Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.2 Trigonometric Integrals - Exercises - Page 403: 1


$$\sin x-\frac{1}{3} \sin ^{3} x+c $$

Work Step by Step

\begin{aligned} \int \cos ^{3} x d x &=\int \cos ^{2} x \cos x d x \\ &=\int\left(1-\sin ^{2} x\right) \cos x d x \\ &=\int(\cos x d x)-\int\left(\sin ^{2} x\right) \cos x d x \\ &=\sin x-\frac{1}{3} \sin ^{3} x+c \end{aligned}
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