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: 23


$$-\frac{1}{6} (\cos x)^6 +c$$

Work Step by Step

Given $$\int \cos ^{5} x \sin x d x$$ Let $$ u=\cos x\ \ \ \Rightarrow \ \ du =-\sin xdx$$ Then \begin{align*} \int \cos ^{5} x \sin x d x&=\int u^{5} d u\\ &= -\frac{1}{6}u^6 +c\\ &= -\frac{1}{6} (\cos x)^6 +c \end{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.