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: 82

Answer

1. Substitution: $u=\tan x$ then 2. Log Rule

Work Step by Step

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