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

Find $$$\int \frac{1}{y^{2} + 1}\, dy$$$.

The integral of $$$\frac{1}{y^{2} + 1}$$$ is $$$\int{\frac{1}{y^{2} + 1} d y} = \operatorname{atan}{\left(y \right)}$$$:

$${\color{red}{\int{\frac{1}{y^{2} + 1} d y}}} = {\color{red}{\operatorname{atan}{\left(y \right)}}}$$

Therefore,

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

Add the constant of integration:

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

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