Calculus, 10th Edition (Anton)

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

Chapter 4 - Integration - Chapter 4 Review Exercises - Page 342: 4

Answer

$$\sec x + x + C$$

Work Step by Step

$$\eqalign{ & \int {\sec x\left( {\tan x + \cos x} \right)} dx \cr & \int {\left( {\sec x\tan x + \sec x\cos x} \right)} dx \cr & {\text{identity }}\sec x = \frac{1}{{\cos x}} \cr & \int {\left( {\sec x\tan x + \frac{1}{{\cos x}}\cos x} \right)} dx \cr & \int {\left( {\sec x\tan x + 1} \right)} dx \cr & {\text{sum rule}} \cr & \int {\sec x\tan x} dx + \int {dx} \cr & {\text{find antiderivatives}} \cr & = \sec x + x + C \cr} $$
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