besseltransforms/7-6-4

   1 Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 4 && q == 6 && 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   )  (63 (-41829913125 + 5320972800 k  x  - 2389770240 k  x  - 11995709440 k  x  + 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (105411381075 - 22348085760 k  x  + 44281036800 k  x  - 58133053440 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   6             29/2
   8                                                                                                                                                   8589934592 k     k0  Sqrt[2 Pi] x
   9 Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 4 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]