besseltransforms/7-4-0

   1 Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
   2
   3                               -8 c x + I k0 x        c x 7                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
   4                              E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 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)))^7*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]