besseltransforms/klarge/5-2-0

   1 Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
   2 Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,2)*x),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 2 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
   3
   4                               -5 c x + I k0 x        c x 5                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
   5                              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]))
   6                                                                                                                                                              4
   7 Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
   8                                                                                                                                                           19/2   2             21/2
   9                                                                                                                                               8589934592 k     k0  Sqrt[2 Pi] x
  10 Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
  11
  12                                                                    12
  13 Simplify::time: Time spent on a transformation exceeded -3.93292 10   seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
  14 Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5]