besseltransforms/klarge/5-5-1

   1 Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && 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(1,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
   3
   4                                 -5 c x + I k0 x        c x 5                                    2  2              4  4              6  6               8  8      Pi                                         2  2               4  4              6  6               8  8      Pi
   5                              -(E                (-1 + E   )  (8 k x (-14783093325 + 1452971520 k  x  - 309657600 k  x  + 251658240 k  x  + 2147483648 k  x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k  x  + 1589575680 k  x  - 587202560 k  x  + 2147483648 k  x ) Sin[-- + k x]))
   6                                                                                                                                                                  4                                                                                                            4
   7 Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
   8                                                                                                                                                     19/2   5             27/2
   9                                                                                                                                         8589934592 k     k0  Sqrt[2 Pi] x
  10 Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
  11
  12 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.
  13 Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5]