This is an exercise from Stein & Shakarchi - Complex Analysis
II.7) Prove that for
How do I start?
I know this function has a pole in
I know the function can be rewritten as: or as
What I do not know: what to do? Do I use the residue theorem? Do I look for a nice contour?
(Also in general: how to tackle complex integrals? Step by step.)