I've been trying to show that

(I've not had any problems with the integration though)

I've tried and as substitutions, but I can only get so far before I get stuck.

The most progress I've made is with as the substitution, where I get but then I can't see how to proceed further.

Incidentally, I noticed that the graphs for and are different, so I think I'm probably using the wrong substitution.

Can anyone point me in the right direction?

(this is part of a question in complex analysis)