I need to show that

If we complexify the integrand and make a sort of pacman-contour

with

with

with

with

As we let

This contour contains the 2 second order singularities

And we can evaluate with the Cauchy integral formula. I was somewhat surprised when I found . It's easy to check that

and

As a result we get

If all steps were ok, somehow I want to conclude that tends to

But I'm not sure how. Also I found working with log(z) somewhat trouble-some. I believe I need to use some nice property of log(z)

Can anyone offer some suggestions?