I want to ask, whether there is possibility to give closed-form value to such expression;
$$ \int_{0}^1i(1-u)^{-1} u^{s-1} \left[e^{\left(2 \pi u+\frac{\pi s}{2}\right)}Li_{1-s}\left(e^{2\pi i n u}\right)-e^{-i\left(2 \pi u+\frac{\pi s}{2}\right)}Li_{1-s}\left(e^{-2 \pi i n u} \right)\right]du $$
Equation is from my previous question :Limiting problem for variable being part of derivative of natural degree, where I found way to represent Riemman's zeta function in the terms of given integral for $s \in \mathbb{N}$, $s \geq 2$.
I'm asking because I'm not good at all with integration, and it seems to have some closed form expression. I'm not shure, if it will be convergence in standard way, but I'm very optimistic about that result.
