## Problem Statement

Calculate the indefinite integral:

$$
\int \frac{x \cdot \cos x+\sin x}{(x \cdot \sin x)^{2}} d x
$$
## Solution

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

Substitution:

$$
\begin{aligned}
& y=x \cdot \sin x \\
& d y=(\sin x+x \cdot \cos x) d x
\end{aligned}
$$

We get:

$$
=\int \frac{d y}{y^{2}}=-\frac{1}{y}+C=
$$

Reverse substitution:

$$
=-\frac{1}{x \cdot \sin x}+C
$$

Source — «http://pluspi.org/wiki/index.php/\�\�\�\�\�\�\�\�\�\�\�\�

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Categories: Kuznetsov's Problem Book Integrals Problem $3 \mid$ Integrals

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## Problem Kuznetsov Integrals 3-13

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