I am trying to solve the following integral using a contour (large semi-circle connected to smaller semi-circle in the upper-half plane):
I have split the contour into 4 parts - the large semi-circle, the small semi-circle, the part on the negative real axis and the part on the positive real axis.
But something goes wrong with me and I can't come up with the result, which is the correct answer is $5\pi^5/32$.
So far what I have is the following:
∮f(z)dz=K1+K2+K3+K4 See image to notice who it is ∮f(z)dz https://i.stack.imgur.com/PuuN7.png
The point is, I'm at a loss to solve k2 and k4. It may be something simple but I still don't see the way.