Complex Analysis, Integral over a Square

Question

Given that $C$ is the boundary of the square with corners at $\pm4 \pm4i$ (sorry my formatting always seems to be stubborn, but that is plus or minus 4 plus or minus 4i, I am asked to compute $$\int_C \frac{e^z}{z^3}dz$$

This problem came a bit out of nowhere in the set I am working on, and while I can "visualize" the process and everything, I don't really see how to apply the theory to solution. Basically, I'm pretty confident you would either use Cauchy's integral formula or some corollary of it, but I am really struggling to see beyond that.

Thanks for any and all help you can provide, everybody.

Answer 1

Rather use the residual theorem: http://en.wikipedia.org/wiki/Residue_theorem

Answer 2

A hint: Write $e^z$ in the form $$e^z=1+z+{z^2\over2}+z^3 g(z)\ ,$$ where $g$ is analytic (even entire); then use your complex analysis toolkit.