Integral of $$$\sec^{2}{\left(y \right)}$$$

Find $$$\int \sec^{2}{\left(y \right)}\, dy$$$.

The integral of $$$\sec^{2}{\left(y \right)}$$$ is $$$\int{\sec^{2}{\left(y \right)} d y} = \tan{\left(y \right)}$$$:

$${\color{red}{\int{\sec^{2}{\left(y \right)} d y}}} = {\color{red}{\tan{\left(y \right)}}}$$

Therefore,

$$\int{\sec^{2}{\left(y \right)} d y} = \tan{\left(y \right)}$$

Add the constant of integration:

$$\int{\sec^{2}{\left(y \right)} d y} = \tan{\left(y \right)}+C$$

$$$\int \sec^{2}{\left(y \right)}\, dy = \tan{\left(y \right)} + C$$$A