I am trying to compute this integral using the residue theorem. To do so, I am integrating in the frontier of this sector of a circle: .
I kwo how to deal with the integrals over the horizontal segment of the sector and over the arc of the circle. My problem is the "diagonal segment". When I parametrize it, I do not get something easy to integrate. How could I approach this?
(The path of integration was suggested in my book, so I do not think that is the problem).