# Math Help - Line Integral

1. ## Line Integral

I need to integrate f(z)dz, where f(z) = (z+i)/[(z^3)+(2z^2)], along C, where C is the circles |z| = 1, |z+2-i| = 2, and |z-2i| = 1, each traversed once counterclockwise (so I'll end up doing the integral once for each C). I started to evaluate it along the first circle using the usual method for line integrals (parameterizing C and integrating f(C(t))C'(t)dt from 0 to 2pi), but I end up with an messy integral. Should I be using a different approach? I'm just now reading up on the residue theorem, should I use that instead?

Sorry if my post is hard to read, I'm planning on learning LaTeX in the near future.

2. Residue theorem sounds fine, if you're allowed to use it.