Calculus II For Dummies
Book image
Explore Book Buy On Amazon

You can integrate even powers of secants with tangents. If you wanted to integrate tanm x secn x when n is even — for example, tan8 x sec6 x — you would follow these steps:

  1. Peel off a sec2 x and place it next to the dx:

    image0.png
  2. Use the trig identity 1 + tan2 x = sec2 x to express the remaining secant factors in terms of tangents:

    image1.png
  3. Use the variable substitution u = tan x and du = sec2x dx:

    image2.png

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

About This Article

This article is from the book:

About the book author:

Mark Zegarelli, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear — and fun — for average readers. He is the author of Logic For Dummies and Basic Math & Pre-Algebra For Dummies.

This article can be found in the category: