besseltransforms/4-4-2

   1 Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
   2
   3                                 -5 c x + I k0 x        c x 4                                 2  2              4  4              6  6               8  8      Pi                                                   2  2              4  4               6  6               8  8
   4                              -(E                (-1 + E   )  (15 (-43692253605 + 3528645120 k  x  - 590413824 k  x  + 352321536 k  x  + 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k  x  + 681246720 k  x  - 1761607680 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x])))
   5                                                                                                                                                               4
   6 Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}.
   7                                                                                                                                                             19/2   4             25/2
   8                                                                                                                                                 8589934592 k     k0  Sqrt[2 Pi] x
   9 Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]