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A Result with Self-Inverse Functions
This post should really be Part 3, being a sequel to the series of posts about the Cauchy-Schlömilch transformation and the Glasser’s master theorem. However, I’ll frame this as a new fact and post. This post concerns functions that are inverses of each other, i.e., functions 
An Incredibly Overpowered Integration Technique – Part 2
In the previous post, we had derived the Cauchy-Schlömilch transformation, which is a wonderful substitution that eases the evaluation of a certain class of definite integrals. We reproduce the result here for convenience. Theorem (Cauchy-Schlömilch transformation): Let 
An Incredibly Overpowered Integration Technique – Part 1
Today, we look at a beautiful transformation/substitution which is not presented in many textbooks and hence is often not part of the standard arsenal of tools for tackling integration problems. It is called the Cauchy-Schlömilch transformation “(after Cauchy who knew it by 1823, and the German mathematician Oskar Schlömilch (1823–1901) who popularized it in an…
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An Ode to Some Beautiful Integrals 