Question

Integrate:
\[ \int_0^{\infty} \frac{\sin (ax)}{e^{2\pi x} - 1}dx\]
Does anyone know how to integrate it by the method of contour?

Answer 1

I'd be curious to learn the answer if you've got it.

Answer 2

this is complicated
http://math.stackexchange.com/questions/395822/integrate-int-0-infty-frac-sinh-ax-sinh-x-cos-bx-dx

Answer 3

Nuugh. Contour integration is so beautiful, but so hard!

Answer 4

I think it's the easiest way you can do with it.
The real methods are rather hard ... requires special functions.