Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 387: 84


$$-\frac{1}{2}e^{\cos^2\theta +1}+c.$$

Work Step by Step

Let $u=\cos^2\theta +1$, then $du=-2\cos \theta \sin \theta d\theta$, hence we have $$\int \cos \theta \sin \theta e^{\cos^2\theta +1}d\theta=-\frac{1}{2}\int e^udu\\ =-\frac{1}{2}e^u+c=-\frac{1}{2}e^{\cos^2\theta +1}+c.$$
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