The aim is to evaluate . The strategy is to do a contour integral of the function for real around the contour consisting of two parts: the semi-circle { }, and the straight line segment from to .

(i) Explain why as .

Now this is where I get stuck.

(ii) Use Cauchy's integral formula to show that .

Now I've tried to use partial fractions so that

Equating the numerators gives but I'm not sure how to solve this equation for A and B.

(iii) Show that and hence that is real.