)*sqrt(z)+c*log(h)+log(a)*b)^2/(f*log(h)))
4031                      ^((j+i+1)/2),i,0,j),j,0,n))
4032  /(f^(2*(n+1))*log(h)^(2*(n+1)))));
4033 0;
4034
4035 /* ----- Involving z^n*a^(b*z^r+d*z)*h^(c*z^r+f*z+g) ------------------------ */
4036
4037 /* Problem 636: NEW 9 */
4038 expand(niceindices(integrate(z^n*a^(d*z+b*z^2)*h^(g+f*z+c*z^2),z))-
4039 (-h^g*%e^-((f*log(h)+log(a)*d)^2/(4*(c*log(h)+log(a)*b)))
4040     *(c*log(h)+log(a)*b)^(-n-1)
4041     *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
4042                                                        -(log(h)*(2*c*z+f)
4043                                                         +log(a)*(2*b*z+d))
4044                                                         ^2
4045                                                         /(4
4046                                                          *(c*log(h)
4047                                                           +log(a)*b)))*2^(i-n)
4048                                      *binomial(n,i)
4049                                      *(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))
4050                                       ^(i+1)
4051             /(-(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))^2/(c*log(h)+log(a)*b))
4052              ^((i+1)/2),i,0,n))/2));
4053 0;
4054
4055 /* Problem 637: NEW 10 */
4056 expand(niceindices(integrate(z^n*a^(d*z+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z))-
4057 (h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
4058    *('sum(4^j*binomial(n,j)
4059              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4060                                                 *(2*(f*log(h)+log(a)*d)
4061                                                    *sqrt(z)
4062                                                  +c*log(h)+log(a)*b)
4063                                                  ^(j+i)
4064                                                 *((c*log(h)+log(a)*b)
4065                                                  *gamma_incomplete(
4066                                                   (j+i+1)/2,
4067                                                   -(2*(f*log(h)+log(a)*d)
4068                                                      *sqrt(z)
4069                                                    +c*log(h)+log(a)*b)
4070                                                    ^2
4071                                                    /(4*(f*log(h)+log(a)*d)))
4072                                                  *(2*(f*log(h)+log(a)*d)
4073                                                     *sqrt(z)
4074                                                   +c*log(h)+log(a)*b)
4075                                                  +2*(f*log(h)+log(a)*d)
4076                                                    *gamma_incomplete(
4077                                                     (j+i+2)/2,
4078                                                     -(2*(f*log(h)+log(a)*d)
4079                                                        *sqrt(z)
4080                                                      +c*log(h)+log(a)*b)
4081                                                      ^2
4082                                                      /(4*(f*log(h)+log(a)*d)))
4083                                                    *sqrt(
4084                                                     -(2*(f*log(h)+log(a)*d)
4085                                                        *sqrt(z)
4086                                                      +c*log(h)+log(a)*b)
4087                                                      ^2
4088                                                      /(f*log(h)+log(a)*d)))
4089                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h)+log(a)*b)^2
4090                      /(f*log(h)+log(a)*d))
4091                      ^((j+i+1)/2),i,0,j),j,0,n))
4092  /(f*log(h)+log(a)*d)^(2*(n+1))));
4093 0;
4094
4095 /* ----- Involving z^n*a^(b*z^r+d*z+e)*h^(c*z^r+f*z+g) ---------------------- */
4096
4097 /* Problem 638: NEW 9 */
4098 expand(niceindices(integrate(z^n*a^(e+d*z+b*z^2)*h^(g+f*z+c*z^2),z))-
4099 (-a^e*h^g*%e^-((f*log(h)+log(a)*d)^2/(4*(c*log(h)+log(a)*b)))
4100     *(c*log(h)+log(a)*b)^(-n-1)
4101     *('sum((-f*log(h)-log(a)*d)^(n-i)*gamma_incomplete((i+1)/2,
4102                                                        -(log(h)*(2*c*z+f)
4103                                                         +log(a)*(2*b*z+d))
4104                                                         ^2
4105                                                         /(4
4106                                                          *(c*log(h)
4107                                                           +log(a)*b)))*2^(i-n)
4108                                      *binomial(n,i)
4109                                      *(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))
4110                                       ^(i+1)
4111             /(-(log(h)*(2*c*z+f)+log(a)*(2*b*z+d))^2/(c*log(h)+log(a)*b))
4112              ^((i+1)/2),i,0,n))
4113  /2));
4114 0;
4115
4116 /* Problem 639: NEW 10 */
4117 expand(niceindices(integrate(z^n*a^(e+d*z+b*sqrt(z))*h^(g+f*z+c*sqrt(z)),z))-
4118 (a^e*h^g*%e^-((c*log(h)+log(a)*b)^2/(4*(f*log(h)+log(a)*d)))*2^(-2*n-1)
4119    *('sum(4^j*binomial(n,j)
4120              *'sum((c*log(h)+log(a)*b)^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4121                                                 *(2*(f*log(h)+log(a)*d)
4122                                                    *sqrt(z)
4123                                                  +c*log(h)+log(a)*b)
4124                                                  ^(j+i)
4125                                                 *((c*log(h)+log(a)*b)
4126                                                  *gamma_incomplete(
4127                                                   (j+i+1)/2,
4128                                                   -(2*(f*log(h)+log(a)*d)
4129                                                      *sqrt(z)
4130                                                    +c*log(h)+log(a)*b)
4131                                                    ^2
4132                                                    /(4*(f*log(h)+log(a)*d)))
4133                                                  *(2*(f*log(h)+log(a)*d)
4134                                                     *sqrt(z)
4135                                                   +c*log(h)+log(a)*b)
4136                                                  +2*(f*log(h)+log(a)*d)
4137                                                    *gamma_incomplete(
4138                                                     (j+i+2)/2,
4139                                                     -(2*(f*log(h)+log(a)*d)
4140                                                        *sqrt(z)
4141                                                      +c*log(h)+log(a)*b)
4142                                                      ^2
4143                                                      /(4*(f*log(h)+log(a)*d)))
4144                                                    *sqrt(
4145                                                     -(2*(f*log(h)+log(a)*d)
4146                                                        *sqrt(z)
4147                                                      +c*log(h)+log(a)*b)
4148                                                      ^2
4149                                                      /(f*log(h)+log(a)*d)))
4150                     /(-(2*(f*log(h)+log(a)*d)*sqrt(z)+c*log(h)+log(a)*b)^2
4151                      /(f*log(h)+log(a)*d))
4152                      ^((j+i+1)/2),i,0,j),j,0,n))
4153  /(f*log(h)+log(a)*d)^(2*(n+1))));
4154 0;
4155
4156 /* ----- Products of powers of the direct function and a power function ----- */
4157
4158 /* ----- Involving z^(v-1)*%e^(c*z)*(%e^(a*z))^u ---------------------------- */
4159
4160 /* Problem 640: NEW 7-1*/
4161 expand(integrate(z^(v-1)*%e^(c*z)*(%e^(a*z))^u,z)-
4162 -gamma_incomplete(v,-(a*u+c)*z)*z^v*(%e^(a*z))^u*%e^(c*z-(a*u+c)*z)
4163  /(-(a*u+c)*z)^v)$
4164 0;
4165
4166 /* Problem 641: NEW 7-1 */
4167 expand(integrate(z^n*%e^(c*z)*(%e^(a*z))^u,z)-
4168 -(-1)^(n+1)*gamma_incomplete(n+1,-(a*u+c)*z)*(a*u+c)^(-n-1)*(%e^(a*z))^u
4169            *%e^(c*z-(a*u+c)*z))$
4170 0;
4171
4172 /* Problem 642: NEW 7-1 */
4173 expand(integrate(z^(1/2+n)*%e^(c*z)*(%e^(a*z))^u,z)-
4174 -gamma_incomplete(n+3/2,-(a*u+c)*z)*z^(n+3/2)*(-(a*u+c)*z)^(-n-3/2)
4175                                    *(%e^(a*z))^u*%e^(c*z-(a*u+c)*z))$
4176 0;
4177
4178 /* ----- Involving z^(v-1)*%e^(c*z+d)*(%e^(a*z))^u -------------------------- */
4179
4180 /* Problem 643: NEW 7-1 */
4181 expand(integrate(z^(v-1)*%e^(c*z+d)*(%e^(a*z))^u,z)-
4182 -gamma_incomplete(v,-(a*u+c)*z)*z^v*(%e^(a*z))^u*%e^(-(a*u+c)*z+c*z+d)
4183  /(-(a*u+c)*z)^v)$
4184 0;
4185
4186 /* Problem 644: NEW 7-1 */
4187 expand(integrate(z^n*%e^(c*z+d)*(%e^(a*z))^u,z)-
4188 -(-1)^(n+1)*gamma_incomplete(n+1,-(a*u+c)*z)*(a*u+c)^(-n-1)*(%e^(a*z))^u
4189            *%e^(-(a*u+c)*z+c*z+d));
4190 0;
4191
4192 /* Problem 645: NEW 7-1 */
4193 expand(integrate(z^(1/2+n)*%e^(c*z+d)*(%e^(a*z))^u,z)-
4194 -gamma_incomplete(n+3/2,-(a*u+c)*z)*z^(n+3/2)*(-(a*u+c)*z)^(-n-3/2)
4195                                    *(%e^(a*z))^u*%e^(-(a*u+c)*z+c*z+d))$
4196 0;
4197
4198 /* ----- Involving z^(v-1)*%e^(c*z)*(%e^(a*z+b))^u -------------------------- */
4199
4200 /* Problem 646: NEW 7-1 */
4201 expand(integrate(z^(v-1)*%e^(c*z)*(%e^(a*z+b))^u,z)-
4202 -gamma_incomplete(v,-(a*u+c)*z)*z^v*(%e^(a*z+b))^u*%e^(c*z-(a*u+c)*z)
4203  /(-(a*u+c)*z)^v);
4204 0;
4205
4206 /* Problem 647: NEW 7-1 */
4207 expand(integrate(z^n*%e^(c*z)*(%e^(a*z+b))^u,z)-
4208 -(-1)^(n+1)*gamma_incomplete(n+1,-(a*u+c)*z)*(a*u+c)^(-n-1)*(%e^(a*z+b))^u
4209            *%e^(c*z-(a*u+c)*z))$
4210 0;
4211
4212 /* Problem 648: NEW 7-1 */
4213 expand(integrate(z^(1/2+n)*%e^(c*z)*(%e^(a*z+b))^u,z)-
4214 -gamma_incomplete(n+3/2,-(a*u+c)*z)*z^(n+3/2)*(-(a*u+c)*z)^(-n-3/2)
4215                                    *(%e^(a*z+b))^u*%e^(c*z-(a*u+c)*z))$
4216 0;
4217
4218 /* ----- Involving z^(v-1)*%e^(c*z+d)*(%e^(a*z+b))^u ------------------------ */
4219
4220 /* Problem 649: NEW 7-1 */
4221 expand(integrate(z^(v-1)*%e^(c*z+d)*(%e^(a*z+b))^u,z)-
4222 -gamma_incomplete(v,-(a*u+c)*z)*z^v*(%e^(a*z+b))^u*%e^(-(a*u+c)*z+c*z+d)
4223  /(-(a*u+c)*z)^v)$
4224 0;
4225
4226 /* Problem 650: NEW 7-1 */
4227 expand(integrate(z^n*%e^(c*z+d)*(%e^(a*z+b))^u,z)-
4228 -(-1)^(n+1)*gamma_incomplete(n+1,-(a*u+c)*z)*(a*u+c)^(-n-1)*(%e^(a*z+b))^u
4229            *%e^(-(a*u+c)*z+c*z+d))$
4230 0;
4231
4232 /* Problem 651: NEW 7-1 */
4233 expand(integrate(z^(1/2+n)*%e^(c*z+d)*(%e^(a*z+b))^u,z)-
4234 -gamma_incomplete(n+3/2,-(a*u+c)*z)*z^(n+3/2)*(-(a*u+c)*z)^(-n-3/2)
4235                                    *(%e^(a*z+b))^u*%e^(-(a*u+c)*z+c*z+d))$
4236 0;
4237
4238 /* ----- Involving z^n*%e^(b*z^r)*(%e^(c*z))^u ------------------------------ */
4239
4240 /* Problem 652: NEW 9-1 */
4241 expand(niceindices(integrate(z^n*%e^(b*z^2)*(%e^(c*z))^u,z))-
4242 (-b^(-n-1)*(%e^(c*z))^u*%e^(b*z^2-z*(b*z+c*u)-c^2*u^2/(4*b))
4243          *('sum(c^(n-i)*gamma_incomplete((i+1)/2,-(2*b*z+c*u)^2/(4*b))
4244                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*u^(n-i)
4245                        *(2*b*z+c*u)^(i+1)
4246                  /(-(2*b*z+c*u)^2/b)^((i+1)/2),i,0,n))
4247  /2));
4248 0;
4249
4250 /* Problem 653: NEW 10-1 */
4251 expand(niceindices(integrate(z^n*%e^(b*sqrt(z))*(%e^(c*z))^u,z))-
4252 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4253                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4254                                      *(2*c*u*sqrt(z)+b)^(j+i)
4255                                      *(b
4256                                       *gamma_incomplete((j+i+1)/2,
4257                                                         -(2*c*u*sqrt(z)+b)^2
4258                                                          /(4*c*u))
4259                                       *(2*c*u*sqrt(z)+b)
4260                                       +2*c
4261                                         *gamma_incomplete((j+i+2)/2,
4262                                                           -(2*c*u*sqrt(z)+b)^2
4263                                                            /(4*c*u))*u
4264                                         *sqrt((2*c*u*sqrt(z)+b)^2/(c*u)))
4265                            /(-(2*c*u*sqrt(z)+b)^2/(c*u))^((j+i+1)/2),i,0,j),j,
4266                  0,n))*(%e^(c*z))^u*%e^(-c*u*z-b^2/(4*c*u))
4267  /(c^(2*(n+1))*u^(2*(n+1)))));
4268 0;
4269
4270 /* ----- Involving z^n*%e^(b*z^r+e)*(%e^(c*z))^u ---------------------------- */
4271
4272 /* Problem 654: NEW 9-1 */
4273 expand(niceindices(integrate(z^n*%e^(e+b*z^2)*(%e^(c*z))^u,z))-
4274 (-b^(-n-1)*(%e^(c*z))^u*%e^(b*z^2-z*(b*z+c*u)-c^2*u^2/(4*b)+e)
4275          *('sum(c^(n-i)*gamma_incomplete((i+1)/2,-(2*b*z+c*u)^2/(4*b))
4276                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*u^(n-i)
4277                        *(2*b*z+c*u)^(i+1)
4278                  /(-(2*b*z+c*u)^2/b)^((i+1)/2),i,0,n))
4279  /2));
4280 0;
4281
4282 /* Problem 655: NEW 10-1 */
4283 expand(niceindices(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(c*z))^u,z))-
4284 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4285                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4286                                      *(2*c*u*sqrt(z)+b)^(j+i)
4287                                      *(b
4288                                       *gamma_incomplete((j+i+1)/2,
4289                                                         -(2*c*u*sqrt(z)+b)^2
4290                                                          /(4*c*u))
4291                                       *(2*c*u*sqrt(z)+b)
4292                                       +2*c
4293                                         *gamma_incomplete((j+i+2)/2,
4294                                                           -(2*c*u*sqrt(z)+b)^2
4295                                                            /(4*c*u))*u
4296                                         *sqrt((2*c*u*sqrt(z)+b)^2/(c*u)))
4297                            /(-(2*c*u*sqrt(z)+b)^2/(c*u))^((j+i+1)/2),i,0,j),j,
4298                  0,n))*(%e^(c*z))^u*%e^(-c*u*z-b^2/(4*c*u)+e)
4299  /(c^(2*(n+1))*u^(2*(n+1)))));
4300 0;
4301
4302 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z))^u -------------------------- */
4303
4304 /* Problem 656: NEW 9-1 */
4305 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(c*z))^u,z))-
4306 (-b^(-n-1)*(%e^(c*z))^u*%e^(-z*(b*z+c*u+d)+z*(b*z+d)-(c*u+d)^2/(4*b))
4307          *('sum(gamma_incomplete((i+1)/2,-(2*b*z+c*u+d)^2/(4*b))
4308                  *2^(i-n)*binomial(n,i)*(-c*u-d)^(n-i)*(2*b*z+c*u+d)^(i+1)
4309                  /(-(2*b*z+c*u+d)^2/b)^((i+1)/2),i,0,n))
4310  /2));
4311 0;
4312
4313 /* Problem 657: NEW 10-1 */
4314 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(c*z))^u,z))-
4315 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4316                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4317                                      *(2*(c*u+d)*sqrt(z)+b)^(j+i)
4318                                      *(b
4319                                       *gamma_incomplete((j+i+1)/2,
4320                                                         -(2*(c*u+d)*sqrt(z)+b)
4321                                                          ^2
4322                                                          /(4*(c*u+d)))
4323                                       *(2*(c*u+d)*sqrt(z)+b)
4324                                       +2
