Answer
$$\int x\,secx\,tanx\,dx=x\,secx-ln\left|secx+tanx\right|+C$$
Work Step by Step
We know that:
$$ {(sec\,x)}'=secx\,tanx$$
so:
$$\ \int x\,secx\,tanx\,dx=x\,secx-\int secx\,dx$$
$$x\,secx-ln\left|secx+tanx\right|+C$$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 7 - Section 7.5 - Strategy for Integration - 7.5 Exercises - Page 507: 15
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