Section 6.4

Strategy for $\int\sin^m x\cos^n x\,dx$

If $m$ is odd, reserve a factor $\sin x$ and use $\sin^2x=1-\cos^2x$ ; then $u=\cos x$ .
If $n$ is odd, reserve a factor $\cos x$ and use $\cos^2x=1-\sin^2x$ ; then $u=\sin x$ .
If both are even, use power-reduction identities.

Loading section…

Section 6.4

If $m$ is odd, reserve a factor $\sin x$ and use $\sin^2x=1-\cos^2x$ ; then $u=\cos x$ .
If $n$ is odd, reserve a factor $\cos x$ and use $\cos^2x=1-\sin^2x$ ; then $u=\sin x$ .
If both are even, use power-reduction identities.