4325                                        *gamma_incomplete((j+i+2)/2,
4326                                                          -(2*(c*u+d)*sqrt(z)
4327                                                           +b)
4328                                                           ^2
4329                                                           /(4*(c*u+d)))
4330                                        *(c*u+d)
4331                                        *sqrt((2*(c*u+d)*sqrt(z)+b)^2/(c*u+d)))
4332                            /((2*(c*u+d)*sqrt(z)+b)^2/(-c*u-d))^((j+i+1)/2),i,
4333                           0,j),j,0,n))*(%e^(c*z))^u
4334           *%e^(-c*u*z-b^2/(4*(c*u+d)))
4335  /(c*u+d)^(2*(n+1))));
4336 0;
4337
4338 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r))^u ---------------------- */
4339
4340 /* Problem 658: NEW 9-1 */
4341 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(c*z))^u,z))-
4342 (-b^(-n-1)*(%e^(c*z))^u*%e^(-z*(b*z+c*u+d)+z*(b*z+d)-(c*u+d)^2/(4*b)+e)
4343          *('sum(gamma_incomplete((i+1)/2,-(2*b*z+c*u+d)^2/(4*b))
4344                  *2^(i-n)*binomial(n,i)*(-c*u-d)^(n-i)*(2*b*z+c*u+d)^(i+1)
4345                  /(-(2*b*z+c*u+d)^2/b)^((i+1)/2),i,0,n))
4346  /2));
4347 0;
4348
4349 /* Problem 659: NEW 10-1 */
4350 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(c*z))^u,z))-
4351 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4352                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4353                                      *(2*(c*u+d)*sqrt(z)+b)^(j+i)
4354                                      *(b
4355                                       *gamma_incomplete((j+i+1)/2,
4356                                                         -(2*(c*u+d)*sqrt(z)+b)
4357                                                          ^2
4358                                                          /(4*(c*u+d)))
4359                                       *(2*(c*u+d)*sqrt(z)+b)
4360                                       +2
4361                                        *gamma_incomplete((j+i+2)/2,
4362                                                          -(2*(c*u+d)*sqrt(z)
4363                                                           +b)
4364                                                           ^2
4365                                                           /(4*(c*u+d)))
4366                                        *(c*u+d)
4367                                        *sqrt((2*(c*u+d)*sqrt(z)+b)^2/(c*u+d)))
4368                            /((2*(c*u+d)*sqrt(z)+b)^2/(-c*u-d))^((j+i+1)/2),i,
4369                           0,j),j,0,n))*(%e^(c*z))^u
4370           *%e^(-c*u*z-b^2/(4*(c*u+d))+e)
4371  /(c*u+d)^(2*(n+1))));
4372 0;
4373
4374 /* ----- Involving z^n*%e^(b*z^r)*(%e^(f*z+g))^u ---------------------------- */
4375
4376 /* Problem 660: NEW 9-1 */
4377 expand(niceindices(integrate(z^n*%e^(b*z^2)*(%e^(g+f*z))^u,z))-
4378 (-b^(-n-1)*(%e^(f*z+g))^u*%e^(b*z^2-z*(b*z+f*u)-f^2*u^2/(4*b))
4379          *('sum(f^(n-i)*gamma_incomplete((i+1)/2,-(2*b*z+f*u)^2/(4*b))
4380                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*u^(n-i)
4381                        *(2*b*z+f*u)^(i+1)
4382                  /(-(2*b*z+f*u)^2/b)^((i+1)/2),i,0,n))
4383  /2));
4384 0;
4385
4386 /* Problem 661: NEW 10-1 */
4387 expand(niceindices(integrate(z^n*%e^(b*sqrt(z))*(%e^(g+f*z))^u,z))-
4388 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4389                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4390                                      *(2*f*u*sqrt(z)+b)^(j+i)
4391                                      *(b
4392                                       *gamma_incomplete((j+i+1)/2,
4393                                                         -(2*f*u*sqrt(z)+b)^2
4394                                                          /(4*f*u))
4395                                       *(2*f*u*sqrt(z)+b)
4396                                       +2*f
4397                                         *gamma_incomplete((j+i+2)/2,
4398                                                           -(2*f*u*sqrt(z)+b)^2
4399                                                            /(4*f*u))*u
4400                                         *sqrt((2*f*u*sqrt(z)+b)^2/(f*u)))
4401                            /(-(2*f*u*sqrt(z)+b)^2/(f*u))^((j+i+1)/2),i,0,j),j,
4402                  0,n))*(%e^(f*z+g))^u*%e^(-f*u*z-b^2/(4*f*u))
4403  /(f^(2*(n+1))*u^(2*(n+1)))));
4404 0;
4405
4406 /* ----- Involving z^n*%e^(b*z^r+e)*(%e^(f*z+g))^u -------------------------- */
4407
4408 /* Problem 662: NEW 9-1 */
4409 expand(niceindices(integrate(z^n*%e^(e+b*z^2)*(%e^(g+f*z))^u,z))-
4410 (-b^(-n-1)*(%e^(f*z+g))^u*%e^(b*z^2-z*(b*z+f*u)-f^2*u^2/(4*b)+e)
4411          *('sum(f^(n-i)*gamma_incomplete((i+1)/2,-(2*b*z+f*u)^2/(4*b))
4412                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*u^(n-i)
4413                        *(2*b*z+f*u)^(i+1)
4414                  /(-(2*b*z+f*u)^2/b)^((i+1)/2),i,0,n))
4415  /2));
4416 0;
4417
4418 /* Problem 663: NEW 10-1 */
4419 expand(niceindices(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(g+f*z))^u,z))-
4420 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4421                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4422                                      *(2*f*u*sqrt(z)+b)^(j+i)
4423                                      *(b
4424                                       *gamma_incomplete((j+i+1)/2,
4425                                                         -(2*f*u*sqrt(z)+b)^2
4426                                                          /(4*f*u))
4427                                       *(2*f*u*sqrt(z)+b)
4428                                       +2*f
4429                                         *gamma_incomplete((j+i+2)/2,
4430                                                           -(2*f*u*sqrt(z)+b)^2
4431                                                            /(4*f*u))*u
4432                                         *sqrt((2*f*u*sqrt(z)+b)^2/(f*u)))
4433                            /(-(2*f*u*sqrt(z)+b)^2/(f*u))^((j+i+1)/2),i,0,j),j,
4434                  0,n))*(%e^(f*z+g))^u*%e^(-f*u*z-b^2/(4*f*u)+e)
4435  /(f^(2*(n+1))*u^(2*(n+1)))));
4436 0;
4437
4438 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(f*z+g))^u ------------------------ */
4439
4440 /* Problem 664: NEW 9-1 */
4441 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(g+f*z))^u,z))-
4442 (-b^(-n-1)*(%e^(f*z+g))^u*%e^(-z*(b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*b))
4443          *('sum(gamma_incomplete((i+1)/2,-(2*b*z+f*u+d)^2/(4*b))
4444                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*b*z+f*u+d)^(i+1)
4445                  /(-(2*b*z+f*u+d)^2/b)^((i+1)/2),i,0,n))
4446  /2));
4447 0;
4448
4449 /* Problem 665: NEW 10-1 */
4450 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(g+f*z))^u,z))-
4451 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4452                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4453                                      *(2*(f*u+d)*sqrt(z)+b)^(j+i)
4454                                      *(b
4455                                       *gamma_incomplete((j+i+1)/2,
4456                                                         -(2*(f*u+d)*sqrt(z)+b)
4457                                                          ^2
4458                                                          /(4*(f*u+d)))
4459                                       *(2*(f*u+d)*sqrt(z)+b)
4460                                       +2
4461                                        *gamma_incomplete((j+i+2)/2,
4462                                                          -(2*(f*u+d)*sqrt(z)
4463                                                           +b)
4464                                                           ^2
4465                                                           /(4*(f*u+d)))
4466                                        *(f*u+d)
4467                                        *sqrt((2*(f*u+d)*sqrt(z)+b)^2/(f*u+d)))
4468                            /((2*(f*u+d)*sqrt(z)+b)^2/(-f*u-d))^((j+i+1)/2),i,
4469                           0,j),j,0,n))*(%e^(f*z+g))^u
4470           *%e^(-f*u*z-b^2/(4*(f*u+d)))
4471  /(f*u+d)^(2*(n+1))));
4472 0;
4473
4474 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(f*z+g))^u ---------------------- */
4475
4476 /* Problem 666: NEW 9-1 */
4477 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(g+f*z))^u,z))-
4478 (-b^(-n-1)*(%e^(f*z+g))^u*%e^(-z*(b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*b)+e)
4479          *('sum(gamma_incomplete((i+1)/2,-(2*b*z+f*u+d)^2/(4*b))
4480                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*b*z+f*u+d)^(i+1)
4481                  /(-(2*b*z+f*u+d)^2/b)^((i+1)/2),i,0,n))
4482  /2));
4483 0;
4484
4485 /* Problem 667: NEW 10-1 */
4486 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(g+f*z))^u,z))-
4487 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4488                     *'sum(b^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)
4489                                      *(2*(f*u+d)*sqrt(z)+b)^(j+i)
4490                                      *(b
4491                                       *gamma_incomplete((j+i+1)/2,
4492                                                         -(2*(f*u+d)*sqrt(z)+b)
4493                                                          ^2
4494                                                          /(4*(f*u+d)))
4495                                       *(2*(f*u+d)*sqrt(z)+b)
4496                                       +2
4497                                        *gamma_incomplete((j+i+2)/2,
4498                                                          -(2*(f*u+d)*sqrt(z)
4499                                                           +b)
4500                                                           ^2
4501                                                           /(4*(f*u+d)))
4502                                        *(f*u+d)
4503                                        *sqrt((2*(f*u+d)*sqrt(z)+b)^2/(f*u+d)))
4504                            /((2*(f*u+d)*sqrt(z)+b)^2/(-f*u-d))^((j+i+1)/2),i,
4505                           0,j),j,0,n))*(%e^(f*z+g))^u
4506           *%e^(-f*u*z-b^2/(4*(f*u+d))+e)
4507  /(f*u+d)^(2*(n+1))));
4508 0;
4509
4510 /* ----- Involving z^n*%e^(d*z)*(%e^(c*z^r))^u ------------------------------ */
4511
4512 /* Problem 668: NEW 9-1 */
4513 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(c*z^2))^u,z))-
4514 (-c^(-n-1)*u^(-n-1)*%e^(-z*(c*u*z+d)+d*z-d^2/(4*c*u))*(%e^(c*z^2))^u
4515          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d)^2/(4*c*u))
4516                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*c*u*z+d)^(i+1)
4517                  /(-(2*c*u*z+d)^2/(c*u))^((i+1)/2),i,0,n))
4518  /2));
4519 0;
4520
4521 /* Problem 669: NEW 10-1 */
4522 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(c*sqrt(z)))^u,z))-
4523 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4524                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4525                                      *(2*d*sqrt(z)+c*u)^(j+i)
4526                                      *(c
4527                                       *gamma_incomplete((j+i+1)/2,
4528                                                         -(2*d*sqrt(z)+c*u)^2
4529                                                          /(4*d))*u
4530                                       *(2*d*sqrt(z)+c*u)
4531                                       +2*d
4532                                         *gamma_incomplete((j+i+2)/2,
4533                                                           -(2*d*sqrt(z)+c*u)^2
4534                                                            /(4*d))
4535                                         *sqrt((2*d*sqrt(z)+c*u)^2/d))
4536                            /(-(2*d*sqrt(z)+c*u)^2/d)^((j+i+1)/2),i,0,j),j,0,
4537                  n))*(%e^(c*sqrt(z)))^u*%e^(-c*u*sqrt(z)-c^2*u^2/(4*d))
4538  /d^(2*(n+1))));
4539 0;
4540
4541 /* ----- Involving z^n*%e^(d*z+e)*(%e^(c*z^r))^u ---------------------------- */
4542
4543 /* Problem 670: NEW 9-1 */
4544 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(c*z^2))^u,z))-
4545 (-c^(-n-1)*u^(-n-1)*%e^(-z*(c*u*z+d)+d*z-d^2/(4*c*u)+e)*(%e^(c*z^2))^u
4546          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d)^2/(4*c*u))
4547                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*c*u*z+d)^(i+1)
4548                  /(-(2*c*u*z+d)^2/(c*u))^((i+1)/2),i,0,n))
4549  /2));
4550 0;
4551
4552 /* Problem 671: NEW 10-1 */
4553 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(c*sqrt(z)))^u,z))-
4554 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4555                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4556                                      *(2*d*sqrt(z)+c*u)^(j+i)
4557                                      *(c
4558                                       *gamma_incomplete((j+i+1)/2,
4559                                                         -(2*d*sqrt(z)+c*u)^2
4560                                                          /(4*d))*u
4561                                       *(2*d*sqrt(z)+c*u)
4562                                       +2*d
4563                                         *gamma_incomplete((j+i+2)/2,
4564                                                           -(2*d*sqrt(z)+c*u)^2
4565                                                            /(4*d))
4566                                         *sqrt((2*d*sqrt(z)+c*u)^2/d))
4567                            /(-(2*d*sqrt(z)+c*u)^2/d)^((j+i+1)/2),i,0,j),j,0,
4568                  n))*(%e^(c*sqrt(z)))^u*%e^(-c*u*sqrt(z)-c^2*u^2/(4*d)+e)
4569  /d^(2*(n+1))));
4570 0;
4571
4572 /* ----- Involving z^(v-1)*%e^(b*z^r)*(%e^(c*z^r))^u ------------------------ */
4573
4574 /* Problem 672: NEW 7-1*/
4575 diffcheck(integrate(z^(v-1)*%e^(b*z^r)*(%e^(c*z^r))^u,z),z,factor);
4576 z^(v-1)*%e^(b*z^r)*(%e^(c*z^r))^u;
4577
4578 /* Problem 673: NEW 7-1 */
4579 diffcheck(integrate(z^n*%e^(b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4580 z^n*%e^(b*z^2)*(%e^(c*z^2))^u;
4581
4582 /* Problem 674: NEW 7-1 */
4583 diffcheck(integrate(z^(2*n)*%e^(b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4584 z^(2*n)*%e^(b*z^2)*(%e^(c*z^2))^u;
4585
4586 /* Problem 675: NEW 7-1 */
4587 diffcheck(integrate(z^(1+2*n)*%e^(b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4588 z^(1+2*n)*%e^(b*z^2)*(%e^(c*z^2))^u;
4589
4590 /* Problem 676: NEW 7-1 */
4591 diffcheck(integrate(z^n*%e^(b*sqrt(z))*(%e^(c*sqrt(z)))^u,z),z,factor);
4592 z^n*%e^(b*sqrt(z))*(%e^(c*sqrt(z)))^u;
4593
4594 /* ----- Involving z^(v-1)*%e^(b*z^r+e)*(%e^(c*z^r))^u ---------------------- */
4595
4596 /* Problem 677: NEW 7-1 */
4597 diffcheck(integrate(z^(v-1)*%e^(e+b*z^r)*(%e^(c*z^r))^u,z),z,factor);
4598 z^(v-1)*%e^(e+b*z^r)*(%e^(c*z^r))^u;
4599
4600 /* Problem 678: NEW 7-1 */
4601 diffcheck(integrate(z^n*%e^(e+b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4602 z^n*%e^(e+b*z^2)*(%e^(c*z^2))^u;
4603
4604 /* Problem 679: NEW 7-1 */
4605 diffcheck(integrate(z^(2*n)*%e^(e+b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4606 z^(2*n)*%e^(e+b*z^2)*(%e^(c*z^2))^u;
4607
4608 /* Problem 680: NEW 7-1 */
4609 diffcheck(integrate(z^(1+2*n)*%e^(e+b*z^2)*(%e^(c*z^2))^u,z),z,factor);
4610 z^(1+2*n)*%e^(e+b*z^2)*(%e^(c*z^2))^u;
4611
4612 /* Problem 681: NEW 7-1 */
4613 diffcheck(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(c*sqrt(z)))^u,z),z,factor);
4614 z^n*%e^(e+b*sqrt(z))*(%e^(c*sqrt(z)))^u;
4615
4616 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z^r))^u ------------------------ */
