Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions - Exercises - Page 415: 18


$$\frac{1}{3} \cosh ^{-1} \frac{3 x}{2}+C$$

Work Step by Step

\begin{aligned} \int \frac{1}{\sqrt{9 x^{2}-4}} d x &=\frac{1}{3} \int \frac{3}{\sqrt{(3 x)^{2}-2^{2}}} d x \\ &=\frac{1}{3} \int \frac{\frac{3}{2}}{\sqrt{\left(\frac{3 x}{2}\right)^{2}-1}} d x \\ &=\frac{1}{3} \cosh ^{-1} \frac{3 x}{2}+C \end{aligned}
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