Funktion $$$\frac{1}{y^{2} + 1}$$$ integraali

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

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

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

Näin ollen,

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

Lisää integrointivakio:

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

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