Integral of $$$\frac{1}{x^{2} + 1}$$$

Find $$$\int \frac{1}{x^{2} + 1}\, dx$$$.

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:

$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}+C$$

$$$\int \frac{1}{x^{2} + 1}\, dx = \operatorname{atan}{\left(x \right)} + C$$$A