Answer
$$\sec^{-1}(5x)+c.$$
Work Step by Step
Let $u=5x$, then $du=5dx$ and hence we have
$$\int \frac{dx}{x\sqrt{25x^2-1}}=\int \frac{du}{u\sqrt{u^2-1}}\\
=\sec^{-1}u+c=\sec^{-1}(5x)+c.$$
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 - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 90
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.
