# Integral of sec^{2} x

How to solve the given integral by using the integral of sec^{2} x: formula, 1 example, and its solution.

## Formula

### Formula

Recall that

the derivative of tan x is

sec^{2} x.

And integral and derivative

are the opposite operations.

So the integral of sec^{2} x is

tan x + C.

For an indefinite integral,

there should be +C.

## Example

### Example

### Solution

cos 2x = 2 cos^{2} x - 1

cos 2A

Split the fraction.

[2 cos^{2} x - 1]/(cos^{2} x)

= (2 cos^{2} x)/(cos^{2} x) - 1/(cos^{2} x)

= 2 - 1/(cos^{2} x)

1/(cos^{2} x) = sec^{2} x

Secant: in a Right Triangle

The integral of 2 is 2x.

Integral of a Polynomial

Write the coefficient -.

The integral of sec^{2} x is tan x.

The given integral is an indefinite integral.

So write +C.

So 2x - tan x + C is the answer.