Thomas' Calculus 13th Edition

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


$x\tan x+\ln|\cos x|+C$

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 $\int x\sec^{2}xdx=x\times \tan x-\int \tan xdx$ $=x\tan x+\ln|\cos x|+C$
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