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

Find $$$\int \sec^{2}{\left(t \right)}\, dt$$$.

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

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

Therefore,

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

Add the constant of integration:

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

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