University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Section 5.5 - Indefinite Integrals and the Substitution Method - Exercises - Page 330: 55


$$\int \frac{dx}{x\ln x}=\ln|\ln x|+C$$

Work Step by Step

$$A=\int \frac{dx}{x\ln x}=\int\Big(\frac{1}{\ln x}\times\frac{dx}{x}\Big)$$ We set $u=\ln x$ Then $$du=\frac{dx}{x}$$ Therefore, $$A=\int\frac{1}{u}du=\ln|u|+C$$ $$A=\ln|\ln x|+C$$
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