Find the Antiderivative sec(x)

$\sec (x)$

Step 1

Write $\sec (x)$ as a function.

$f (x) = \sec (x)$

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.

$F (x) = \int \sec (x) d x$

Step 4

The integral of $\sec (x)$ with respect to $x$ is $\ln (| \sec (x) + \tan (x) |)$ .

$\ln (| \sec (x) + \tan (x) |) + C$

Step 5

The answer is the antiderivative of the function $f (x) = \sec (x)$ .

$F (x) =$ $\ln (| \sec (x) + \tan (x) |) + C$