Few days before I posted one problem on MSE here in which it was asked to determine the residue. I understood almost entire but got stuck the following
Note that after step 4, in step 5 it is written that $$\frac{x^2}{2\zeta(2)}\frac{1}{u-1}+O(1)$$
I am unable to understand the steps. Can some one please help me to make it clear for me ?
Thank you