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: 49


$$-\frac{1}{7}\sin^7x +\frac{3}{5}\sin^5x-\sin^3x+\sin x+C$$

Work Step by Step

\begin{align*} \int\cos^7xdx&=\int\cos^6x\cos xdx\\ &=\int (1-\sin^2 x)^3\cos xdx\\ &=\int (-\sin^6x+3\sin^4x-3\sin^2x+1)\cos xdx\\ &=-\frac{1}{7}\sin^7x +\frac{3}{5}\sin^5x-\sin^3x+\sin x+C \end{align*}
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