As an exercise in complex analysis, we shall compute
Integral $\int_{-\infty}^{\infty} \frac{1}{e^x+e^{-x}}e^{-ix\xi}dx$ for $\xi \in \mathbb R$.
I would love to present the things I've tried, but there is not much. I tried to change the $\pm\infty$ to $\pm r$ by writing a limit in front of the integral and then I tried to write this integral as a line integral, hoping that then I could apply some of the theorems and lemmas from the lectures. However, I fail to write this as a line integral. It's frustrating that the prof just expects us to calculate some integrals even though we never, not once, did something similar in lecture. So I really don't know how to approach this integral and would appreciate any help.
