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

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

A integral de $$$\frac{1}{y^{2} + 1}$$$ é $$$\int{\frac{1}{y^{2} + 1} d y} = \operatorname{atan}{\left(y \right)}$$$:

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

Portanto,

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

Adicione a constante de integração:

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

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