1. How can I calculate the residue in z=1 of the next function:

??

I've tried using Laurent expansion but couldn't figure out how to expand this function into a series (using the known expansion of the exponent don't help us here... ).

2. Calculate the next Integral:

.

My problem with this question is that we have n singularities and they are all inside our contour... I've tried to paramterize but without any success..

Hope you'll be able to help me

Thanks in advance!