Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 460: 19


$$\frac{1}{3} \tan ^{3} \theta+ \tan\theta+C $$

Work Step by Step

\begin{aligned} \int \frac{d \theta}{\cos ^{4} \theta} &=\int \sec ^{4} \theta d \theta \\ &=\int \sec ^{2} \theta \cdot \sec ^{2} \theta d \theta \\ &=\int\left(\tan ^{2} \theta+1\right) \cdot \sec ^{2} \theta d \theta \\ &= \int \tan ^{2} \theta \sec ^{2} \theta d \theta+\int \sec ^{2} \theta d \theta\\ &=\frac{1}{3} \tan ^{3} \theta+ \tan\theta+C \end{aligned}
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