Contour Integrals, which contour to use?

[xago]

Homework Statement

http://img404.imageshack.us/img404/3952/contf.png

The Attempt at a Solution

Is there a set of rules or postulate that refer to which contour to use for specific integrals?
I tried to use the residue theorem for the first integral but I didn't get the right answer

 

[susskind_leon]

No, there is no general rule, but it depends entirely on the integral which path to chose.
What have you done exactly for a)? Which path did you chose and what result did you get?