There shouldn't be a problem there. Can you show me your calculation of the residue of f?
The integral is . I'll probably choose a semi circle as contour since the poles aren't on the real axis. Furthermore I think that .
Let . The singularities of f are when .
Now I want to calculate the residue of f at say one singularity. But it gives infinity I think. So I believe it's a pole of order greater than 1 but I'm unsure. I tried to use the Taylor series of sin(z) in order to see what happens in but I didn't reach anything.
So I don't know how to go further.