Online Test Banks
Score higher
See Online Test Banks
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

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 cot8 x csc6 x:

  1. Peel off a csc2 x and place it next to the dx:

  2. Use the trig identity 1 + cot2 x = csc2 x to express the remaining cosecant factors in terms of cotangents:

  3. Use the variable substitution u = cot x and du = –csc2 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:

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus

Inside Sweepstakes

Win $500. Easy.