Find the Antiderivative sec(X)^2

$\sec^{2} (X)$

Step 1

Write $\sec^{2} (X)$ as a function.

$f (X) = \sec^{2} (X)$

Step 2

The function $F (X)$ can be found by finding the indefinite integral of the derivative $f (X)$ .

$F (X) = \int f (X) d X$

Step 3

Set up the integral to solve.

$F (X) = \int \sec^{2} (X) d X$

Step 4

Since the derivative of $\tan (X)$ is $\sec^{2} (X)$ , the integral of $\sec^{2} (X)$ is $\tan (X)$ .

$\tan (X) + C$

Step 5

The answer is the antiderivative of the function $f (X) = \sec^{2} (X)$ .

$F (X) =$ $\tan (X) + C$