Just wanted to share this moment. This is our 7th lecture in complex analysis. Last time we spoke about singularities, he quickly introduced the residue and we proved the integral equality with the sums over the residues of the singularities, just with some pictures :) (after taking real analysis with huge technical proofs, these proofs in complex analysis are such a relieve)
Then he showed us how you can use this formula to calculate some real integrals over rational, reel functions. This idea by taking this real line, then drawing a half circle above or under the real axis, wow!