## Problem Statement

Calculate the definite integral:

$$
\int_{0}^{1} \frac{x}{x^{4}+1} d x
$$
## Solution

$$
\begin{aligned}
& \int_{0}^{1} \frac{x}{x^{4}+1} d x=\frac{1}{2} \cdot \int_{0}^{1} \frac{d\left(x^{2}\right)}{x^{4}+1}=\frac{1}{2} \cdot \int_{0}^{1} \frac{d\left(x^{2}\right)}{x^{4}+1}=\left.\frac{1}{2} \cdot \operatorname{arctg} x^{2}\right|_{0} ^{1}= \\
& =\frac{1}{2} \cdot \operatorname{arctg} 1^{2}-\frac{1}{2} \cdot \operatorname{arctg} 0^{2}=\frac{1}{2} \cdot \frac{\pi}{4}-\frac{1}{2} \cdot 0=\frac{\pi}{8}
\end{aligned}
$$

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 $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} 5 \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B} 4-9$ "

Categories: Kuznetsov Problem Book Integrals Problem 4 | Integrals

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## Problem Kuznetsov Integrals 4-10

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