Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 94


$$2\sqrt{ e^x+1} +c$$

Work Step by Step

Let $u=e^x$, then $du=e^xdx$. Now, we have $$\int \frac{e^x }{\sqrt{ e^x+1}} dx=\int \frac{1 }{\sqrt{ u+1}} du=\frac{1}{1/2}\sqrt{ u+1} +c\\ =2\sqrt{ e^x+1} +c$$
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