Why Isn’t There an Inverse Quotient Rule?

In this paper, I derive an integration technique reminiscent of the integration by parts formula: \[\int\frac{p\cdot dq}{q^2}=\frac{-p}{q}+\int\frac{dp}{q}.\] The technique can be used to more easily solve integrals that could otherwise be computed using a different technique, and it is especially useful to integrate quotients of trig functions. I also explore why this technique is not often taught: many straightforward applications of the rule are only possible in integrals that do not necessarily look like a quotient, or that are easily solved with a simpler method.

Recommended citation: Hauptman, Edison. (2024). "Why Isnt There an Inverse Quotient Rule?." Pittsburgh Interdiscplinary Mathematics Review. 1 (1-18).
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