besseltransforms/klarge/5-5-3

   1 Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
   2 Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(3,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
   3
   4                                                                                                                                                                                                             2  2              4  4               6  6               8  8
   5                               -5 c x + I k0 x        c x 5                                    2  2               4  4                6  6               8  8      Pi          35 (33129291195 - 3192583680 k  x  + 759103488 k  x  - 1660944384 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x])
   6                              E                (-1 + E   )  (8 k x (-41247931725 + 5881075200 k  x  - 2952069120 k  x  - 15854469120 k  x  + 2147483648 k  x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------)
   7                                                                                                                                                                   4                                                                Sqrt[2]
   8 Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}.
   9                                                                                                                                                         19/2   5             27/2
  10                                                                                                                                             8589934592 k     k0  Sqrt[2 Pi] x
  11 Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
  12
  13 Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
  14 Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5]