# Computer Science Resources

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Vade Mecum

# Vade Mecum

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

## Differentiation

## Integration

### 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

## Trigonometry

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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