Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.6 Strategies for Integration - Exercises - Page 431: 30



Work Step by Step

Given $$\int \sec ^{5} y \tan y d y$$ Let $$ \sec y \to \sec y \tan y d y$$ Then \begin{align*} \int \sec ^{5} y \tan y d y&=\int \sec ^{4} y \sec y \tan y d y\\ &=\int u^4 du\\ &=\frac{1}{5}u^5+C\\ &=\frac{1}{5}\sec^5y+C \end{align*}
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