# How do you integrate int cot^2xdx?

We have to integrate cos2x

### Solution

We know the trigonometric identity

$1+\cot ^{2}x=\csc ^{2}x$ $\cot ^{2}x=\csc ^{2}x – 1$ $\int \cot ^{2}x=\int \csc ^{2}x – 1$

=$\int \csc ^{2}x – \int dx$

=$-\cot x-x+C$ $\int \cot ^{2}x=-\cot x-x+C$

$\int \cot ^{2}x=-\cot x-x+C$