4617
4618 /* Problem 682: NEW 9-1 */
4619 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(c*z^2))^u,z))-
4620 (-(c*u+b)^(-n-1)*%e^(-z*(c*u*z+b*z+d)+z*(b*z+d)-d^2/(4*(c*u+b)))*(%e^(c*z^2))^u
4621                *('sum(d^(n-i)*gamma_incomplete((i+1)/2,
4622                                                -(2*(c*u+b)*z+d)^2/(4*(c*u+b)))
4623                              *(-1)^(i-n)*2^(i-n)*binomial(n,i)
4624                              *(2*(c*u+b)*z+d)^(i+1)
4625                        /((2*(c*u+b)*z+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
4626  /2));
4627 0;
4628
4629 /* Problem 683: NEW 10-1 */
4630 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^u,z))-
4631 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4632                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4633                                     *(2*d*sqrt(z)+c*u+b)^(j+i)
4634                                     *(gamma_incomplete((j+i+1)/2,
4635                                                        -(2*d*sqrt(z)+c*u+b)^2
4636                                                         /(4*d))
4637                                      *(c*u+b)*(2*d*sqrt(z)+c*u+b)
4638                                      +2*d
4639                                        *gamma_incomplete((j+i+2)/2,
4640                                                          -(2*d*sqrt(z)+c*u+b)
4641                                                           ^2
4642                                                           /(4*d))
4643                                        *sqrt((2*d*sqrt(z)+c*u+b)^2/d))
4644                            /(-(2*d*sqrt(z)+c*u+b)^2/d)^((j+i+1)/2),i,0,j),j,0,
4645                  n))*(%e^(c*sqrt(z)))^u*%e^(-c*u*sqrt(z)-(c*u+b)^2/(4*d))
4646  /d^(2*(n+1))));
4647 0;
4648
4649 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r))^u ---------------------- */
4650
4651 /* Problem 684: NEW 9-1 */
4652 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(c*z^2))^u,z))-
4653 (-(c*u+b)^(-n-1)*%e^(-z*(c*u*z+b*z+d)+z*(b*z+d)-d^2/(4*(c*u+b))+e)
4654                *(%e^(c*z^2))^u
4655                *('sum(d^(n-i)*gamma_incomplete((i+1)/2,
4656                                                -(2*(c*u+b)*z+d)^2/(4*(c*u+b)))
4657                              *(-1)^(i-n)*2^(i-n)*binomial(n,i)
4658                              *(2*(c*u+b)*z+d)^(i+1)
4659                        /((2*(c*u+b)*z+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
4660  /2));
4661 0;
4662
4663 /* Problem 685: NEW 10-1 */
4664 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(c*sqrt(z)))^u,z))-
4665 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4666                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4667                                     *(2*d*sqrt(z)+c*u+b)^(j+i)
4668                                     *(gamma_incomplete((j+i+1)/2,
4669                                                        -(2*d*sqrt(z)+c*u+b)^2
4670                                                         /(4*d))
4671                                      *(c*u+b)*(2*d*sqrt(z)+c*u+b)
4672                                      +2*d
4673                                        *gamma_incomplete((j+i+2)/2,
4674                                                          -(2*d*sqrt(z)+c*u+b)
4675                                                           ^2
4676                                                           /(4*d))
4677                                        *sqrt((2*d*sqrt(z)+c*u+b)^2/d))
4678                            /(-(2*d*sqrt(z)+c*u+b)^2/d)^((j+i+1)/2),i,0,j),j,0,
4679                  n))*(%e^(c*sqrt(z)))^u*%e^(-c*u*sqrt(z)-(c*u+b)^2/(4*d)+e)
4680  /d^(2*(n+1))));
4681 0;
4682
4683 /* ----- Involving z^n*%e^(d*z)*(%e^(c*z^r+g))^u ---------------------------- */
4684
4685 /* Problem 686: NEW 9-1 */
4686 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(g+c*z^2))^u,z))-
4687 (-c^(-n-1)*u^(-n-1)*%e^(-z*(c*u*z+d)+d*z-d^2/(4*c*u))*(%e^(c*z^2+g))^u
4688          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d)^2/(4*c*u))
4689                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*c*u*z+d)^(i+1)
4690                  /(-(2*c*u*z+d)^2/(c*u))^((i+1)/2),i,0,n))
4691  /2));
4692 0;
4693
4694 /* Problem 687: NEW 10-1 */
4695 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(g+c*sqrt(z)))^u,z))-
4696 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4697                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4698                                      *(2*d*sqrt(z)+c*u)^(j+i)
4699                                      *(c
4700                                       *gamma_incomplete((j+i+1)/2,
4701                                                         -(2*d*sqrt(z)+c*u)^2
4702                                                          /(4*d))*u
4703                                       *(2*d*sqrt(z)+c*u)
4704                                       +2*d
4705                                         *gamma_incomplete((j+i+2)/2,
4706                                                           -(2*d*sqrt(z)+c*u)^2
4707                                                            /(4*d))
4708                                         *sqrt((2*d*sqrt(z)+c*u)^2/d))
4709                            /(-(2*d*sqrt(z)+c*u)^2/d)^((j+i+1)/2),i,0,j),j,0,
4710                  n))*(%e^(c*sqrt(z)+g))^u*%e^(-c*u*sqrt(z)-c^2*u^2/(4*d))
4711  /d^(2*(n+1))));
4712 0;
4713
4714 /* ----- Involving z^n*%e^(d*z+e)*(%e^(c*z^r+g))^u -------------------------- */
4715
4716 /* Problem 688: NEW 9-1 */
4717 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(g+c*z^2))^u,z))-
4718 (-c^(-n-1)*u^(-n-1)*%e^(-z*(c*u*z+d)+d*z-d^2/(4*c*u)+e)*(%e^(c*z^2+g))^u
4719          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d)^2/(4*c*u))
4720                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*(2*c*u*z+d)^(i+1)
4721                  /(-(2*c*u*z+d)^2/(c*u))^((i+1)/2),i,0,n))
4722  /2));
4723 0;
4724
4725 /* Problem 689: NEW 10-1 */
4726 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(g+c*sqrt(z)))^u,z))-
4727 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4728                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4729                                      *(2*d*sqrt(z)+c*u)^(j+i)
4730                                      *(c
4731                                       *gamma_incomplete((j+i+1)/2,
4732                                                         -(2*d*sqrt(z)+c*u)^2
4733                                                          /(4*d))*u
4734                                       *(2*d*sqrt(z)+c*u)
4735                                       +2*d
4736                                         *gamma_incomplete((j+i+2)/2,
4737                                                           -(2*d*sqrt(z)+c*u)^2
4738                                                            /(4*d))
4739                                         *sqrt((2*d*sqrt(z)+c*u)^2/d))
4740                            /(-(2*d*sqrt(z)+c*u)^2/d)^((j+i+1)/2),i,0,j),j,0,
4741                  n))*(%e^(c*sqrt(z)+g))^u*%e^(-c*u*sqrt(z)-c^2*u^2/(4*d)+e)
4742  /d^(2*(n+1))));
4743 0;
4744
4745 /* ----- Involving z^(v-1)*%e^(b*z^r)*(%e^(c*z^r+g))^u ---------------------- */
4746
4747 /* Problem 690: NEW 7-1 */
4748 diffcheck(integrate(z^(v-1)*%e^(b*z^r)*(%e^(g+c*z^r))^u,z),z,factor);
4749 z^(v-1)*%e^(b*z^r)*(%e^(g+c*z^r))^u;
4750
4751 /* Problem 691: NEW 7-1 */
4752 diffcheck(integrate(z^n*%e^(b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4753 z^n*%e^(b*z^2)*(%e^(g+c*z^2))^u;
4754
4755 /* Problem 692: NEW 7-1 */
4756 diffcheck(integrate(z^(2*n)*%e^(b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4757 z^(2*n)*%e^(b*z^2)*(%e^(g+c*z^2))^u;
4758
4759 /* Problem 693: NEW 7-1 */
4760 diffcheck(integrate(z^(1+2*n)*%e^(b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4761 z^(1+2*n)*%e^(b*z^2)*(%e^(g+c*z^2))^u;
4762
4763 /* Problem 694: NEW 7-1*/
4764 diffcheck(integrate(z^n*%e^(b*sqrt(z))*(%e^(g+c*sqrt(z)))^u,z),z,factor);
4765 z^n*%e^(b*sqrt(z))*(%e^(g+c*sqrt(z)))^u;
4766
4767 /* ----- Involving z^(v-1)*%e^(b*z^r+e)*(%e^(c*z^r+g))^u -------------------- */
4768
4769 /* Problem 695: NEW 7-1 */
4770 diffcheck(integrate(z^(v-1)*%e^(e+b*z^r)*(%e^(g+c*z^r))^u,z),z,factor);
4771 z^(v-1)*%e^(e+b*z^r)*(%e^(g+c*z^r))^u;
4772
4773 /* Problem 696: NEW 7-1 */
4774 diffcheck(integrate(z^n*%e^(e+b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4775 z^n*%e^(e+b*z^2)*(%e^(g+c*z^2))^u;
4776
4777 /* Problem 697: NEW 7-1 */
4778 diffcheck(integrate(z^(2*n)*%e^(e+b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4779 z^(2*n)*%e^(e+b*z^2)*(%e^(g+c*z^2))^u;
4780
4781 /* Problem 698: NEW 7-1 */
4782 diffcheck(integrate(z^(1+2*n)*%e^(e+b*z^2)*(%e^(g+c*z^2))^u,z),z,factor);
4783 z^(1+2*n)*%e^(e+b*z^2)*(%e^(g+c*z^2))^u;
4784
4785 /* Problem 699: NEW 7-1 */
4786 diffcheck(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(g+c*sqrt(z)))^u,z),z,factor);
4787 z^n*%e^(e+b*sqrt(z))*(%e^(g+c*sqrt(z)))^u;
4788
4789 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z^r+g))^u ---------------------- */
4790
4791 /* Problem 700: NEW 9-1 */
4792 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(g+c*z^2))^u,z))-
4793 (-(c*u+b)^(-n-1)*%e^(-z*(c*u*z+b*z+d)+z*(b*z+d)-d^2/(4*(c*u+b)))
4794                *(%e^(c*z^2+g))^u
4795                *('sum(d^(n-i)*gamma_incomplete((i+1)/2,
4796                                                -(2*(c*u+b)*z+d)^2/(4*(c*u+b)))
4797                              *(-1)^(i-n)*2^(i-n)*binomial(n,i)
4798                              *(2*(c*u+b)*z+d)^(i+1)
4799                        /((2*(c*u+b)*z+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
4800  /2));
4801 0;
4802
4803 /* Problem 701: NEW 10-1 */
4804 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(g+c*sqrt(z)))^u,z))-
4805 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4806                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4807                                     *(2*d*sqrt(z)+c*u+b)^(j+i)
4808                                     *(gamma_incomplete((j+i+1)/2,
4809                                                        -(2*d*sqrt(z)+c*u+b)^2
4810                                                         /(4*d))
4811                                      *(c*u+b)*(2*d*sqrt(z)+c*u+b)
4812                                      +2*d
4813                                        *gamma_incomplete((j+i+2)/2,
4814                                                          -(2*d*sqrt(z)+c*u+b)
4815                                                           ^2
4816                                                           /(4*d))
4817                                        *sqrt((2*d*sqrt(z)+c*u+b)^2/d))
4818                            /(-(2*d*sqrt(z)+c*u+b)^2/d)^((j+i+1)/2),i,0,j),j,0,
4819                  n))*(%e^(c*sqrt(z)+g))^u*%e^(-c*u*sqrt(z)-(c*u+b)^2/(4*d))
4820  /d^(2*(n+1))));
4821 0;
4822
4823 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r+g))^u -------------------- */
4824
4825 /* Problem 702: NEW 9-1 */
4826 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(g+c*z^2))^u,z))-
4827 (-(c*u+b)^(-n-1)*%e^(-z*(c*u*z+b*z+d)+z*(b*z+d)-d^2/(4*(c*u+b))+e)
4828                *(%e^(c*z^2+g))^u
4829                *('sum(d^(n-i)*gamma_incomplete((i+1)/2,
4830                                                -(2*(c*u+b)*z+d)^2/(4*(c*u+b)))
4831                              *(-1)^(i-n)*2^(i-n)*binomial(n,i)
4832                              *(2*(c*u+b)*z+d)^(i+1)
4833                        /((2*(c*u+b)*z+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
4834  /2));
4835 0;
4836
4837 /* Problem 703: NEW 10-1 */
4838 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(g+c*sqrt(z)))^u,z))-
4839 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4840                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4841                                     *(2*d*sqrt(z)+c*u+b)^(j+i)
4842                                     *(gamma_incomplete((j+i+1)/2,
4843                                                        -(2*d*sqrt(z)+c*u+b)^2
4844                                                         /(4*d))
4845                                      *(c*u+b)*(2*d*sqrt(z)+c*u+b)
4846                                      +2*d
4847                                        *gamma_incomplete((j+i+2)/2,
4848                                                          -(2*d*sqrt(z)+c*u+b)
4849                                                           ^2
4850                                                           /(4*d))
4851                                        *sqrt((2*d*sqrt(z)+c*u+b)^2/d))
4852                            /(-(2*d*sqrt(z)+c*u+b)^2/d)^((j+i+1)/2),i,0,j),j,0,
4853                  n))*(%e^(c*sqrt(z)+g))^u*%e^(-c*u*sqrt(z)-(c*u+b)^2/(4*d)+e)
4854  /d^(2*(n+1))));
4855  0;
4856
4857 /* ----- Involving z^n*%e^(d*z)*(%e^(c*z^r+f*z))^u -------------------------- */
4858
4859 /* Problem 704: NEW 9-1 */
4860 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(f*z+c*z^2))^u,z))-
4861 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)))^u
4862          *%e^(-z*(c*u*z+f*u+d)+d*z-(f*u+d)^2/(4*c*u))
4863          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d)^2/(4*c*u))
4864                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*c*u*z+f*u+d)^(i+1)
4865                  /(-(2*c*u*z+f*u+d)^2/(c*u))^((i+1)/2),i,0,n))
4866  /2));
4867 0;
4868
4869 /* Problem 705: NEW 10-1 */
4870 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(f*z+c*sqrt(z)))^u,z))-
4871 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4872                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4873                                      *(2*(f*u+d)*sqrt(z)+c*u)^(j+i)
4874                                      *(c
4875                                       *gamma_incomplete((j+i+1)/2,
4876                                                         -(2*(f*u+d)*sqrt(z)
4877                                                          +c*u)
4878                                                          ^2
4879                                                          /(4*(f*u+d)))*u
4880                                       *(2*(f*u+d)*sqrt(z)+c*u)
4881                                       +2
4882                                        *gamma_incomplete((j+i+2)/2,
4883                                                          -(2*(f*u+d)*sqrt(z)
4884                                                           +c*u)
4885                                                           ^2
4886                                                           /(4*(f*u+d)))
4887                                        *(f*u+d)
4888                                        *sqrt(
4889                                         (2*(f*u+d)*sqrt(z)+c*u)^2/(f*u+d)))
4890                            /((2*(f*u+d)*sqrt(z)+c*u)^2/(-f*u-d))^((j+i+1)/2),
4891                           i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
4892           *%e^(-f*u*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d)))
4893  /(f*u+d)^(2*(n+1))));
4894 0;
4895
4896 /* ----- Involving z^n*%e^(d*z+e)*(%e^(c*z^r+f*z))^u ------------------------ */
4897
4898 /* Problem 706: NEW 9-1 */
4899 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(f*z+c*z^2))^u,z))-
4900 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)))^u
4901          *%e^(-z*(c*u*z+f*u+d)+d*z-(f*u+d)^2/(4*c*u)+e)
4902          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d)^2/(4*c*u))
4903                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*c*u*z+f*u+d)^(i+1)
