Why Does This Integral Not Converge?

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nikos749
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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!
 
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Hi.
How about trying complex integral. The integrand seem to have a pole of order 2 at z=0. You may calculate residue there.
 

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