$$$\frac{1}{y^{2} + 1}$$$の積分

$$$\int \frac{1}{y^{2} + 1}\, dy$$$ を求めよ。

$$$\frac{1}{y^{2} + 1}$$$ の不定積分は $$$\int{\frac{1}{y^{2} + 1} d y} = \operatorname{atan}{\left(y \right)}$$$ です:

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

したがって、

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

積分定数を加える:

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

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