Can someone tell me if my method is valid and my solution correct:
if the curve C is the circle:
Okay, the integrand is analytic on and inside the second curve, so the integral is zero there.
For the first curve I rewrite:
Then each term is easy to calculate using residues (noting the only singularity is at pi):
Which evaluated at is
Does this work?
can't I simply evaluate as -1 (since cos is the 9th derivitive of sin), then use algebra to isolate the integral and get the answer?