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

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

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

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

Oleh karena itu,

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

Tambahkan konstanta integrasi:

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

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