Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Practice Exercises - Page 518: 37


$$-\frac{\cos ^{5} x}{5}+\frac{\cos ^{7} x}{7}+C $$

Work Step by Step

We integrate as follows: \begin{align*} \int \sin ^{3} x \cos ^{4} x d x&=\int \cos ^{4} x\left(1-\cos ^{2} x\right) \sin x d x\\ &=\int \cos ^{4} x \sin x d x-\int \cos ^{6} x \sin x d x\\ &=-\frac{\cos ^{5} x}{5}+\frac{\cos ^{7} x}{7}+C \end{align*} Where we used the fact that $\sin^2 x + \cos^2 x=1$
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.