Integral of $$$\frac{1}{\sqrt{1 - y^{2}}}$$$

Find $$$\int \frac{1}{\sqrt{1 - y^{2}}}\, dy$$$.

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

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

Therefore,

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

Add the constant of integration:

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

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