Find the residue in of .

My attempt : I notice that is analytic except in . (well I think so! I guess I should show that is analytic. Is that sufficient that f satisfy C-R equations? Because as you'll see, I need the analyticity of for the coming part)

I believe that .

I forgot something very important : why does ? I mean, I think there's a theorem that justify it (it seems it's not Cauchy-Goursat theorem) but I forgot which one.

Am I right?