Primitive of Power of Sine of a x by Power of Cosine of a x/Examples

Examples of Use of Primitive of $\sin^m x \cos^n x$

Primitive of $\cos^3 x \sin^4 x$

$\ds \int \cos^3 x \sin^4 x \rd x = \dfrac {\sin^5 x} 5 - \dfrac {\sin^7 x} 7 + C$

Primitive of $\sin^2 x \cos^3 x$

$\ds \int \sin^2 x \cos^3 x \rd x = \dfrac {\sin^3 x} 3 - \dfrac {\sin^5 x} 5 + C$

Primitive of $\cos^2 x \sin^4 x$

$\ds \int \cos^2 x \sin^4 x \rd x = \dfrac 1 {32} \paren {2 x - \dfrac {\sin 2 x} 2 - \dfrac {2 \sin 4 x} 4 + \dfrac {\sin 6 x} 6} + C$