Answer
$$2\sqrt{ e^x+1} +c$$
Work Step by Step
Let $u=e^x$, then $du=e^xdx$. Now, we have
$$\int \frac{e^x }{\sqrt{ e^x+1}} dx=\int \frac{1 }{\sqrt{ u+1}} du=\frac{1}{1/2}\sqrt{ u+1} +c\\
=2\sqrt{ e^x+1} +c$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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