Hi there

I've been trying to revise and have come across a question in Schaum's Advanced Calculus that has done out a question but has skipped a lot of steps and so I can't completely follow what's going on. I'd be ever so grateful if anyone could fill in the gaps for me.

The question is:

Show that =

I understand it all up to where he gets to

=

and I understand why he tries to find the residue at z=0 and .

I'd really appreciate it if anyone could tell me step by step how when

z=0 the residue =

and when the residue =

I'm new to these residue problems and am trying my best to work through them but skipping big steps in books doesn't help so if anyone could fill in the missing steps, I'd really appreciate it.

Regards

Michaela