Integral of $$$\frac{1}{x^{2} + 1}$$$
The calculator will find the integral/antiderivative of $$$\frac{1}{x^{2} + 1}$$$, with steps shown.
Related calculator: Integral Calculator
Solution
The integral of $$$\frac{1}{x^{2} + 1}$$$ is $$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}$$$:
$${\color{red}{\int{\frac{1}{x^{2} + 1} d x}}} = {\color{red}{\operatorname{atan}{\left(x \right)}}}$$
Therefore,
$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}$$
Add the constant of integration:
$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}+C$$
Answer
$$$\int \frac{1}{x^{2} + 1}\, dx = \operatorname{atan}{\left(x \right)} + C$$$A