University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.5 - Integral Tables and Computer Algebra Systems - Exercises - Page 451: 11



Work Step by Step

$$A=\int\frac{dx}{x\sqrt{7+x^2}}$$ Use Formula 40, which states that $$\int \frac{dx}{x\sqrt{a^2+x^2}}=-\frac{1}{a}\ln\Big|\frac{a+\sqrt{a^2+x^2}}{x}\Big|+C$$ for $a=\sqrt7$ here: $$A=-\frac{1}{\sqrt7}\ln\Big|\frac{\sqrt7+\sqrt{7+x^2}}{x}\Big|+C$$
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