4904                  /(-(2*c*u*z+f*u+d)^2/(c*u))^((i+1)/2),i,0,n))
4905  /2));
4906 0;
4907
4908 /* Problem 707: NEW 10-1 */
4909 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(f*z+c*sqrt(z)))^u,z))-
4910 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4911                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
4912                                      *(2*(f*u+d)*sqrt(z)+c*u)^(j+i)
4913                                      *(c
4914                                       *gamma_incomplete((j+i+1)/2,
4915                                                         -(2*(f*u+d)*sqrt(z)
4916                                                          +c*u)
4917                                                          ^2
4918                                                          /(4*(f*u+d)))*u
4919                                       *(2*(f*u+d)*sqrt(z)+c*u)
4920                                       +2
4921                                        *gamma_incomplete((j+i+2)/2,
4922                                                          -(2*(f*u+d)*sqrt(z)
4923                                                           +c*u)
4924                                                           ^2
4925                                                           /(4*(f*u+d)))
4926                                        *(f*u+d)
4927                                        *sqrt(
4928                                         (2*(f*u+d)*sqrt(z)+c*u)^2/(f*u+d)))
4929                            /((2*(f*u+d)*sqrt(z)+c*u)^2/(-f*u-d))^((j+i+1)/2),
4930                           i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
4931           *%e^(-f*u*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d))+e)
4932  /(f*u+d)^(2*(n+1))));
4933 0;
4934
4935 /* ----- Involving z^n*%e^(b*z^r)*(%e^(c*z^r+f*z))^u ------------------------ */
4936
4937 /* Problem 708: NEW 9-1 */
4938 expand(niceindices(integrate(z^n*%e^(b*z^2)*(%e^(f*z+c*z^2))^u,z))-
4939 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)))^u
4940                *%e^(b*z^2-z*(c*u*z+b*z+f*u)-f^2*u^2/(4*(c*u+b)))
4941                *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
4942                                                -(2*(c*u+b)*z+f*u)^2
4943                                                 /(4*(c*u+b)))*(-1)^(i-n)
4944                              *2^(i-n)*binomial(n,i)*u^(n-i)
4945                              *(2*(c*u+b)*z+f*u)^(i+1)
4946                        /((2*(c*u+b)*z+f*u)^2/(-c*u-b))^((i+1)/2),i,0,n))
4947  /2));
4948 0;
4949
4950 /* Problem 709: NEW 10-1 */
4951 expand(niceindices(integrate(z^n*%e^(b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^u,z))-
4952 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4953                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4954                                     *(2*f*u*sqrt(z)+c*u+b)^(j+i)
4955                                     *(gamma_incomplete((j+i+1)/2,
4956                                                        -(2*f*u*sqrt(z)+c*u+b)
4957                                                         ^2
4958                                                         /(4*f*u))
4959                                      *(c*u+b)*(2*f*u*sqrt(z)+c*u+b)
4960                                      +2*f
4961                                        *gamma_incomplete((j+i+2)/2,
4962                                                          -(2*f*u*sqrt(z)
4963                                                           +c*u+b)
4964                                                           ^2
4965                                                           /(4*f*u))*u
4966                                        *sqrt((2*f*u*sqrt(z)+c*u+b)^2/(f*u)))
4967                            /(-(2*f*u*sqrt(z)+c*u+b)^2/(f*u))^((j+i+1)/2),i,0,
4968                           j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
4969           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*f*u))
4970  /(f^(2*(n+1))*u^(2*(n+1)))));
4971 0;
4972
4973 /* ----- Involving z^n*%e^(b*z^r+e)*(%e^(c*z^r+f*z))^u ---------------------- */
4974
4975 /* Problem 710: NEW 9-1 */
4976 expand(niceindices(integrate(z^n*%e^(e+b*z^2)*(%e^(f*z+c*z^2))^u,z))-
4977 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)))^u
4978                *%e^(b*z^2-z*(c*u*z+b*z+f*u)-f^2*u^2/(4*(c*u+b))+e)
4979                *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
4980                                                -(2*(c*u+b)*z+f*u)^2
4981                                                 /(4*(c*u+b)))*(-1)^(i-n)
4982                              *2^(i-n)*binomial(n,i)*u^(n-i)
4983                              *(2*(c*u+b)*z+f*u)^(i+1)
4984                        /((2*(c*u+b)*z+f*u)^2/(-c*u-b))^((i+1)/2),i,0,n))
4985  /2));
4986 0;
4987
4988 /* Problem 711: NEW 10-1 */
4989 expand(niceindices(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^u,z))-
4990 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
4991                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
4992                                     *(2*f*u*sqrt(z)+c*u+b)^(j+i)
4993                                     *(gamma_incomplete((j+i+1)/2,
4994                                                        -(2*f*u*sqrt(z)+c*u+b)
4995                                                         ^2
4996                                                         /(4*f*u))
4997                                      *(c*u+b)*(2*f*u*sqrt(z)+c*u+b)
4998                                      +2*f
4999                                        *gamma_incomplete((j+i+2)/2,
5000                                                          -(2*f*u*sqrt(z)
5001                                                           +c*u+b)
5002                                                           ^2
5003                                                           /(4*f*u))*u
5004                                        *sqrt((2*f*u*sqrt(z)+c*u+b)^2/(f*u)))
5005                            /(-(2*f*u*sqrt(z)+c*u+b)^2/(f*u))^((j+i+1)/2),i,0,
5006                           j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
5007           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*f*u)+e)
5008  /(f^(2*(n+1))*u^(2*(n+1)))));
5009 0;
5010
5011 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z^r+f*z))^u -------------------- */
5012
5013 /* Problem 712: NEW 9-1 */
5014 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(f*z+c*z^2))^u,z))-
5015 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)))^u
5016                *%e^(-z*(c*u*z+b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*(c*u+b)))
5017                *('sum(gamma_incomplete((i+1)/2,
5018                                        -(2*(c*u+b)*z+f*u+d)^2/(4*(c*u+b)))
5019                        *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)
5020                        *(2*(c*u+b)*z+f*u+d)^(i+1)
5021                        /((2*(c*u+b)*z+f*u+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
5022  /2));
5023 0;
5024
5025 /* Problem 713: NEW 10-1 */
5026 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^u,z))-
5027 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5028                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5029                                     *(2*(f*u+d)*sqrt(z)+c*u+b)^(j+i)
5030                                     *(gamma_incomplete((j+i+1)/2,
5031                                                        -(2*(f*u+d)*sqrt(z)
5032                                                         +c*u+b)
5033                                                         ^2
5034                                                         /(4*(f*u+d)))
5035                                      *(c*u+b)*(2*(f*u+d)*sqrt(z)+c*u+b)
5036                                      +2*gamma_incomplete((j+i+2)/2,
5037                                                          -(2*(f*u+d)*sqrt(z)
5038                                                           +c*u+b)
5039                                                           ^2
5040                                                           /(4*(f*u+d)))
5041                                        *(f*u+d)
5042                                        *sqrt(
5043                                         (2*(f*u+d)*sqrt(z)+c*u+b)^2/(f*u+d)))
5044                            /((2*(f*u+d)*sqrt(z)+c*u+b)^2/(-f*u-d))
5045                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
5046           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*(f*u+d)))
5047  /(f*u+d)^(2*(n+1))));
5048 0;
5049
5050 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r+f*z))^u ------------------ */
5051
5052 /* Problem 714: NEW 9-1 */
5053 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(f*z+c*z^2))^u,z))-
5054 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)))^u
5055                *%e^(-z*(c*u*z+b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*(c*u+b))+e)
5056                *('sum(gamma_incomplete((i+1)/2,
5057                                        -(2*(c*u+b)*z+f*u+d)^2/(4*(c*u+b)))
5058                        *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)
5059                        *(2*(c*u+b)*z+f*u+d)^(i+1)
5060                        /((2*(c*u+b)*z+f*u+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
5061  /2));
5062 0;
5063
5064 /* Problem 715: NEW 10-1 */
5065 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(f*z+c*sqrt(z)))^u,z))-
5066 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5067                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5068                                     *(2*(f*u+d)*sqrt(z)+c*u+b)^(j+i)
5069                                     *(gamma_incomplete((j+i+1)/2,
5070                                                        -(2*(f*u+d)*sqrt(z)
5071                                                         +c*u+b)
5072                                                         ^2
5073                                                         /(4*(f*u+d)))
5074                                      *(c*u+b)*(2*(f*u+d)*sqrt(z)+c*u+b)
5075                                      +2*gamma_incomplete((j+i+2)/2,
5076                                                          -(2*(f*u+d)*sqrt(z)
5077                                                           +c*u+b)
5078                                                           ^2
5079                                                           /(4*(f*u+d)))
5080                                        *(f*u+d)
5081                                        *sqrt(
5082                                         (2*(f*u+d)*sqrt(z)+c*u+b)^2/(f*u+d)))
5083                            /((2*(f*u+d)*sqrt(z)+c*u+b)^2/(-f*u-d))
5084                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)))^u
5085           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*(f*u+d))+e)
5086  /(f*u+d)^(2*(n+1))));
5087 0;
5088
5089 /* ----- Involving z^n*%e^(d*z)*(%e^(c*z^r+f*z+g))^u ------------------------ */
5090
5091 /* Problem 716: NEW 9-1 */
5092 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(g+f*z+c*z^2))^u,z))-
5093 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)+g))^u
5094          *%e^(-z*(c*u*z+f*u+d)+d*z-(f*u+d)^2/(4*c*u))
5095          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d)^2/(4*c*u))
5096                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*c*u*z+f*u+d)^(i+1)
5097                  /(-(2*c*u*z+f*u+d)^2/(c*u))^((i+1)/2),i,0,n))
5098  /2));
5099 0;
5100
5101 /* Problem 717: NEW 10-1 */
5102 expand(niceindices(integrate(z^n*%e^(d*z)*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5103 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5104                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5105                                      *(2*(f*u+d)*sqrt(z)+c*u)^(j+i)
5106                                      *(c
5107                                       *gamma_incomplete((j+i+1)/2,
5108                                                         -(2*(f*u+d)*sqrt(z)
5109                                                          +c*u)
5110                                                          ^2
5111                                                          /(4*(f*u+d)))*u
5112                                       *(2*(f*u+d)*sqrt(z)+c*u)
5113                                       +2
5114                                        *gamma_incomplete((j+i+2)/2,
5115                                                          -(2*(f*u+d)*sqrt(z)
5116                                                           +c*u)
5117                                                           ^2
5118                                                           /(4*(f*u+d)))
5119                                        *(f*u+d)
5120                                        *sqrt(
5121                                         (2*(f*u+d)*sqrt(z)+c*u)^2/(f*u+d)))
5122                            /((2*(f*u+d)*sqrt(z)+c*u)^2/(-f*u-d))^((j+i+1)/2),
5123                           i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)+g))^u
5124           *%e^(-f*u*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d)))
5125  /(f*u+d)^(2*(n+1))));
5126 0;
5127
5128 /* ----- Involving z^n*%e^(d*z+e)*(%e^(c*z^r+f*z+g))^u ---------------------- */
5129
5130 /* Problem 718: NEW 9-1 */
5131 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(g+f*z+c*z^2))^u,z))-
5132 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)+g))^u
5133          *%e^(-z*(c*u*z+f*u+d)+d*z-(f*u+d)^2/(4*c*u)+e)
5134          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d)^2/(4*c*u))
5135                  *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)*(2*c*u*z+f*u+d)^(i+1)
5136                  /(-(2*c*u*z+f*u+d)^2/(c*u))^((i+1)/2),i,0,n))
5137  /2));
5138 0;
5139
5140 /* Problem 719: NEW 10-1 */
5141 expand(niceindices(integrate(z^n*%e^(e+d*z)*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5142 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5143                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5144                                      *(2*(f*u+d)*sqrt(z)+c*u)^(j+i)
5145                                      *(c
5146                                       *gamma_incomplete((j+i+1)/2,
5147                                                         -(2*(f*u+d)*sqrt(z)
5148                                                          +c*u)
5149                                                          ^2
5150                                                          /(4*(f*u+d)))*u
5151                                       *(2*(f*u+d)*sqrt(z)+c*u)
5152                                       +2
5153                                        *gamma_incomplete((j+i+2)/2,
5154                                                          -(2*(f*u+d)*sqrt(z)
5155                                                           +c*u)
5156                                                           ^2
5157                                                           /(4*(f*u+d)))
5158                                        *(f*u+d)
5159                                        *sqrt(
5160                                         (2*(f*u+d)*sqrt(z)+c*u)^2/(f*u+d)))
5161                            /((2*(f*u+d)*sqrt(z)+c*u)^2/(-f*u-d))^((j+i+1)/2),
5162                           i,0,j),j,0,n))*(%e^(f*z+c*sqrt(z)+g))^u
5163           *%e^(-f*u*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d))+e)
5164  /(f*u+d)^(2*(n+1))));
5165 0;
5166
5167 /* ----- Involving z^n*%e^(b*z^r)*(%e^(c*z^r+f*z+g))^u ---------------------- */
5168
