besseltransforms/7-6-3

   1 Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 3 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
   2
   3                                                                                                                                                                                                             2  2              4  4               6  6               8  8
   4                               -8 c x + I k0 x        c x 7                                    2  2               4  4                6  6               8  8      Pi          35 (33129291195 - 3192583680 k  x  + 759103488 k  x  - 1660944384 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x])
   5                              E                (-1 + E   )  (8 k x (-41247931725 + 5881075200 k  x  - 2952069120 k  x  - 15854469120 k  x  + 2147483648 k  x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------)
   6                                                                                                                                                                   4                                                                Sqrt[2]
   7 Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}.
   8                                                                                                                                                         19/2   6             29/2
   9                                                                                                                                             8589934592 k     k0  Sqrt[2 Pi] x
  10 Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 3 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]