[SOLVED] Calculating an improper integral via complex analysis

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.