Example 1. Find the integral $\int \cos x \sin ^{2} x d x$.
Solution. Since $\cos x d x=d(\sin x)$, then based on formula (4. $5^{\prime}$ ) for $u=\sin x$ we obtain

$$
\int \cos x \sin ^{2} x d x=\int \sin ^{2} x d(\sin x)=\frac{\sin ^{3} x}{3}+C
$$