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:

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

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