211. $\int x^{2} \sin x d x$
Solution. We have

$$
\int x^{2} \sin x d x=\left|\begin{array}{l}
u=x^{2}, d v=\sin x d x \\
d u=2 x d x, v=-\cos x
\end{array}\right|=-x^{2} \cos x+2 \int x \cos x d x
$$

To find the integral obtained on the right side of the equation, we integrate by parts again:

$$
\int x \cos x d x=x \sin x+\cos x+C
$$

(see the solution of example 207). As a result, we obtain the final answer:

$$
\int x^{2} \sin x d x=-x^{2} \cos x+2 x \sin x+2 \cos x+C
$$