What is the integral of 1/(cos(2x)-cos^2(x)) ?

The integral of 1/(cos(2x)-cos^2(x)) is cot(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(cos(2x)-cos^2(x))

\int \frac{1}{cos ( 2 x ) - cos ^{2} ( x )} d x

cot (x) + C

Solution steps

\int \frac{1}{cos ( 2 x ) - cos ^{2} ( x )} d x

Rewrite using trig identities

= \int - \frac{1}{sin ^{2} ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{sin ^{2} ( x )} d x

Use the common integral:

\int \frac{1}{sin ^{2} ( x )} d x = - cot (x)

= - (- cot (x))

Simplify

= cot (x)

Add a constant to the solution

= cot (x) + C

What is the integral of 1/(cos(2x)-cos^2(x)) ?
The integral of 1/(cos(2x)-cos^2(x)) is cot(x)+C