I must calculate

.

My attempt :

Let

. I've calculated the poles of

to be

,

,

and

.

I chose the curve

as being the circle centered at

with radius

.

So I have that

.

It remains to calculate the residues of

, which I wasn't able to do.

I tried to express

as a Laurent series but I didn't succeed in it.

I also tried to use the fact that the residues are worth

but without success in evaluating the limit.

So how could I find the residues of

?

Thanks in advance... and sorry! I find all this very difficult to grasp in such a few time.