I have to calculate analytically this integral:
$$
{\rm J}\left(q\right)
=
\int_{0}^{\infty}{{\rm d}x \over x^{q}\left({\rm e}^{kx}-1\right)}
$$
where $-1\le q\le N$
with:
$N\in\mathbb{N}$ and $q\in\mathbb{N}$, $k\le 5\times10^{-5}$
I didn't find anything on the Gradshteyn Ryzhik and Mathematica isn't able to integrate it. Is it possible to make some approximation because the little value of $k$? Thanks in advance.