Hi, I need some help with my Complex analysis homework.

It is required to evaluate the integral

in TWO different ways using contour integration.

I have to consider the function

with a branch cut on [-1,1] Re(z) given the choice of

I need to find the value of:

around a circle of large radius

Which I am struggling with.

So far, I know it has cut from -1 to +1, and there are poles at +i and -i

Any help is appreciated.

Thanks.