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: 20

Answer

$$\frac{1}{3} \sinh ^{-1}(\sqrt{3} x)+C$$

Work Step by Step

\begin{aligned} \int \frac{1}{\sqrt{1+3 x^{2}}} d x &=\frac{1}{\sqrt{3}} \int \frac{\sqrt{3}}{\sqrt{1+(\sqrt{3} x)^{2}}} d x \\ &=\frac{1}{3} \sinh ^{-1}(\sqrt{3} x)+C \end{aligned}
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