I need a hint to evaluate the integrals:
$ \int _{0}^{p}\tanh(\pi k)k\,dk\quad \text{and}\quad \int _{0}^{s-1/2}\tan(\pi k)k\,dk $ Here $p$ and $s$ are real numbers.
I know I can evaluate them by power series but how else can I evaluate these two integrals ?
I know I can expand $ \tanh(x) $ and $ \tan(x) $ into a power series but I would like to get some 'closed' result in terms of $ \Gamma (x) $ function or similar.