Thank you for the opportunity to help you with your question!
We will use the semicircle as the contour of integration. Just for simplicity, to justify this integration, the integral on the arc going from : π to -π, vanishes, so I only need to evaluate the integral on the x-axis, i.e. real line:
The function of choice should be :
I need to find the roots of the following equation:Let z = (re^iθ)