5169 /* Problem 720: NEW 9-1 */
5170 expand(niceindices(integrate(z^n*%e^(b*z^2)*(%e^(g+f*z+c*z^2))^u,z))-
5171 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5172                *%e^(b*z^2-z*(c*u*z+b*z+f*u)-f^2*u^2/(4*(c*u+b)))
5173                *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5174                                                -(2*(c*u+b)*z+f*u)^2
5175                                                 /(4*(c*u+b)))*(-1)^(i-n)
5176                              *2^(i-n)*binomial(n,i)*u^(n-i)
5177                              *(2*(c*u+b)*z+f*u)^(i+1)
5178                        /((2*(c*u+b)*z+f*u)^2/(-c*u-b))^((i+1)/2),i,0,n))
5179  /2));
5180 0;
5181
5182 /* Problem 721: NEW 10-1 */
5183 expand(niceindices(integrate(z^n*%e^(b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5184 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5185                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5186                                     *(2*f*u*sqrt(z)+c*u+b)^(j+i)
5187                                     *(gamma_incomplete((j+i+1)/2,
5188                                                        -(2*f*u*sqrt(z)+c*u+b)
5189                                                         ^2
5190                                                         /(4*f*u))
5191                                      *(c*u+b)*(2*f*u*sqrt(z)+c*u+b)
5192                                      +2*f
5193                                        *gamma_incomplete((j+i+2)/2,
5194                                                          -(2*f*u*sqrt(z)
5195                                                           +c*u+b)
5196                                                           ^2
5197                                                           /(4*f*u))*u
5198                                        *sqrt((2*f*u*sqrt(z)+c*u+b)^2/(f*u)))
5199                            /(-(2*f*u*sqrt(z)+c*u+b)^2/(f*u))^((j+i+1)/2),i,0,
5200                           j),j,0,n))*(%e^(f*z+c*sqrt(z)+g))^u
5201           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*f*u))
5202  /(f^(2*(n+1))*u^(2*(n+1)))));
5203 0;
5204
5205 /* ----- Involving z^n*%e^(b*z^r+e)*(%e^(c*z^r+f*z+g))^u -------------------- */
5206
5207 /* Problem 722: NEW 9-1 */
5208 expand(niceindices(integrate(z^n*%e^(e+b*z^2)*(%e^(g+f*z+c*z^2))^u,z))-
5209 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5210                *%e^(b*z^2-z*(c*u*z+b*z+f*u)-f^2*u^2/(4*(c*u+b))+e)
5211                *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5212                                                -(2*(c*u+b)*z+f*u)^2
5213                                                 /(4*(c*u+b)))*(-1)^(i-n)
5214                              *2^(i-n)*binomial(n,i)*u^(n-i)
5215                              *(2*(c*u+b)*z+f*u)^(i+1)
5216                        /((2*(c*u+b)*z+f*u)^2/(-c*u-b))^((i+1)/2),i,0,n))
5217  /2));
5218  0;
5219
5220 /* Problem 723: NEW 10-1 */
5221 expand(niceindices(integrate(z^n*%e^(e+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5222 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5223                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5224                                     *(2*f*u*sqrt(z)+c*u+b)^(j+i)
5225                                     *(gamma_incomplete((j+i+1)/2,
5226                                                        -(2*f*u*sqrt(z)+c*u+b)
5227                                                         ^2
5228                                                         /(4*f*u))
5229                                      *(c*u+b)*(2*f*u*sqrt(z)+c*u+b)
5230                                      +2*f
5231                                        *gamma_incomplete((j+i+2)/2,
5232                                                          -(2*f*u*sqrt(z)
5233                                                           +c*u+b)
5234                                                           ^2
5235                                                           /(4*f*u))*u
5236                                        *sqrt((2*f*u*sqrt(z)+c*u+b)^2/(f*u)))
5237                            /(-(2*f*u*sqrt(z)+c*u+b)^2/(f*u))^((j+i+1)/2),i,0,
5238                           j),j,0,n))*(%e^(f*z+c*sqrt(z)+g))^u
5239           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*f*u)+e)
5240  /(f^(2*(n+1))*u^(2*(n+1)))));
5241 0;
5242
5243 /* ----- Involving z^n*%e^(b*z^r+d*z)*(%e^(c*z^r+f*z+g))^u ------------------ */
5244
5245 /* Problem 724: NEW 9-1 */
5246 expand(niceindices(integrate(z^n*%e^(d*z+b*z^2)*(%e^(g+f*z+c*z^2))^u,z))-
5247 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5248                *%e^(-z*(c*u*z+b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*(c*u+b)))
5249                *('sum(gamma_incomplete((i+1)/2,
5250                                        -(2*(c*u+b)*z+f*u+d)^2/(4*(c*u+b)))
5251                        *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)
5252                        *(2*(c*u+b)*z+f*u+d)^(i+1)
5253                        /((2*(c*u+b)*z+f*u+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
5254  /2));
5255 0;
5256
5257 /* Problem 725: NEW 10-1 */
5258 expand(niceindices(integrate(z^n*%e^(d*z+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5259 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5260                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5261                                     *(2*(f*u+d)*sqrt(z)+c*u+b)^(j+i)
5262                                     *(gamma_incomplete((j+i+1)/2,
5263                                                        -(2*(f*u+d)*sqrt(z)
5264                                                         +c*u+b)
5265                                                         ^2
5266                                                         /(4*(f*u+d)))
5267                                      *(c*u+b)*(2*(f*u+d)*sqrt(z)+c*u+b)
5268                                      +2*gamma_incomplete((j+i+2)/2,
5269                                                          -(2*(f*u+d)*sqrt(z)
5270                                                           +c*u+b)
5271                                                           ^2
5272                                                           /(4*(f*u+d)))
5273                                        *(f*u+d)
5274                                        *sqrt(
5275                                         (2*(f*u+d)*sqrt(z)+c*u+b)^2/(f*u+d)))
5276                            /((2*(f*u+d)*sqrt(z)+c*u+b)^2/(-f*u-d))
5277                             ^((j+i+1)/2),i,0,j),j,0,n))
5278           *(%e^(f*z+c*sqrt(z)+g))^u
5279           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*(f*u+d)))
5280  /(f*u+d)^(2*(n+1))));
5281 0;
5282
5283 /* ----- Involving z^n*%e^(b*z^r+d*z+e)*(%e^(c*z^r+f*z+g))^u ---------------- */
5284
5285 /* Problem 726: NEW 9-1 */
5286 expand(niceindices(integrate(z^n*%e^(e+d*z+b*z^2)*(%e^(g+f*z+c*z^2))^u,z))-
5287 (-(c*u+b)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5288                *%e^(-z*(c*u*z+b*z+f*u+d)+z*(b*z+d)-(f*u+d)^2/(4*(c*u+b))+e)
5289                *('sum(gamma_incomplete((i+1)/2,
5290                                        -(2*(c*u+b)*z+f*u+d)^2/(4*(c*u+b)))
5291                        *2^(i-n)*binomial(n,i)*(-f*u-d)^(n-i)
5292                        *(2*(c*u+b)*z+f*u+d)^(i+1)
5293                        /((2*(c*u+b)*z+f*u+d)^2/(-c*u-b))^((i+1)/2),i,0,n))
5294  /2));
5295 0;
5296
5297 /* Problem 727: NEW 10-1 */
5298 expand(niceindices(integrate(z^n*%e^(e+d*z+b*sqrt(z))*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5299 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5300                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b)^(2*n-j-i)
5301                                     *(2*(f*u+d)*sqrt(z)+c*u+b)^(j+i)
5302                                     *(gamma_incomplete((j+i+1)/2,
5303                                                        -(2*(f*u+d)*sqrt(z)
5304                                                         +c*u+b)
5305                                                         ^2
5306                                                         /(4*(f*u+d)))
5307                                      *(c*u+b)*(2*(f*u+d)*sqrt(z)+c*u+b)
5308                                      +2*gamma_incomplete((j+i+2)/2,
5309                                                          -(2*(f*u+d)*sqrt(z)
5310                                                           +c*u+b)
5311                                                           ^2
5312                                                           /(4*(f*u+d)))
5313                                        *(f*u+d)
5314                                        *sqrt(
5315                                         (2*(f*u+d)*sqrt(z)+c*u+b)^2/(f*u+d)))
5316                            /((2*(f*u+d)*sqrt(z)+c*u+b)^2/(-f*u-d))
5317                             ^((j+i+1)/2),i,0,j),j,0,n))
5318           *(%e^(f*z+c*sqrt(z)+g))^u
5319           *%e^(-f*u*z-c*u*sqrt(z)-(c*u+b)^2/(4*(f*u+d))+e)
5320  /(f*u+d)^(2*(n+1))));
5321 0;
5322
5323 /* ----- Involving z^(v-1)*(%e^(c*z))^q*(%e^(a*z))^u ------------------------ */
5324
5325 /* Problem 728: NEW 7-1 */
5326 diffcheck(integrate(z^(v-1)*(%e^(d*z))^q*(%e^(f*z))^u,z),z,factor);
5327 z^(v-1)*(%e^(d*z))^q*(%e^(f*z))^u;
5328
5329 /* Problem 729: NEW 7-1 */
5330 diffcheck(integrate(z^n*(%e^(d*z))^q*(%e^(f*z))^u,z),z,factor);
5331 z^n*(%e^(d*z))^q*(%e^(f*z))^u;
5332
5333 /* Problem 730: NEW 7-1 */
5334 diffcheck(integrate(z^(1/2+n)*(%e^(d*z))^q*(%e^(f*z))^u,z),z,factor);
5335 z^(1/2+n)*(%e^(d*z))^q*(%e^(f*z))^u;
5336
5337 /* ----- Involving z^(v-1)*(%e^(c*z))^q*(%e^(a*z+b))^u ---------------------- */
5338
5339 /* Problem 731: NEW 7-1 */
5340 diffcheck(integrate(z^(v-1)*(%e^(d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5341 z^(v-1)*(%e^(d*z))^q*(%e^(g+f*z))^u;
5342
5343 /* Problem 732: NEW 7-1 */
5344 diffcheck(integrate(z^n*(%e^(d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5345 z^n*(%e^(d*z))^q*(%e^(g+f*z))^u;
5346
5347 /* Problem 733: NEW 7-1 */
5348 diffcheck(integrate(z^(1/2+n)*(%e^(d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5349 z^(1/2+n)*(%e^(d*z))^q*(%e^(g+f*z))^u;
5350
5351 /* ----- Involving z^(v-1)*(%e^(c*z+d))^q*(%e^(a*z+b))^u -------------------- */
5352
5353 /* Problem 734: NEW 7-1 */
5354 diffcheck(integrate(z^(v-1)*(%e^(e+d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5355 z^(v-1)*(%e^(e+d*z))^q*(%e^(g+f*z))^u;
5356
5357 /* Problem 735: NEW 7-1 */
5358 diffcheck(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5359 z^n*(%e^(e+d*z))^q*(%e^(g+f*z))^u;
5360
5361 /* Problem 736: NEW 7-1 */
5362 diffcheck(integrate(z^(1/2+n)*(%e^(e+d*z))^q*(%e^(g+f*z))^u,z),z,factor);
5363 z^(1/2+n)*(%e^(e+d*z))^q*(%e^(g+f*z))^u;
5364
5365 /* ----- Involving z^n*(%e^(d*z))^q*(%e^(c*z^r))^u -------------------------- */
5366
5367 /* Problem 737: NEW 9-1 */
5368 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(c*z^2))^u,z))-
5369 (-c^(-n-1)*u^(-n-1)*(%e^(d*z))^q*%e^(-z*(c*u*z+d*q)-d^2*q^2/(4*c*u))
5370          *(%e^(c*z^2))^u
5371          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d*q)^2/(4*c*u))
5372                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*q^(n-i)
5373                        *(2*c*u*z+d*q)^(i+1)
5374                  /(-(2*c*u*z+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5375  /2));
5376 0;
5377
5378 /* Problem 738: NEW 10-1 */
5379 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(c*sqrt(z)))^u,z))-
5380 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5381                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5382                                      *(2*d*q*sqrt(z)+c*u)^(j+i)
5383                                      *(c
5384                                       *gamma_incomplete((j+i+1)/2,
5385                                                         -(2*d*q*sqrt(z)+c*u)^2
5386                                                          /(4*d*q))*u
5387                                       *(2*d*q*sqrt(z)+c*u)
5388                                       +2*d
5389                                         *gamma_incomplete((j+i+2)/2,
5390                                                           -(2*d*q*sqrt(z)+c*u)
5391                                                            ^2
5392                                                            /(4*d*q))*q
5393                                         *sqrt((2*d*q*sqrt(z)+c*u)^2/(d*q)))
5394                            /(-(2*d*q*sqrt(z)+c*u)^2/(d*q))^((j+i+1)/2),i,0,j),
5395                  j,0,n))*(%e^(c*sqrt(z)))^u*(%e^(d*z))^q
5396           *%e^(-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*d*q))
5397  /(d^(2*(n+1))*q^(2*(n+1)))));
5398 0;
5399
5400 /* ----- Involving z^n*(%e^(d*z+e))^q*(%e^(c*z^r))^u ------------------------ */
5401
5402 /* Problem 739: NEW 9-1 */
5403 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(c*z^2))^u,z)) -
5404 (-c^(-n-1)*u^(-n-1)*(%e^(d*z+e))^q*%e^(-z*(c*u*z+d*q)-d^2*q^2/(4*c*u))
5405          *(%e^(c*z^2))^u
5406          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d*q)^2/(4*c*u))
5407                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*q^(n-i)
5408                        *(2*c*u*z+d*q)^(i+1)
5409                  /(-(2*c*u*z+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5410  /2));
5411 0;
5412
5413 /* Problem 740: NEW 10-1 */
5414 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(c*sqrt(z)))^u,z))-
5415 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5416                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5417                                      *(2*d*q*sqrt(z)+c*u)^(j+i)
5418                                      *(c
5419                                       *gamma_incomplete((j+i+1)/2,
5420                                                         -(2*d*q*sqrt(z)+c*u)^2
5421                                                          /(4*d*q))*u
5422                                       *(2*d*q*sqrt(z)+c*u)
5423                                       +2*d
5424                                         *gamma_incomplete((j+i+2)/2,
5425                                                           -(2*d*q*sqrt(z)+c*u)
5426                                                            ^2
5427                                                            /(4*d*q))*q
5428                                         *sqrt((2*d*q*sqrt(z)+c*u)^2/(d*q)))
5429                            /(-(2*d*q*sqrt(z)+c*u)^2/(d*q))^((j+i+1)/2),i,0,j),
5430                  j,0,n))*(%e^(c*sqrt(z)))^u*(%e^(d*z+e))^q
5431           *%e^(-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*d*q))
5432  /(d^(2*(n+1))*q^(2*(n+1)))));
5433 0;
5434
5435 /* ----- Involving z^(v-1)*(%e^(b*z^r))^q*(%e^(c*z^r))^u -------------------- */
5436
5437 /* Problem 741: NEW 7-1 */
5438 diffcheck(integrate(z^(v-1)*(%e^(b*z^r))^q*(%e^(c*z^r))^u,z),z,factor);
5439 z^(v-1)*(%e^(b*z^r))^q*(%e^(c*z^r))^u;
5440
5441 /* Problem 742: NEW 7-1 */
5442 diffcheck(integrate(z^n*(%e^(b*z^2))^q*(%e^(c*z^2))^u,z),z,factor);
5443 z^n*(%e^(b*z^2))^q*(%e^(c*z^2))^u;
5444
5445 /* Problem 743: NEW 7-1 */
5446 diffcheck(integrate(z^(2*n)*(%e^(b*z^2))^q*(%e^(c*z^2))^u,z),z,factor);
5447 z^(2*n)*(%e^(b*z^2))^q*(%e^(c*z^2))^u;
5448
5449 /* Problem 744: NEW 7-1 */
5450 diffcheck(integrate(z^(1+2*n)*(%e^(b*z^2))^q*(%e^(c*z^2))^u,z),z,factor);
5451 z^(1+2*n)*(%e^(b*z^2))^q*(%e^(c*z^2))^u;
5452
5453 /* Problem 745: NEW 7-1 */
5454 diffcheck(integrate(z^n*(%e^(b*sqrt(z)))^q*(%e^(c*sqrt(z)))^u,z),z,factor);
5455 z^n*(%e^(b*sqrt(z)))^q*(%e^(c*sqrt(z)))^u;
5456
