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Vade Mecum

Vade Mecum

A list of common formulas, not in any way complete.



Trigonometric substitutions

shape substitution
\(\sqrt{r^2 - x^2}\) \(x = r \sin u\) (or \(x = r \cos u\))
\(\sqrt{x^2 - r^2}\) \(x = \frac{r}{\cos u}\)
\(\sqrt{x^2 + r^2}\) \(x = r \tan u\)

Integration by parts


Most, if not all, trigonometric problems become trivial using following substitutions.

The proof of everything in this vade mecum is left as an exercise to the reader. ;-)

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