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

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

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

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

- cot (w) + C

Solution steps

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

Simplify

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

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

Use the common integral:

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

= - cot (w)

Add a constant to the solution

= - cot (w) + C

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