# How do you integrate (cscx)^2?

Apr 25, 2018

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

#### Explanation:

This is actually a common integral.

Recall that $\frac{d}{\mathrm{dx}} \cot x = - {\csc}^{2} x$

Then,

$\frac{d}{\mathrm{dx}} \left(- \cot x\right) = {\csc}^{2} x$

So, since we differentiate $- \cot x$ to get ${\csc}^{2} x$,

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