# Integrating Powers of Cotangents and Cosecants

You can integrate powers of cotangents and cosecants similar to the way you do tangents and secant. For example, here’s how to integrate cot^{8} *x* csc^{6} *x:*

Peel off a csc

^{2}*x*and place it next to the*dx**:*Use the trig identity 1 + cot

^{2 }*x*= csc^{2}*x*to express the remaining cosecant factors in terms of cotangents:Use the variable substitution

*u*= cot*x*and*du*= –csc^{2}*x**dx**:*

At this point, the integral is a polynomial, and you can evaluate it.

Sometimes, knowing how to integrate cotangents and cosecants can be useful for integrating negative powers of other trig functions — that is, powers of trig functions in the denominator of a fraction.

For example, suppose that you want to integrate

You can use trig identities to express it as cotangents and cosecants: