I have to calculate analytically this integral: $$J(q)=\int_{0}^{+\infty}\frac{1}{x^q\left(\exp(kx)-1\right)}dx$$ 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.