University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 8 - Section 8.1 - Integration by Parts - Exercises - Page 427: 44


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

Work Step by Step

$$A=\int\frac{e^{\sqrt x}}{\sqrt x}dx$$ We set $a=\sqrt x$, which means $$da=\frac{1}{2\sqrt x}dx$$ $$\frac{1}{\sqrt x}dx=2da$$ Therefore, $$A=2\int e^ada$$ $$A=2e^a+C$$ $$A=2e^{\sqrt x}+C$$
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.