Question

Evaluate: $\int {\cos }^{3}x\sin xdx$.

Answer 1

Using uv rule of integration

$\Rightarrow I={\cos }^{3}x(-\cos x)-\int 3{\cos }^{2}x(-\sin x)(-\cos x)dx$

$\Rightarrow I=-{\cos }^{4}x-3\int {\cos }^{3}x\sin xdx$

$\Rightarrow I=-{\cos }^{4}x-3I$

$\Rightarrow I=-\frac{{\cos }^{4}x}{4}$