$$$\frac{1}{\sqrt{1 - y^{2}}}$$$の積分

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

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

$${\color{red}{\int{\frac{1}{\sqrt{1 - y^{2}}} d y}}} = {\color{red}{\operatorname{asin}{\left(y \right)}}}$$

したがって、

$$\int{\frac{1}{\sqrt{1 - y^{2}}} d y} = \operatorname{asin}{\left(y \right)}$$

積分定数を加える:

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

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