5457 /* ----- Involving z^n*(%e^(d*z)^q*(%e^(c*z^r+g))^u ------------------------- */
5458
5459 /* Problem 746: NEW 9-1 */
5460 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(g+c*z^2))^u,z))-
5461 (-c^(-n-1)*u^(-n-1)*(%e^(d*z))^q*%e^(-z*(c*u*z+d*q)-d^2*q^2/(4*c*u))
5462          *(%e^(c*z^2+g))^u
5463          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d*q)^2/(4*c*u))
5464                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*q^(n-i)
5465                        *(2*c*u*z+d*q)^(i+1)
5466                  /(-(2*c*u*z+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5467  /2));
5468 0;
5469
5470 /* Problem 747: NEW 10-1 */
5471 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(g+c*sqrt(z)))^u,z))-
5472 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5473                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5474                                      *(2*d*q*sqrt(z)+c*u)^(j+i)
5475                                      *(c
5476                                       *gamma_incomplete((j+i+1)/2,
5477                                                         -(2*d*q*sqrt(z)+c*u)^2
5478                                                          /(4*d*q))*u
5479                                       *(2*d*q*sqrt(z)+c*u)
5480                                       +2*d
5481                                         *gamma_incomplete((j+i+2)/2,
5482                                                           -(2*d*q*sqrt(z)+c*u)
5483                                                            ^2
5484                                                            /(4*d*q))*q
5485                                         *sqrt((2*d*q*sqrt(z)+c*u)^2/(d*q)))
5486                            /(-(2*d*q*sqrt(z)+c*u)^2/(d*q))^((j+i+1)/2),i,0,j),
5487                  j,0,n))*(%e^(c*sqrt(z)+g))^u*(%e^(d*z))^q
5488           *%e^(-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*d*q))
5489  /(d^(2*(n+1))*q^(2*(n+1)))));
5490 0;
5491
5492 /* ----- Involving z^n*(%e^(d*z+e)^q*(%e^(c*z^r+g))^u ----------------------- */
5493
5494 /* Problem 748: NEW 9-1 */
5495 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+c*z^2))^u,z))-
5496 (-c^(-n-1)*u^(-n-1)*(%e^(d*z+e))^q*%e^(-z*(c*u*z+d*q)-d^2*q^2/(4*c*u))
5497          *(%e^(c*z^2+g))^u
5498          *('sum(d^(n-i)*gamma_incomplete((i+1)/2,-(2*c*u*z+d*q)^2/(4*c*u))
5499                        *(-1)^(i-n)*2^(i-n)*binomial(n,i)*q^(n-i)
5500                        *(2*c*u*z+d*q)^(i+1)
5501                  /(-(2*c*u*z+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5502  /2));
5503 0;
5504
5505 /* Problem 749: NEW 10-1 */
5506 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+c*sqrt(z)))^u,z))-
5507 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5508                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5509                                      *(2*d*q*sqrt(z)+c*u)^(j+i)
5510                                      *(c
5511                                       *gamma_incomplete((j+i+1)/2,
5512                                                         -(2*d*q*sqrt(z)+c*u)^2
5513                                                          /(4*d*q))*u
5514                                       *(2*d*q*sqrt(z)+c*u)
5515                                       +2*d
5516                                         *gamma_incomplete((j+i+2)/2,
5517                                                           -(2*d*q*sqrt(z)+c*u)
5518                                                            ^2
5519                                                            /(4*d*q))*q
5520                                         *sqrt((2*d*q*sqrt(z)+c*u)^2/(d*q)))
5521                            /(-(2*d*q*sqrt(z)+c*u)^2/(d*q))^((j+i+1)/2),i,0,j),
5522                  j,0,n))*(%e^(c*sqrt(z)+g))^u*(%e^(d*z+e))^q
5523           *%e^(-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*d*q))
5524  /(d^(2*(n+1))*q^(2*(n+1)))));
5525 0;
5526
5527 /* ----- Involving z^(v-1)*(%e^(b*z^r)^q*(%e^(c*z^r+g))^u ------------------- */
5528
5529 /* Problem 750: NEW 7-1 */
5530 diffcheck(integrate(z^(v-1)*(%e^(b*z^r))^q*(%e^(g+c*z^r))^u,z),z,factor);
5531 z^(v-1)*(%e^(b*z^r))^q*(%e^(g+c*z^r))^u;
5532
5533 /* Problem 751: NEW 7-1 */
5534 diffcheck(integrate(z^n*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5535 z^n*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u;
5536
5537 /* Problem 752: NEW 7-1 */
5538 diffcheck(integrate(z^(2*n)*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5539 z^(2*n)*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u;
5540
5541 /* Problem 753: NEW 7-1 */
5542 diffcheck(integrate(z^(1+2*n)*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5543 z^(1+2*n)*(%e^(b*z^2))^q*(%e^(g+c*z^2))^u;
5544
5545 /* Problem 754: NEW 7-1 */
5546 diffcheck(integrate(z^n*(%e^(b*sqrt(z)))^q*(%e^(g+c*sqrt(z)))^u,z),z,factor);
5547 z^n*(%e^(b*sqrt(z)))^q*(%e^(g+c*sqrt(z)))^u;
5548
5549 /* ----- Involving z^(v-1)*(%e^(b*z^r+e)^q*(%e^(c*z^r+g))^u ----------------- */
5550
5551 /* Problem 755: NEW 7-1 */
5552 diffcheck(integrate(z^(v-1)*(%e^(e+b*z^r))^q*(%e^(g+c*z^r))^u,z),z,factor);
5553 z^(v-1)*(%e^(e+b*z^r))^q*(%e^(g+c*z^r))^u;
5554
5555 /* Problem 756: NEW 7-1 */
5556 diffcheck(integrate(z^n*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5557 z^n*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u;
5558
5559 /* Problem 757: NEW 7-1 */
5560 diffcheck(integrate(z^(2*n)*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5561 z^(2*n)*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u;
5562
5563 /* Problem 758: NEW 7-1 */
5564 diffcheck(integrate(z^(1+2*n)*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u,z),z,factor);
5565 z^(1+2*n)*(%e^(e+b*z^2))^q*(%e^(g+c*z^2))^u;
5566
5567 /* Problem 759: NEW 7-1 */
5568 diffcheck(integrate(z^n*(%e^(e+b*sqrt(z)))^q*(%e^(g+c*sqrt(z)))^u,z),z,factor);
5569 z^n*(%e^(e+b*sqrt(z)))^q*(%e^(g+c*sqrt(z)))^u;
5570
5571 /* ----- Involving z^n*(%e^(d*z)^q*(%e^(c*z^r+f*z))^u ----------------------- */
5572
5573 /* Problem 760: NEW 9-1 */
5574 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(f*z+c*z^2))^u,z))-
5575 (-c^(-n-1)*u^(-n-1)*(%e^(d*z))^q*(%e^(z*(c*z+f)))^u
5576          *%e^(-z*(c*u*z+f*u+d*q)-(f*u+d*q)^2/(4*c*u))
5577          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d*q)^2/(4*c*u))
5578                  *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5579                  *(2*c*u*z+f*u+d*q)^(i+1)
5580                  /(-(2*c*u*z+f*u+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5581  /2));
5582 0;
5583
5584 /* Problem 761: NEW 10-1 */
5585 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5586 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5587                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5588                                      *(2*(f*u+d*q)*sqrt(z)+c*u)^(j+i)
5589                                      *(c
5590                                       *gamma_incomplete((j+i+1)/2,
5591                                                         -(2*(f*u+d*q)*sqrt(z)
5592                                                          +c*u)
5593                                                          ^2
5594                                                          /(4*(f*u+d*q)))*u
5595                                       *(2*(f*u+d*q)*sqrt(z)+c*u)
5596                                       +2
5597                                        *gamma_incomplete((j+i+2)/2,
5598                                                          -(2*(f*u+d*q)*sqrt(z)
5599                                                           +c*u)
5600                                                           ^2
5601                                                           /(4*(f*u+d*q)))
5602                                        *(f*u+d*q)
5603                                        *sqrt(
5604                                         (2*(f*u+d*q)*sqrt(z)+c*u)^2
5605                                          /(f*u+d*q)))
5606                            /((2*(f*u+d*q)*sqrt(z)+c*u)^2/(-f*u-d*q))
5607                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z))^q
5608           *(%e^(f*z+c*sqrt(z)))^u
5609           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d*q)))
5610  /(f*u+d*q)^(2*(n+1))));
5611 0;
5612
5613 /* ----- Involving z^n*(%e^(d*z+e)^q*(%e^(c*z^r+f*z))^u --------------------- */
5614
5615 /* Problem 762: NEW 9-1 */
5616 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(f*z+c*z^2))^u,z))-
5617 (-c^(-n-1)*u^(-n-1)*(%e^(z*(c*z+f)))^u*(%e^(d*z+e))^q
5618          *%e^(-z*(c*u*z+f*u+d*q)-(f*u+d*q)^2/(4*c*u))
5619          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d*q)^2/(4*c*u))
5620                  *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5621                  *(2*c*u*z+f*u+d*q)^(i+1)
5622                  /(-(2*c*u*z+f*u+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5623  /2));
5624 0;
5625
5626 /* Problem 763: NEW 10-1 */
5627 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5628 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5629                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5630                                      *(2*(f*u+d*q)*sqrt(z)+c*u)^(j+i)
5631                                      *(c
5632                                       *gamma_incomplete((j+i+1)/2,
5633                                                         -(2*(f*u+d*q)*sqrt(z)
5634                                                          +c*u)
5635                                                          ^2
5636                                                          /(4*(f*u+d*q)))*u
5637                                       *(2*(f*u+d*q)*sqrt(z)+c*u)
5638                                       +2
5639                                        *gamma_incomplete((j+i+2)/2,
5640                                                          -(2*(f*u+d*q)*sqrt(z)
5641                                                           +c*u)
5642                                                           ^2
5643                                                           /(4*(f*u+d*q)))
5644                                        *(f*u+d*q)
5645                                        *sqrt(
5646                                         (2*(f*u+d*q)*sqrt(z)+c*u)^2
5647                                          /(f*u+d*q)))
5648                            /((2*(f*u+d*q)*sqrt(z)+c*u)^2/(-f*u-d*q))
5649                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z+e))^q
5650           *(%e^(f*z+c*sqrt(z)))^u
5651           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d*q)))
5652  /(f*u+d*q)^(2*(n+1))));
5653 0;
5654
5655 /* ----- Involving z^n*(%e^(b*z^r)^q*(%e^(c*z^r+f*z))^u --------------------- */
5656
5657 /* Problem 764: NEW 9-1 */
5658 expand(niceindices(integrate(z^n*(%e^(b*z^2))^q*(%e^(f*z+c*z^2))^u,z))-
5659 (-(c*u+b*q)^(-n-1)*(%e^(z*(c*z+f)))^u
5660                  *%e^(-z*(c*u*z+b*q*z+f*u)-f^2*u^2/(4*(c*u+b*q)))
5661                  *(%e^(b*z^2))^q
5662                  *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5663                                                  -(2*(c*u+b*q)*z+f*u)^2
5664                                                   /(4*(c*u+b*q)))*(-1)^(i-n)
5665                                *2^(i-n)*binomial(n,i)*u^(n-i)
5666                                *(2*(c*u+b*q)*z+f*u)^(i+1)
5667                          /((2*(c*u+b*q)*z+f*u)^2/(-c*u-b*q))^((i+1)/2),i,0,n))
5668  /2));
5669 0;
5670
5671 /* Problem 765: NEW 10-1 */
5672 expand(niceindices(integrate(z^n*(%e^(b*sqrt(z)))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5673 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5674                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5675                                     *(2*f*u*sqrt(z)+c*u+b*q)^(j+i)
5676                                     *(gamma_incomplete((j+i+1)/2,
5677                                                        -(2*f*u*sqrt(z)
5678                                                         +c*u+b*q)
5679                                                         ^2
5680                                                         /(4*f*u))
5681                                      *(c*u+b*q)*(2*f*u*sqrt(z)+c*u+b*q)
5682                                      +2*f
5683                                        *gamma_incomplete((j+i+2)/2,
5684                                                          -(2*f*u*sqrt(z)
5685                                                           +c*u+b*q)
5686                                                           ^2
5687                                                           /(4*f*u))*u
5688                                        *sqrt((2*f*u*sqrt(z)+c*u+b*q)^2/(f*u)))
5689                            /(-(2*f*u*sqrt(z)+c*u+b*q)^2/(f*u))^((j+i+1)/2),i,
5690                           0,j),j,0,n))*(%e^(b*sqrt(z)))^q
5691           *(%e^(f*z+c*sqrt(z)))^u
5692           *%e^(-f*u*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*f*u))
5693  /(f^(2*(n+1))*u^(2*(n+1)))));
5694 0;
5695
5696 /* ----- Involving z^n*(%e^(b*z^r+e)^q*(%e^(c*z^r+f*z))^u ------------------- */
5697
5698 /* Problem 766: NEW 9-1 */
5699 expand(niceindices(integrate(z^n*(%e^(e+b*z^2))^q*(%e^(f*z+c*z^2))^u,z))-
5700 (-(c*u+b*q)^(-n-1)*(%e^(z*(c*z+f)))^u
5701                  *%e^(-z*(c*u*z+b*q*z+f*u)-f^2*u^2/(4*(c*u+b*q)))
5702                  *(%e^(b*z^2+e))^q
5703                  *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5704                                                  -(2*(c*u+b*q)*z+f*u)^2
5705                                                   /(4*(c*u+b*q)))*(-1)^(i-n)
5706                                *2^(i-n)*binomial(n,i)*u^(n-i)
5707                                *(2*(c*u+b*q)*z+f*u)^(i+1)
5708                          /((2*(c*u+b*q)*z+f*u)^2/(-c*u-b*q))^((i+1)/2),i,0,n))
5709  /2));
5710 0;
5711
5712 /* Problem 767: NEW 10-1 */
5713 expand(niceindices(integrate(z^n*(%e^(e+b*sqrt(z)))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5714 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5715                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5716                                     *(2*f*u*sqrt(z)+c*u+b*q)^(j+i)
5717                                     *(gamma_incomplete((j+i+1)/2,
5718                                                        -(2*f*u*sqrt(z)
5719                                                         +c*u+b*q)
5720                                                         ^2
5721                                                         /(4*f*u))
5722                                      *(c*u+b*q)*(2*f*u*sqrt(z)+c*u+b*q)
5723                                      +2*f
5724                                        *gamma_incomplete((j+i+2)/2,
5725                                                          -(2*f*u*sqrt(z)
5726                                                           +c*u+b*q)
5727                                                           ^2
5728                                                           /(4*f*u))*u
5729                                        *sqrt((2*f*u*sqrt(z)+c*u+b*q)^2/(f*u)))
5730                            /(-(2*f*u*sqrt(z)+c*u+b*q)^2/(f*u))^((j+i+1)/2),i,
5731                           0,j),j,0,n))*(%e^(b*sqrt(z)+e))^q
5732           *(%e^(f*z+c*sqrt(z)))^u
5733           *%e^(-f*u*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*f*u))
5734  /(f^(2*(n+1))*u^(2*(n+1)))));
5735 0;
5736
5737 /* ----- Involving z^n*(%e^(b*z^r+d*z)^q*(%e^(c*z^r+f*z))^u ----------------- */
5738
5739 /* Problem 768: NEW 9-1 */
5740 expand(niceindices(integrate(z^n*(%e^(d*z+b*z^2))^q*(%e^(f*z+c*z^2))^u,z))-
