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

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

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

\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

Simplify

\frac{1}{cos ^{2} ( x ) - cos ( 2 x )} : csc^{2} (x)

= \int csc^{2} (x) d x

Use the common integral:

\int csc^{2} (x) d x = - cot (x)

= - cot (x)

Add a constant to the solution

= - cot (x) + C

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