Question

What is the antiderivative of ${\sec }^2\left(x\right)$?

Answer 1

Find the antiderivatives.

It's known that the derivative of $\tan x$ is ${\sec }^2\left(x\right)$. Then,

$\int se{c}^{2}xdx=\tan x+C$

Therefore, the antiderivative of ${\mathbf{sec}}^{\mathbf{2}}\mathbf{\left(}\mathit{x}\mathbf{\right)}$ is $\mathbf{tan}\mathit{x}$.