5741 (-(c*u+b*q)^(-n-1)*(%e^(z*(b*z+d)))^q*(%e^(z*(c*z+f)))^u
5742                  *%e^(-z*(c*u*z+b*q*z+f*u+d*q)-(f*u+d*q)^2/(4*(c*u+b*q)))
5743                  *('sum(gamma_incomplete((i+1)/2,
5744                                          -(2*(c*u+b*q)*z+f*u+d*q)^2
5745                                           /(4*(c*u+b*q)))
5746                          *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5747                          *(2*(c*u+b*q)*z+f*u+d*q)^(i+1)
5748                          /((2*(c*u+b*q)*z+f*u+d*q)^2/(-c*u-b*q))^((i+1)/2),i,
5749                         0,n))
5750  /2));
5751 0;
5752
5753 /* Problem 769: NEW 10-1 */
5754 expand(niceindices(integrate(z^n*(%e^(d*z+b*sqrt(z)))^q*(%e^(f*z+c*sqrt(z)))^u,z))-
5755 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5756                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5757                                     *(2*(f*u+d*q)*sqrt(z)+c*u+b*q)^(j+i)
5758                                     *(gamma_incomplete((j+i+1)/2,
5759                                                        -(2*(f*u+d*q)*sqrt(z)
5760                                                         +c*u+b*q)
5761                                                         ^2
5762                                                         /(4*(f*u+d*q)))
5763                                      *(c*u+b*q)*(2*(f*u+d*q)*sqrt(z)+c*u+b*q)
5764                                      +2*gamma_incomplete((j+i+2)/2,
5765                                                          -(2*(f*u+d*q)*sqrt(z)
5766                                                           +c*u+b*q)
5767                                                           ^2
5768                                                           /(4*(f*u+d*q)))
5769                                        *(f*u+d*q)
5770                                        *sqrt(
5771                                         (2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2
5772                                          /(f*u+d*q)))
5773                            /((2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2/(-f*u-d*q))
5774                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z+b*sqrt(z)))^q
5775           *(%e^(f*z+c*sqrt(z)))^u
5776           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*(f*u+d*q)))
5777  /(f*u+d*q)^(2*(n+1))));
5778 0;
5779
5780 /* ----- Involving z^n*(%e^(d*z)^q*(%e^(c*z^r+f*z+g))^u --------------------- */
5781
5782 /* Problem 770: NEW 9-1 */
5783 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(g+f*z+c*z^2))^u,z))-
5784 (-c^(-n-1)*u^(-n-1)*(%e^(d*z))^q*(%e^(z*(c*z+f)+g))^u
5785          *%e^(-z*(c*u*z+f*u+d*q)-(f*u+d*q)^2/(4*c*u))
5786          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d*q)^2/(4*c*u))
5787                  *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5788                  *(2*c*u*z+f*u+d*q)^(i+1)
5789                  /(-(2*c*u*z+f*u+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5790  /2));
5791 0;
5792
5793 /* Problem 771: NEW 10-1 */
5794 expand(niceindices(integrate(z^n*(%e^(d*z))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5795 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5796                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5797                                      *(2*(f*u+d*q)*sqrt(z)+c*u)^(j+i)
5798                                      *(c
5799                                       *gamma_incomplete((j+i+1)/2,
5800                                                         -(2*(f*u+d*q)*sqrt(z)
5801                                                          +c*u)
5802                                                          ^2
5803                                                          /(4*(f*u+d*q)))*u
5804                                       *(2*(f*u+d*q)*sqrt(z)+c*u)
5805                                       +2
5806                                        *gamma_incomplete((j+i+2)/2,
5807                                                          -(2*(f*u+d*q)*sqrt(z)
5808                                                           +c*u)
5809                                                           ^2
5810                                                           /(4*(f*u+d*q)))
5811                                        *(f*u+d*q)
5812                                        *sqrt(
5813                                         (2*(f*u+d*q)*sqrt(z)+c*u)^2
5814                                          /(f*u+d*q)))
5815                            /((2*(f*u+d*q)*sqrt(z)+c*u)^2/(-f*u-d*q))
5816                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z))^q
5817           *(%e^(f*z+c*sqrt(z)+g))^u
5818           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d*q)))
5819  /(f*u+d*q)^(2*(n+1))));
5820  0;
5821
5822 /* ----- Involving z^n*(%e^(d*z+e)^q*(%e^(c*z^r+f*z+g))^u ------------------- */
5823
5824 /* Problem 772: NEW 9-1 */
5825 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+f*z+c*z^2))^u,z))-
5826 (-c^(-n-1)*u^(-n-1)*(%e^(d*z+e))^q*(%e^(z*(c*z+f)+g))^u
5827          *%e^(-z*(c*u*z+f*u+d*q)-(f*u+d*q)^2/(4*c*u))
5828          *('sum(gamma_incomplete((i+1)/2,-(2*c*u*z+f*u+d*q)^2/(4*c*u))
5829                  *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5830                  *(2*c*u*z+f*u+d*q)^(i+1)
5831                  /(-(2*c*u*z+f*u+d*q)^2/(c*u))^((i+1)/2),i,0,n))
5832  /2));
5833 0;
5834
5835 /* Problem 773: NEW 10-1 */
5836 expand(niceindices(integrate(z^n*(%e^(e+d*z))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5837 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5838                     *'sum(c^(2*n-j-i)*(-1)^(i-j)*binomial(j,i)*u^(2*n-j-i)
5839                                      *(2*(f*u+d*q)*sqrt(z)+c*u)^(j+i)
5840                                      *(c
5841                                       *gamma_incomplete((j+i+1)/2,
5842                                                         -(2*(f*u+d*q)*sqrt(z)
5843                                                          +c*u)
5844                                                          ^2
5845                                                          /(4*(f*u+d*q)))*u
5846                                       *(2*(f*u+d*q)*sqrt(z)+c*u)
5847                                       +2
5848                                        *gamma_incomplete((j+i+2)/2,
5849                                                          -(2*(f*u+d*q)*sqrt(z)
5850                                                           +c*u)
5851                                                           ^2
5852                                                           /(4*(f*u+d*q)))
5853                                        *(f*u+d*q)
5854                                        *sqrt(
5855                                         (2*(f*u+d*q)*sqrt(z)+c*u)^2
5856                                          /(f*u+d*q)))
5857                            /((2*(f*u+d*q)*sqrt(z)+c*u)^2/(-f*u-d*q))
5858                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z+e))^q
5859           *(%e^(f*z+c*sqrt(z)+g))^u
5860           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-c^2*u^2/(4*(f*u+d*q)))
5861  /(f*u+d*q)^(2*(n+1))));
5862 0;
5863
5864 /* ----- Involving z^n*(%e^(b*z^r)^q*(%e^(c*z^r+f*z+g))^u ------------------- */
5865
5866 /* Problem 774: NEW 9-1 */
5867 expand(niceindices(integrate(z^n*(%e^(b*z^2))^q*(%e^(g+f*z+c*z^2))^u,z))-
5868 (-(c*u+b*q)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5869                  *%e^(-z*(c*u*z+b*q*z+f*u)-f^2*u^2/(4*(c*u+b*q)))
5870                  *(%e^(b*z^2))^q
5871                  *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5872                                                  -(2*(c*u+b*q)*z+f*u)^2
5873                                                   /(4*(c*u+b*q)))*(-1)^(i-n)
5874                                *2^(i-n)*binomial(n,i)*u^(n-i)
5875                                *(2*(c*u+b*q)*z+f*u)^(i+1)
5876                          /((2*(c*u+b*q)*z+f*u)^2/(-c*u-b*q))^((i+1)/2),i,0,n))
5877  /2));
5878 0;
5879
5880 /* Problem 775: NEW 10-1 */
5881 expand(niceindices(integrate(z^n*(%e^(b*sqrt(z)))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5882 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5883                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5884                                     *(2*f*u*sqrt(z)+c*u+b*q)^(j+i)
5885                                     *(gamma_incomplete((j+i+1)/2,
5886                                                        -(2*f*u*sqrt(z)
5887                                                         +c*u+b*q)
5888                                                         ^2
5889                                                         /(4*f*u))
5890                                      *(c*u+b*q)*(2*f*u*sqrt(z)+c*u+b*q)
5891                                      +2*f
5892                                        *gamma_incomplete((j+i+2)/2,
5893                                                          -(2*f*u*sqrt(z)
5894                                                           +c*u+b*q)
5895                                                           ^2
5896                                                           /(4*f*u))*u
5897                                        *sqrt((2*f*u*sqrt(z)+c*u+b*q)^2/(f*u)))
5898                            /(-(2*f*u*sqrt(z)+c*u+b*q)^2/(f*u))^((j+i+1)/2),i,
5899                           0,j),j,0,n))*(%e^(b*sqrt(z)))^q
5900           *(%e^(f*z+c*sqrt(z)+g))^u
5901           *%e^(-f*u*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*f*u))
5902  /(f^(2*(n+1))*u^(2*(n+1)))));
5903 0;
5904
5905 /* ----- Involving z^n*(%e^(b*z^r+e)^q*(%e^(c*z^r+f*z+g))^u ----------------- */
5906
5907 /* Problem 776: NEW 9-1 */
5908 expand(niceindices(integrate(z^n*(%e^(e+b*z^2))^q*(%e^(g+f*z+c*z^2))^u,z))-
5909 (-(c*u+b*q)^(-n-1)*(%e^(z*(c*z+f)+g))^u
5910                  *%e^(-z*(c*u*z+b*q*z+f*u)-f^2*u^2/(4*(c*u+b*q)))
5911                  *(%e^(b*z^2+e))^q
5912                  *('sum(f^(n-i)*gamma_incomplete((i+1)/2,
5913                                                  -(2*(c*u+b*q)*z+f*u)^2
5914                                                   /(4*(c*u+b*q)))*(-1)^(i-n)
5915                                *2^(i-n)*binomial(n,i)*u^(n-i)
5916                                *(2*(c*u+b*q)*z+f*u)^(i+1)
5917                          /((2*(c*u+b*q)*z+f*u)^2/(-c*u-b*q))^((i+1)/2),i,0,n))
5918  /2));
5919 0;
5920
5921 /* Problem 777: NEW 10-1 */
5922 expand(niceindices(integrate(z^n*(%e^(e+b*sqrt(z)))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5923 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5924                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5925                                     *(2*f*u*sqrt(z)+c*u+b*q)^(j+i)
5926                                     *(gamma_incomplete((j+i+1)/2,
5927                                                        -(2*f*u*sqrt(z)
5928                                                         +c*u+b*q)
5929                                                         ^2
5930                                                         /(4*f*u))
5931                                      *(c*u+b*q)*(2*f*u*sqrt(z)+c*u+b*q)
5932                                      +2*f
5933                                        *gamma_incomplete((j+i+2)/2,
5934                                                          -(2*f*u*sqrt(z)
5935                                                           +c*u+b*q)
5936                                                           ^2
5937                                                           /(4*f*u))*u
5938                                        *sqrt((2*f*u*sqrt(z)+c*u+b*q)^2/(f*u)))
5939                            /(-(2*f*u*sqrt(z)+c*u+b*q)^2/(f*u))^((j+i+1)/2),i,
5940                           0,j),j,0,n))*(%e^(b*sqrt(z)+e))^q
5941           *(%e^(f*z+c*sqrt(z)+g))^u
5942           *%e^(-f*u*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*f*u))
5943  /(f^(2*(n+1))*u^(2*(n+1)))));
5944 0;
5945
5946 /* ----- Involving z^n*(%e^(b*z^r+d*z)^q*(%e^(c*z^r+f*z+g))^u --------------- */
5947
5948 /* Problem 778: NEW 9-1 */
5949 expand(niceindices(integrate(z^n*(%e^(d*z+b*z^2))^q*(%e^(g+f*z+c*z^2))^u,z))-
5950 (-(c*u+b*q)^(-n-1)*(%e^(z*(b*z+d)))^q*(%e^(z*(c*z+f)+g))^u
5951                  *%e^(-z*(c*u*z+b*q*z+f*u+d*q)-(f*u+d*q)^2/(4*(c*u+b*q)))
5952                  *('sum(gamma_incomplete((i+1)/2,
5953                                          -(2*(c*u+b*q)*z+f*u+d*q)^2
5954                                           /(4*(c*u+b*q)))
5955                          *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
5956                          *(2*(c*u+b*q)*z+f*u+d*q)^(i+1)
5957                          /((2*(c*u+b*q)*z+f*u+d*q)^2/(-c*u-b*q))^((i+1)/2),i,
5958                         0,n))
5959  /2));
5960 0;
5961
5962 /* Problem 779: NEW 10-1 */
5963 expand(
5964   niceindices(integrate(z^n*(%e^(d*z+b*sqrt(z)))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
5965 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
5966                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
5967                                     *(2*(f*u+d*q)*sqrt(z)+c*u+b*q)^(j+i)
5968                                     *(gamma_incomplete((j+i+1)/2,
5969                                                        -(2*(f*u+d*q)*sqrt(z)
5970                                                         +c*u+b*q)
5971                                                         ^2
5972                                                         /(4*(f*u+d*q)))
5973                                      *(c*u+b*q)*(2*(f*u+d*q)*sqrt(z)+c*u+b*q)
5974                                      +2*gamma_incomplete((j+i+2)/2,
5975                                                          -(2*(f*u+d*q)*sqrt(z)
5976                                                           +c*u+b*q)
5977                                                           ^2
5978                                                           /(4*(f*u+d*q)))
5979                                        *(f*u+d*q)
5980                                        *sqrt(
5981                                         (2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2
5982                                          /(f*u+d*q)))
5983                            /((2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2/(-f*u-d*q))
5984                             ^((j+i+1)/2),i,0,j),j,0,n))*(%e^(d*z+b*sqrt(z)))^q
5985           *(%e^(f*z+c*sqrt(z)+g))^u
5986           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*(f*u+d*q)))
5987  /(f*u+d*q)^(2*(n+1))))$
5988 0;
5989
5990 /* ----- Involving z^n*(%e^(b*z^r+d*z+e)^q*(%e^(c*z^r+f*z+g))^u ------------- */
5991
5992 /* Problem 780: NEW 9-1 */
5993 expand(niceindices(integrate(z^n*(%e^(e+d*z+b*z^2))^q*(%e^(g+f*z+c*z^2))^u,z))-
5994 (-(c*u+b*q)^(-n-1)*(%e^(z*(b*z+d)+e))^q*(%e^(z*(c*z+f)+g))^u
5995                  *%e^(-z*(c*u*z+b*q*z+f*u+d*q)-(f*u+d*q)^2/(4*(c*u+b*q)))
5996                  *('sum(gamma_incomplete((i+1)/2,
5997                                          -(2*(c*u+b*q)*z+f*u+d*q)^2
5998                                           /(4*(c*u+b*q)))
5999                          *2^(i-n)*binomial(n,i)*(-f*u-d*q)^(n-i)
6000                          *(2*(c*u+b*q)*z+f*u+d*q)^(i+1)
6001                          /((2*(c*u+b*q)*z+f*u+d*q)^2/(-c*u-b*q))^((i+1)/2),i,
6002                         0,n))
6003  /2));
6004 0;
6005
6006 /* Problem 781: NEW 10-1
6007  * This result must be checked more carefully.
