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 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0]
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 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0))
-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
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]))
4
Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
19/2 2 21/2
8589934592 k k0 Sqrt[2 Pi] x
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 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}]
