Answer
$$\int x\,tan\,x\,sec\,xdx=x\,sec\,x-ln|sec\,x+tan\,x|+C$$
Work Step by Step
$${\left ( x\,secx \right )}'=secx+x\,tan\,x\,sec\,x$$
$$\int x\,tan\,x\,sec\,xdx=x\,secx-\int sec\,x\,dx$$
$$=x\,sec\,x-ln|sec\,x+tan\,x|+C$$
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 7.2 - Trigonometric Integrals - 7.2 Exercises - Page 485: 33
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