Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises - Page 335: 81

Answer

1. Substitution: $u=x^{2}+4$ then 2. Log Rule

Work Step by Step

The derivative of $(x^{2}+4)$ is $x, $which is in the numerator... 1. we substitute $\left[\begin{array}{ll} u=x^{2}+4, & \\ du=2xdx & xdx=\frac{1}{2}du \end{array}\right]$ after which the integral takes the form $\displaystyle \frac{1}{2}\int\frac{1}{u}du$ 2. The form $\displaystyle \int\frac{1}{u}du$ is solved by applying the Log Rule
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