University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Section 5.5 - Indefinite Integrals and the Substitution Method - Exercises - Page 330: 62


$$\int \frac{e^{\cos^{-1}x}dx}{\sqrt{1-x^2}}=-e^{\cos^{-1}x}+C$$

Work Step by Step

$$A=\int \frac{e^{\cos^{-1}x}dx}{\sqrt{1-x^2}}$$ We set $u=\cos^{-1}x$ Then $$du=-\frac{1}{\sqrt{1-x^2}}dx$$ $$\frac{1}{\sqrt{1-x^2}}dx=-du$$ Therefore, $$A=-\int e^udu=-e^u+C$$ $$A=-e^{\cos^{-1}x}+C$$
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.