Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 460: 28


$$2 \sec x+2 \tan x-x+C$$

Work Step by Step

\begin{aligned} \int(\sec x+\tan x)^{2} d x &=\int \sec ^{2} x+2 \sec x \tan x+\tan ^{2} x d x \\ &=\int \sec ^{2} x d x+2 \int \sec x \tan x d x+\int \tan ^{2} x d x \\ &=\int \sec ^{2} x d x+2 \int \sec x \tan x d x+\int\left(\sec ^{2} x-1\right) d x \\ & =2 \sec x+2 \tan x-x+C \end{aligned}
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