Calculus Examples

{sec}^{2} (x)

$\sec^{2} (x)$

Step 1

Write

{sec}^{2} (x)

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

f (x) = {sec}^{2} (x)

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

Step 2

The function

F (x)

$F (x)$ can be found by finding the indefinite integral of the derivative

f (x)

$f (x)$ .

F (x) = \int f (x) d x

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

Step 3

Set up the integral to solve.

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

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

Step 4

Since the derivative of

tan (x)

$\tan (x)$ is

{sec}^{2} (x)

$\sec^{2} (x)$ , the integral of

{sec}^{2} (x)

$\sec^{2} (x)$ is

tan (x)

$\tan (x)$ .

tan (x) + C

$\tan (x) + C$

Step 5

The answer is the antiderivative of the function

f (x) = {sec}^{2} (x)

$f (x) = \sec^{2} (x)$ .

F (x) =

$F (x) =$

tan (x) + C

$\tan (x) + C$