Solution 1 (a).

See text and/or instructor's solution manual.

Solution.  Factor the denominator to see that  .  

The integrand    is analytic everywhere except at the points     which lie outside the contour  .

Hence, by the Cauchy-Goursat Theorem we have   .  

                    The points    and    which lie outside the contour  .

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell