Integral of sec2 x

How to solve the given integral by using the integral of sec2 x: formula, 1 example, and its solution.

Formula

Formula

Recall that
the derivative of tan x is
sec2 x.

And integral and derivative
are the opposite operations.

So the integral of sec2 x is
tan x + C.

For an indefinite integral,
there should be +C.

Example

Example

Solution

cos 2x = 2 cos2 x - 1

cos 2A

Split the fraction.
[2 cos2 x - 1]/(cos2 x)
= (2 cos2 x)/(cos2 x) - 1/(cos2 x)
= 2 - 1/(cos2 x)

1/(cos2 x) = sec2 x

Secant: in a Right Triangle

The integral of 2 is 2x.

Integral of a Polynomial

Write the coefficient -.

The integral of sec2 x is tan x.

The given integral is an indefinite integral.
So write +C.

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