Example 1.13. Find $\int \sin 7 x \cos 3 x d x$.
Solution.

$$
\begin{gathered}
\int \sin 7 x \cos 3 x d x=\frac{1}{2} \int(\sin 10 x+\sin 4 x) d x= \\
=\frac{1}{20} \int \sin 10 x d(10 x)+\frac{1}{8} \int \sin 4 x d(4 x)= \\
=-\frac{1}{20} \cos 10 x-\frac{1}{8} \cos 4 x+C
\end{gathered}
$$

Using formulas (1.21), indefinite integrals of functions that are the product of three or more trigonometric sine and cosine functions, whose arguments are proportional to $x$, can similarly be found in this manner.