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:
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