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: 23


$$2 \tanh ^{-1}\left(\frac{1}{2}\right)$$

Work Step by Step

\begin{aligned} \int_{-\frac{1}{2}}^{\frac{1}{2}} \frac{1}{\left(1-x^{2}\right)} d x &=\left.\tanh ^{-1} x\right|_{-\frac{1}{2}} ^{\frac{1}{2}} \\ &=\tanh ^{-1}\left(\frac{1}{2}\right)-\tanh ^{-1}\left(-\frac{1}{2}\right) \\&=2 \tanh ^{-1}\left(\frac{1}{2}\right) \end{aligned}
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