University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 8 - Section 8.3 - Trigonometric Substitutions - Exercises - Page 439: 16


$x-2 \tan^{-1}(x/2)+C$

Work Step by Step

Let us consider $x = 2 \tan \theta $ and $dx=2 \sec^2 \theta d\theta $ Now, the given integral becomes: $\int \dfrac{4 \tan^2 \theta }{4+4 \tan^2 \theta} d \theta = 2 \int (\sec^2 d \theta -1) d \theta$ Now, integrate and plug in $x = 2 \tan \theta $: $2 \tan \theta -2 \theta+C=x-2 \tan^{-1}(x/2)+C$
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