Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 7 - Principles Of Integral Evaluation - 7.3 Integrating Trigonometric Functions - Exercises Set 7.3 - Page 507: 38


$$\frac{{{{\sec }^5}x}}{5} + C$$

Work Step by Step

$$\eqalign{ & \int {\tan x{{\sec }^5}x} dx \cr & {\text{split exponent se}}{{\text{c}}^3}x \cr & \int {\tan x{{\sec }^4}x} \sec xdx \cr & \int {{{\sec }^4}x} \sec x\tan xdx \cr & {\text{substitute }}u = \sec x,{\text{ }}du = \sec x\tan xdx \cr & = \int {{u^4}} du \cr & {\text{find the antiderivative by the power rule}} \cr & = \frac{{{u^5}}}{5} + C \cr & {\text{write in terms of }}x,{\text{ replace }}u = \sec x \cr & = \frac{{{{\sec }^5}x}}{5} + C \cr} $$
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