Answer
$x\tan x+\ln|\cos x|+C$
Work Step by Step
We use the formula
$\int udv=uv-\int vdu$
with $u=x$, $dv=\sec^{2}xdx$
$du=dx$, $v=\tan x$
Then $\int x\sec^{2}xdx=x\times \tan x-\int \tan xdx$
$=x\tan x+\ln|\cos x|+C$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 8: Techniques of Integration - Section 8.2 - Integration by Parts - Exercises 8.2 - Page 455: 13
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