## Problem Statement

Calculate the indefinite integral:

$$
\int \frac{x^{3}+x}{x^{4}+1} d x
$$
## Solution

$$
\begin{aligned}
& \int \frac{x^{3}+x}{x^{4}+1} d x=\int \frac{x^{3}}{x^{4}+1} d x+\int \frac{x}{x^{4}+1} d x= \\
& =\frac{1}{4} \cdot \int \frac{1}{x^{4}+1} d\left(x^{4}+1\right)+\frac{1}{2} \cdot \int \frac{1}{x^{4}+1} d\left(x^{2}\right)= \\
& =\frac{1}{4} \cdot \ln \left|x^{4}+1\right|+\frac{1}{2} \cdot \operatorname{arctg} x^{2}+C
\end{aligned}
$$

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%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D1%8B_%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_3-13"

Categories: Kuznetsov Integral Problems 3 | Integrals

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## Problem Kuznetsov Integrals 3-14

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