Answer
$$2\sqrt{\ln x}+c.$$
Work Step by Step
Let $ u=\ln x $, then $ du=\frac{1}{x}dx $.
Now, we have
$$\int \frac{1}{x\sqrt{\ln x}}dx =\int \frac{1}{\sqrt{u}}du
= \int u^{-1/2}du\\
=\frac{1}{1/2}u^{1/2}+c=2\sqrt{\ln x}+c.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
