Evaluate $\displaystyle \frac{1}{2 \pi i } \int_{\gamma} \frac{dz}{z(z^2-1)}$, where $\displaystyle \gamma$ is the closed path indicated in the picture.

http://i719.photobucket.com/albums/w...anghu21/11.png

Hint:Proceed directly with partial fractions.

Attempt:

Using partial fractions, we get $\displaystyle \frac{.5}{z+1}+\frac{.5}{z-1}-\frac{1}{z}$. Now, I do not see where to go from here. How does using partial fractions help in this problem? Thank you.