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: 26



Work Step by Step

\begin{aligned} \int_{2}^{10} \frac{1}{4 x^{2}-1} d x &=\int_{2}^{10} \frac{1}{-\left(1-4 x^{2}\right)} d x \\ &=-\frac{1}{2} \int_{2}^{10} \frac{2}{\left(1-(2 x)^{2}\right)} d x \\ &=-\left.\frac{1}{2} \operatorname{coth}^{-1}(2 x)\right|_{2} ^{10} \\ &=\frac{1}{2}\left[\operatorname{coth}^{-1}(4)-\operatorname{coth}^{-1}(20)\right] \end{aligned}
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