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

Find $$$\int \sec^{2}{\left(x \right)}\, dx$$$.

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

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

Therefore,

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

Add the constant of integration:

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

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