greetings . we have the integral :

$I(s)=\int_{0}^{\infty}\frac{s(E_{s}(x^{s})-1)-x}{x(e^{x}-1)}dx $

$E_{\alpha}(z)$ being the mittag-leffler function

the integral above behaves well for Re(s)>1 . i am trying to extend the domain of $I(s)$ to the whole complex plane except for some points. but i have no idea where to start !!