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(really really sorry, I don't know how to use latex yet but as of today I will begin learning!)

I chose to evaluate it around a semi-circle of radius R, R>3 (y>0 quadrants) and have found that there are poles at +/-3i and +/-2i. Though only two poles, 3i and 2i lie inside my contour.

I've calculated the residues and confirmed that they are indeed correct with wolfram. I suspect I'm doing something wrong with my region of integration since the integration limits are from 0-->infinity I may have chosen a stupid contour?

My final answer is pi/100 whereas wolfram calculates pi/200..