besseltransforms/4-4-1

   1 Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && 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      Pi
   4                              -(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]))
   5                                                                                                                                                                  4                                                                                                            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[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]