$$\iint\cdots\int_{\mathbb R^n}\left(\prod_{i=1}^n x_i^m\frac{e^{-x_i^2}}{e^\frac{x_i}{2}\cosh\left(\frac{x_i}{2}\right)}\right)d^nx$$
I have managed to bring it to a form where the elements of the gamma function appear but there are more terms that don't allow it to turn into said gamma function. $$\prod_{i=1}^n \int\left(\ x_i^m\frac{e^{-x_i^2}}{e^\frac{x_i}{2}\cosh\left(\frac{x_i}{2}\right)}\right)dx_i$$ so the product of the independent
$$ \int\ 2x^m\frac{e^{-x^2}}{e^x + 1}dx\ $$ I just don't know how to shake the $e^x + 1$
So...what I ended up with is $$ \sum_{n=0}^∞\sum_{k=0}^∞\ [\frac{(-1)^{n+k}*(m+2k)!}{k!}*[\frac{(-1)^m}{n^{m+2k+1}} +\frac{1}{(n+1)^{m+2k+1}}]]\ $$