Hi, I'm new (and sorry for my bad english ), I'm trying to solve this complex integral and the result should be . I write what I did:

The function is integrable and it is not even, and I choose the auxiliary function with the square natural log.

The regular path I choose is the superior semicircle excluding singularity points: and . The two poles are (which falls inside) and .

.

The integral calculated on the semicicrcle centred in is and also the integral on the big semicircle is while the integral on the semicircle centred in is . Finally the residue on the pole is so:

so:

I change the sign of the integral I want find:

Considering only the coefficients with .

but this is not the result... :|

Some ideas?? Thanks for understanding