Bioche's rules

{{short description|Aids the computation of indefinite integrals involving sines and cosines}}{{Inline|date=June 2022}}

Bioche's rules, formulated by the French mathematician {{ill|Charles Bioche|fr}} (1859–1949), are rules to aid in the computation of certain indefinite integrals in which the integrand contains sines and cosines.

In the following, $f(t)$ is a rational expression in $\backslash sin\; t$ and $\backslash cos\; t$. In order to calculate $\backslash int\; f(t)\backslash ,dt$, consider the integrand $\backslash omega(t)=f(t)\backslash ,dt$. We consider the behavior of this entire integrand, including the