besseltransforms/7-7-5

   1 Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[5, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 5 && q == 7 && 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          99 (79857106875 - 15575938560 k  x  + 28894494720 k  x  - 38168166400 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x])
   5                              -(E                (-1 + E   )  (8 k x (-376469218125 + 156436600320 k  x  + 752777625600 k  x  - 151145938944 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   7             31/2
   9                                                                                                                                                   8589934592 k     k0  Sqrt[2 Pi] x
  10 Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[5, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 5 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]