Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 59


$$\frac{1}{2}\left(\operatorname{coth}^{-1} 4-\operatorname{coth}^{-1} 20\right)$$

Work Step by Step

Since $$ \frac{d}{dx} \operatorname{coth}^{-1} x=\frac{1}{1-x^2}$$ Then \begin{align*} \int_{2}^{10} \frac{d x}{4 x^{2}-1}&=-\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{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After 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.