# Complex analysis, solving integral $\oint \frac{dz}{1-z^2}$

So I'm stuck with the question: Calculate, for example with the usage of a primitive function, the integral:

integral $\oint \frac{dz}{1-z^2}$ where the integration path is:

the composition of the half circle $|z-1|=1$, $\mbox{Im}z \leqslant0$ and the imaginary axis. I don't really know how to calculate it, the half circle below the imaginary axis is easy to understand, but the imaginary axis? It would make more sense to me if it was the real axis. Thanks in advance!

• Yes, you are right, imaginary axis is tangent to the circle at $(0,0)$, i.e. the only common point. It's probably a typo and it should have been the real axis instead. – rtybase Oct 4 '16 at 10:17