## Problem Statement

Calculate the indefinite integral:

$$
\int \frac{\operatorname{arctg} x + x}{1 + x^{2}} d x
$$
## Solution

$$
\begin{aligned}
& \int \frac{\operatorname{arctg} x + x}{1 + x^2} \, dx = \int \frac{\operatorname{arctg} x}{1 + x^2} \, dx + \int \frac{x}{1 + x^2} \, dx = \\
& = \int \operatorname{arctg} x \, d(\operatorname{arctg} x) + \frac{1}{2} \int \frac{d(1 + x^2)}{1 + x^2} = \frac{1}{2} \left( \operatorname{arctg}^2 x + \ln \left| 1 + x^2 \right| \right) + C
\end{aligned}
$$

Source — «http://pluspi.org/wiki/index.php/\�\�\�\�\�\�\�\�\�\�\�\� \%D0\%9A\%D1\%83\%D0\%B7\%D0\%BD\%D0\%B5\%D1\%86\%D0\%BE\%D0\%B2_\%D0\%98\%D0\%BD $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} 5 \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B} \_3-27$ » Categories: Kuznetsov's Problem Book Integrals Problem $3 \mid$ Integrals

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## Problem Kuznetsov Integrals 3-28

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