Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 387: 72


$$2\sqrt{\ln x}+c.$$

Work Step by Step

Let $ u=\ln x $, then $ du=\frac{1}{x}dx $. Now, we have $$\int \frac{1}{x\sqrt{\ln x}}dx =\int \frac{1}{\sqrt{u}}du = \int u^{-1/2}du\\ =\frac{1}{1/2}u^{1/2}+c=2\sqrt{\ln x}+c.$$
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