6008  */
6009 expand(
6010   niceindices(integrate(z^n*(%e^(e+d*z+b*sqrt(z)))^q*(%e^(g+f*z+c*sqrt(z)))^u,z))-
6011 (2^(-2*n-1)*('sum(4^j*binomial(n,j)
6012                     *'sum((-1)^(i-j)*binomial(j,i)*(c*u+b*q)^(2*n-j-i)
6013                                     *(2*(f*u+d*q)*sqrt(z)+c*u+b*q)^(j+i)
6014                                     *(gamma_incomplete((j+i+1)/2,
6015                                                        -(2*(f*u+d*q)*sqrt(z)
6016                                                         +c*u+b*q)
6017                                                         ^2
6018                                                         /(4*(f*u+d*q)))
6019                                      *(c*u+b*q)*(2*(f*u+d*q)*sqrt(z)+c*u+b*q)
6020                                      +2*gamma_incomplete((j+i+2)/2,
6021                                                          -(2*(f*u+d*q)*sqrt(z)
6022                                                           +c*u+b*q)
6023                                                           ^2
6024                                                           /(4*(f*u+d*q)))
6025                                        *(f*u+d*q)
6026                                        *sqrt(
6027                                         (2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2
6028                                          /(f*u+d*q)))
6029                            /((2*(f*u+d*q)*sqrt(z)+c*u+b*q)^2/(-f*u-d*q))
6030                             ^((j+i+1)/2),i,0,j),j,0,n))
6031           *(%e^(d*z+b*sqrt(z)+e))^q*(%e^(f*z+c*sqrt(z)+g))^u
6032           *%e^(-f*u*z-d*q*z-c*u*sqrt(z)-b*q*sqrt(z)-(c*u+b*q)^2/(4*(f*u+d*q)))
6033  /(f*u+d*q)^(2*(n+1))))$
6034 0;
6035
6036 /* Involving rational functions of the direct functions and a power function  */
6037
6038 /* ----- Involving z^n/(a+b*%e^(c*z)) --------------------------------------- */
6039
6040 /* Problem 782: OK */
6041 integrate(z/(b*%e^(c*z)+a),z);
6042 log(%e^(c*z))^2/(2*a*c^2)-(log(%e^(c*z))*log(b*%e^(c*z)/a+1)
6043                           +li[2](-b*%e^(c*z)/a))
6044                           /(a*c^2)$
6045
6046 /* Problem 783: OK */
6047 integrate(z^2/(b*%e^(c*z)+a),z);
6048 2*(-log(%e^(c*z))^2*log(b*%e^(c*z)/a+1)/2
6049   +li[3](-b*%e^(c*z)/a)-log(%e^(c*z))*li[2](-b*%e^(c*z)/a))
6050  /(a*c^3)
6051  +log(%e^(c*z))^3/(3*a*c^3)$
6052
6053 /* Problem 784: OK */
6054 integrate(z^3/(b*%e^(c*z)+a),z);
6055 log(%e^(c*z))^4/(4*a*c^4)-6*(log(%e^(c*z))^3*log(b*%e^(c*z)/a+1)/6
6056                             +li[4](-b*%e^(c*z)/a)
6057                             -log(%e^(c*z))*li[3](-b*%e^(c*z)/a)
6058                             +log(%e^(c*z))^2*li[2](-b*%e^(c*z)/a)/2)
6059                           /(a*c^4)$
6060
6061 /* Problem 785: OK */
6062 integrate(z^4/(b*%e^(c*z)+a),z);
6063 24*(-log(%e^(c*z))^4*log(b*%e^(c*z)/a+1)/24
6064    +li[5](-b*%e^(c*z)/a)-log(%e^(c*z))*li[4](-b*%e^(c*z)/a)
6065    +log(%e^(c*z))^2*li[3](-b*%e^(c*z)/a)/2
6066    -log(%e^(c*z))^3*li[2](-b*%e^(c*z)/a)/6)
6067  /(a*c^5)
6068  +log(%e^(c*z))^5/(5*a*c^5)$
6069
6070 /* Problem 786: NOUN */
6071 integrate(z^n/(1-%e^(c*z)),z);
6072 'integrate(z^n/(1-%e^(c*z)),z);
6073
6074 /* ----- Involving z^n*(a+b*c^(d*z))^-m ------------------------------------- */
6075
6076 /* Problem 787: OK */
6077 expand(integrate(z/(b*c^(d*z)+a)^2,z));
6078 -log(%e^(log(c)*d*z))*log(b*%e^(log(c)*d*z)/a+1)/(a^2*log(c)^2*d^2)
6079  +log(b*%e^(log(c)*d*z)+a)/(a^2*log(c)^2*d^2)
6080  -li[2](-b*%e^(log(c)*d*z)/a)/(a^2*log(c)^2*d^2)
6081  +log(%e^(log(c)*d*z))^2/(2*a^2*log(c)^2*d^2)
6082  -log(%e^(log(c)*d*z))/(a^2*log(c)^2*d^2)
6083  +z/(a*b*log(c)*d*%e^(log(c)*d*z)+a^2*log(c)*d)$
6084
6085 /* Problem 788: OK */
6086 integrate(z^2/(b*c^(d*z)+a)^2,z);
6087 2*(-log(%e^(log(c)*d*z))^2*log(b*%e^(log(c)*d*z)/a+1)/2
6088   +li[3](-b*%e^(log(c)*d*z)/a)
6089   -log(%e^(log(c)*d*z))*li[2](-b*%e^(log(c)*d*z)/a))
6090  /(a^2*log(c)^3*d^3)
6091  +2*(log(%e^(log(c)*d*z))*log(b*%e^(log(c)*d*z)/a+1)
6092     +li[2](-b*%e^(log(c)*d*z)/a))
6093   /(a^2*log(c)^3*d^3)
6094  +(log(%e^(log(c)*d*z))^3-3*log(%e^(log(c)*d*z))^2)/(3*a^2*log(c)^3*d^3)
6095  +z^2/(a*b*log(c)*d*%e^(log(c)*d*z)+a^2*log(c)*d)$
6096
6097 /* Problem 789: OK */
6098 integrate(z^3/(b*c^(d*z)+a)^2,z);
6099 -6*(log(%e^(log(c)*d*z))^3*log(b*%e^(log(c)*d*z)/a+1)/6
6100    +li[4](-b*%e^(log(c)*d*z)/a)
6101    -log(%e^(log(c)*d*z))*li[3](-b*%e^(log(c)*d*z)/a)
6102    +log(%e^(log(c)*d*z))^2*li[2](-b*%e^(log(c)*d*z)/a)/2)
6103  /(a^2*log(c)^4*d^4)
6104  -6*(-log(%e^(log(c)*d*z))^2*log(b*%e^(log(c)*d*z)/a+1)/2
6105     +li[3](-b*%e^(log(c)*d*z)/a)
6106     -log(%e^(log(c)*d*z))*li[2](-b*%e^(log(c)*d*z)/a))
6107   /(a^2*log(c)^4*d^4)
6108  +(log(%e^(log(c)*d*z))^4-4*log(%e^(log(c)*d*z))^3)/(4*a^2*log(c)^4*d^4)
6109  +z^3/(a*b*log(c)*d*%e^(log(c)*d*z)+a^2*log(c)*d)$
6110
6111 /* Problem 790: OK */
6112 integrate(z^4/(b*c^(d*z)+a)^2,z);
6113 24*(-log(%e^(log(c)*d*z))^4*log(b*%e^(log(c)*d*z)/a+1)/24
6114    +li[5](-b*%e^(log(c)*d*z)/a)
6115    -log(%e^(log(c)*d*z))*li[4](-b*%e^(log(c)*d*z)/a)
6116    +log(%e^(log(c)*d*z))^2*li[3](-b*%e^(log(c)*d*z)/a)/2
6117    -log(%e^(log(c)*d*z))^3*li[2](-b*%e^(log(c)*d*z)/a)/6)
6118  /(a^2*log(c)^5*d^5)
6119  +24*(log(%e^(log(c)*d*z))^3*log(b*%e^(log(c)*d*z)/a+1)/6
6120      +li[4](-b*%e^(log(c)*d*z)/a)
6121      -log(%e^(log(c)*d*z))*li[3](-b*%e^(log(c)*d*z)/a)
6122      +log(%e^(log(c)*d*z))^2*li[2](-b*%e^(log(c)*d*z)/a)/2)
6123   /(a^2*log(c)^5*d^5)
6124  +(log(%e^(log(c)*d*z))^5-5*log(%e^(log(c)*d*z))^4)/(5*a^2*log(c)^5*d^5)
6125  +z^4/(a*b*log(c)*d*%e^(log(c)*d*z)+a^2*log(c)*d)$
6126
6127 /* ----- Involving z^n*%e^(c*z)/(a+b*%e^(c*z)) ------------------------------ */
6128
6129 /* Problem 791: NOUN */
6130 integrate(z*%e^(f*z)/(b*c^(d*z)+a),z);
6131 'integrate(z*%e^(f*z)/(b*c^(d*z)+a),z);
6132 /*  'integrate((a*(log(c)^2*d^2-log(c)*d*f)*z+a*log(c)*d)*%e^(f*z)
6133             /(b^2*(f^2-2*log(c)*d*f+log(c)^2*d^2)*%e^(2*log(c)*d*z)
6134              +a*b*(2*f^2-4*log(c)*d*f+2*log(c)^2*d^2)*%e^(log(c)*d*z)
6135              +a^2*(f^2-2*log(c)*d*f+log(c)^2*d^2)),z)
6136  -((log(c)*d-f)*z+1)*%e^(f*z)/(b*(f^2-2*log(c)*d*f+log(c)^2*d^2)
6137                                 *%e^(log(c)*d*z)
6138                               +a*(f^2-2*log(c)*d*f+log(c)^2*d^2));
6139 */
6140
6141 /* Problem 792: NOUN */
6142 integrate(z*%e^(d*z)/(b*%e^(c*z)+a),z);
6143 'integrate((a*(c^2-c*d)*z+a*c)*%e^(d*z)/(b^2*(d^2-2*c*d+c^2)*%e^(2*c*z)
6144                                         +a*b*(2*d^2-4*c*d+2*c^2)*%e^(c*z)
6145                                         +a^2*(d^2-2*c*d+c^2)),z)
6146  -((c-d)*z+1)*%e^(d*z)/(b*(d^2-2*c*d+c^2)*%e^(c*z)+a*(d^2-2*c*d+c^2));
6147
6148 /* Problem 793: OK */
6149 integrate(z*%e^(2*c*z)/(b*%e^(c*z)+a),z);
6150 -a*(log(%e^(c*z))*log(b*%e^(c*z)/a+1)+li[2](-b*%e^(c*z)/a))/(b^2*c^2)
6151  +a*log(%e^(c*z))^2/(2*b^2*c^2)+((2*b*c*z-2*b)*%e^(c*z)-a*c^2*z^2)/(2*b^2*c^2)$
6152
6153 /* Problem 794: OK */
6154 integrate(z*%e^-(2*c*z)/(b*%e^(c*z)+a),z);
6155 -b^2*(log(%e^(c*z))*log(b*%e^(c*z)/a+1)+li[2](-b*%e^(c*z)/a))/(a^3*c^2)
6156  +b^2*log(%e^(c*z))^2/(2*a^3*c^2)
6157  +((4*b*c*z+4*b)*%e^-(c*z)+(-2*a*c*z-a)*%e^-(2*c*z))/(4*a^2*c^2)$
6158
6159 /* Problem 795: OK */
6160 integrate(z*%e^(c*z)/(b*%e^(c*z)+a),z);
6161 (log(%e^(c*z))*log(b*%e^(c*z)/a+1)+li[2](-b*%e^(c*z)/a))/(b*c^2)
6162  -log(%e^(c*z))^2/(2*b*c^2)+z^2/(2*b)$
6163
6164 /* Problem 796: NOUN */
6165 integrate(z^2*%e^(f*z)/(b*c^(d*z)+a),z);
6166 'integrate(z^2*%e^(f*z)/(b*c^(d*z)+a),z);
6167 /* 'integrate((a*(log(c)*d*f^2-2*log(c)^2*d^2*f+log(c)^3*d^3)*z^2
6168             +a*(2*log(c)^2*d^2-2*log(c)*d*f)*z+2*a*log(c)*d)
6169             *%e^(f*z)
6170             /(b^2*(-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3)
6171                  *%e^(2*log(c)*d*z)
6172              +a*b*(-2*f^3+6*log(c)*d*f^2-6*log(c)^2*d^2*f+2*log(c)^3*d^3)
6173                *%e^(log(c)*d*z)
6174              +a^2*(-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3)),z)
6175  -((f^2-2*log(c)*d*f+log(c)^2*d^2)*z^2+(2*log(c)*d-2*f)*z+2)*%e^(f*z)
6176   /(b*(-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3)*%e^(log(c)*d*z)
6177    +a*(-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3));
6178 */
6179
6180 /* Problem 797: OK */
6181 integrate(z^2*%e^(c*z)/(b*%e^(c*z)+a),z);
6182 -2*(-log(%e^(c*z))^2*log(b*%e^(c*z)/a+1)/2
6183    +li[3](-b*%e^(c*z)/a)-log(%e^(c*z))*li[2](-b*%e^(c*z)/a))
6184  /(b*c^3)
6185  -log(%e^(c*z))^3/(3*b*c^3)+z^3/(3*b)$
6186
6187
6188 /* Problem 798: NOUN */
6189 integrate(z^3*%e^(f*z)/(b*c^(d*z)+a),z);
6190 'integrate(z^3*%e^(f*z)/(b*c^(d*z)+a),z);
6191 /* 'integrate((a*(-log(c)*d*f^3+3*log(c)^2*d^2*f^2-3*log(c)^3*d^3*f+log(c)^4*d^4)
6192              *z^3
6193             +a*(3*log(c)*d*f^2-6*log(c)^2*d^2*f+3*log(c)^3*d^3)*z^2
6194             +a*(6*log(c)^2*d^2-6*log(c)*d*f)*z+6*a*log(c)*d)
6195             *%e^(f*z)
6196             /(b^2*(f^4-4*log(c)*d*f^3+6*log(c)^2*d^2*f^2-4*log(c)^3*d^3*f
6197                       +log(c)^4*d^4)*%e^(2*log(c)*d*z)
6198              +a*b
6199                *(2*f^4-8*log(c)*d*f^3+12*log(c)^2*d^2*f^2-8*log(c)^3*d^3*f
6200                       +2*log(c)^4*d^4)*%e^(log(c)*d*z)
6201              +a^2*(f^4-4*log(c)*d*f^3+6*log(c)^2*d^2*f^2-4*log(c)^3*d^3*f
6202                       +log(c)^4*d^4)),z)
6203  -((-f^3+3*log(c)*d*f^2-3*log(c)^2*d^2*f+log(c)^3*d^3)*z^3
6204   +(3*f^2-6*log(c)*d*f+3*log(c)^2*d^2)*z^2+(6*log(c)*d-6*f)*z+6)
6205   *%e^(f*z)
6206   /(b*(f^4-4*log(c)*d*f^3+6*log(c)^2*d^2*f^2-4*log(c)^3*d^3*f+log(c)^4*d^4)
6207      *%e^(log(c)*d*z)
6208    +a*(f^4-4*log(c)*d*f^3+6*log(c)^2*d^2*f^2-4*log(c)^3*d^3*f+log(c)^4*d^4));
6209 */
6210
6211 /* Problem 799: OK */
6212 integrate(z^3*%e^(c*z)/(b*%e^(c*z)+a),z);
6213 6*(log(%e^(c*z))^3*log(b*%e^(c*z)/a+1)/6
6214   +li[4](-b*%e^(c*z)/a)-log(%e^(c*z))*li[3](-b*%e^(c*z)/a)
6215   +log(%e^(c*z))^2*li[2](-b*%e^(c*z)/a)/2)
6216  /(b*c^4)
6217  -log(%e^(c*z))^4/(4*b*c^4)+z^4/(4*b)$
6218
6219 /* Problem 800: OK */
6220 integrate(z^4*%e^(c*z)/(b*%e^(c*z)+a),z);
6221 -24*(-log(%e^(c*z))^4*log(b*%e^(c*z)/a+1)/24
6222     +li[5](-b*%e^(c*z)/a)-log(%e^(c*z))*li[4](-b*%e^(c*z)/a)
6223     +log(%e^(c*z))^2*li[3](-b*%e^(c*z)/a)/2
6224     -log(%e^(c*z))^3*li[2](-b*%e^(c*z)/a)/6)
6225  /(b*c^5)
6226  -log(%e^(c*z))^5/(5*b*c^5)+z^5/(5*b)$
6227
6228 /* ---- Involving z^n/(a*%e^(2*d*z)+b*%e^(d*z)+c) --------------------------- */
6229
6230 assume(4*a*c>b^2);
6231 [4*a*c>b^2];
6232
6233 /* Problem 802: NOUN */
6234 integrate(z/(c+b*%e^(d*z)+a*%e^(2*d*z)),z);
6235 'integrate(z/(a*%e^(2*d*z)+b*%e^(d*z)+c),z);
6236
6237 /* Problem 803: NOUN */
6238 integrate(z^2/(c+b*%e^(d*z)+a*%e^(2*d*z)),z);
6239 'integrate(z^2/(a*%e^(2*d*z)+b*%e^(d*z)+c),z);
6240
6241 /* Problem 804: NOUN */
6242 integrate(z^3/(c+b*%e^(d*z)+a*%e^(2*d*z)),z);
6243 'integrate(z^3/(a*%e^(2*d*z)+b*%e^(d*z)+c),z);
6244
6245 forget(4*a*c>b^2);
6246 [4*a*c>b^2];
6247
6248 /* ----- Involing z^n*(a+b*c^(d*z)^p ---------------------------------------- */
6249
6250 /* Problem 806: NOUN */
6251 integrate(z*(b*c^(d*z)+a)^p,z);
6252 'integrate((b*c^(d*z)+a)^p*z,z);
6253
6254 /* Problem 807: NOUN */
6255 integrate(z^2*(b*c^(d*z)+a)^p,z);
6256 'integrate((b*c^(d*z)+a)^p*z^2,z);
6257
6258 /* Problem 808: NOUN */
6259 integrate(z^3*(b*c^(d*z)+a)^p,z);
6260 'integrate((b*c^(d*z)+a)^p*z^3,z);
6261
6262 /* ----- Involing z^n*%e^(f*z)*(a+b*c^(d*z)^p ------------------------------- */
6263
6264 /* Problem 809: NOUN */
6265 integrate(z*%e^(f*z)*(b*c^(d*z)+a)^p,z);
6266 'integrate((b*c^(d*z)+a)^p*z*%e^(f*z),z);
6267
6268 /* Problem 810: NOUN */
6269 integrate(z^2*%e^(f*z)*(b*c^(d*z)+a)^p,z);
6270 'integrate((b*c^(d*z)+a)^p*z^2*%e^(f*z),z);
6271
6272 /* Problem 811: NOUN */
6273 integrate(z^3*%e^(f*z)*(b*c^(d*z)+a)^p,z);
6274 'integrate((b*c^(d*z)+a)^p*z^3*%e^(f*z),z);
6275
6276 /* Problem 812: NOUN */
6277 integrate(z^4*%e^(f*z)*(b*c^(d*z)+a)^p,z);
6278 'integrate((b*c^(d*z)+a)^p*z^4*%e^(f*z),z);
6279
6280 /* From the mailing list/20180123 */
6281 integrate(1/(r^2+1),r);
6282 atan(r);
6283
6284 /* SF bug report #3985: "integrate(sin(x*cos(x)), x), risch; causes unlimited recursion"
6285  * If ever Maxima knows an antiderivative for these,
6286  * we can fix up the expected results.
6287  */
6288 integrate (sin(x*cos(x)), x), risch;
6289 'integrate (sin(x*cos(x)), x);
6290
6291 risch (sin(x*cos(x)), x);
6292 'integrate (sin(x*cos(x)), x);
6293
6294 integrate (sin(x*cos(x)), x);
6295 'integrate (sin(x*cos(x)), x);
6296
6297 /* Tidy up */
6298 (reset(),
6299  forget(n>0,notequal(v,0)),
6300  remove(z,complex,n,integer),
6301  kill(all),
6302  0);
6303 0;
6304
6305 /* ----- End of file -------------------------------------------------------- */