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: 24


$$\frac{1}{4} \cos^4(2- x) +c$$

Work Step by Step

Given $$\int \cos ^{3} (2-x) \sin (2-x) d x$$ Let $$ u=\cos(2-x)\ \ \ \Rightarrow \ \ du =\sin (2-x)dx$$ Then \begin{align*} \int \cos ^{3} (2-x) \sin (2-x) d x&=\int u^{3} d u\\ &= \frac{1}{4}u^4 +c\\ &= \frac{1}{4} \cos^4(2- x) +c \end{align*}
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