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 \sin t and \cos t. In order to calculate \int f(t)\,dt, consider the integrand \omega(t)=f(t)\,dt. We consider the behavior of this entire integrand, including the