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: 28



Work Step by Step

Let us consider $x = \sin \theta $ and $dx= \cos \theta d \theta $ Now, the given integral becomes: $\int \dfrac{\cos \theta}{\sin ^4 \theta} (\cos \theta) d\theta=\int csc^2 \theta (\cot^2 \theta) d \theta $ Now, integrate: $-\dfrac{\cot^3 \theta}{3} +C=-\dfrac{1}{3}(\dfrac{\sqrt{1-x^2}}{x})^3+C$
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