I am in the process of studying a little complex analysis when I have time.

What is the best way to approach something like this?:

$\displaystyle \int\frac{z^{2}+sinh(2z)}{z^{3}-31z^{2}+4z-12i}$

First, I thought about using $\displaystyle sinh(2z)=\frac{1}{2}(e^{2z}-e^{-2z})$

Do the roots of the denominator have a lot to do with it?.

Just like some input from those in the know.