I'm stuck on a question of complex integration; there doesn't seem to be any way to integrate the function, so I imagine there must be a 'trick' somewhere, but I can't work it out Here's the problem:

Compute

$\displaystyle \oint \frac{log(z)}{z^2 + 9}dz$

around $\displaystyle |z-4i|=3$.

I parametrized the path as

$\displaystyle \gamma (t) = 4i + 3e^{it},\ 0 \leq t \leq 2\pi $

but then I end up trying to integrate

$\displaystyle \int_0^{2\pi} \frac{log(4i+3e^{it})3ie^{it}}{(4i+3e^{it})^2 + 9}dt$

which I can't work out. Thanks for any help