Mathematics

The key is recognizing that $\sec^2 x$ is the derivative of a basic trigonometric function you've already seen. Rather than using integration techniques, recall what happens when you differentiate $\tan x$—the result is exactly $\sec^2 x$. So finding the antiderivative means reversing that process and remembering to add the constant of integration.

The key is recognizing that $\sec^2 x$ is the derivative of a basic trigonometric function you've already seen. Rather than using integration techniques, recall what happens when you differentiate $\tan x$—the result is exactly $\sec^2 x$. So finding the antiderivative means reversing that process and remembering to add the constant of integration.