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Students of math at university level typically get a toolbox full of neat techniques, tricks, and transformations for solving integrals, and the list is long: Integration by parts, substitution, Laplace transforms, Fourier transforms, Feynman tricks, etc. I have even found some interesting tools

Polar Coordinates

Before I can state the formula I have discovered (or perhaps rediscovered ?), we need to recall a thing or two about the polar coordinate system . In the usual Cartesian coordinate system , two coordinates give us a unique position in the 2D plane, let’s call it the (x, y)-plane.

In the same way, we could just as well define a... See more