A Why Does This Integral Not Converge?

[nikos749]

How to solve $$\int_{-\infty}^{\infty} \frac{e^{-iax}coth[sinh[bx]]}{sinh[bx]} dx$$
mathematica gives the result ::idiv: "Integral of E^(-Iax)\ Coth[Sinh[bx]]\ Csch[bx] does not converge on {-\[Infinity],\[Infinity]}."
thanks!

 

[mitochan]

Hi.
How about trying complex integral. The integrand seem to have a pole of order 2 at z=0. You may calculate residue there.