# Math Help - Complex Analysis: Line Integrals

1. ## Complex Analysis: Line Integrals

I have a problem as follows:
Let $\gamma=\beta+[e^2\pi,1]$ where $\beta$ is given by $\beta(t)=e^{t+it}$ for $0\leq t\leq 2\pi$. Evaluate $\int_\gamma z^{-1} dz$.

I know that I need to parameterize the path and I have come up with the path as $[e^2\pi,1]$. I also know that I need to integrate this problem along the path and then integrate the function and add the parts together. However, I can't seem to come up with the right way to accomplish this task. I will appreciate your help. Thank you.