Answer
$$\frac{2}{3}(e^t+1)^{3/2}+c
$$
Work Step by Step
Let $u=e^t+1$, then $du=e^t dt$. Now, we have
$$
\int e^{t} \sqrt{e^{t}+1} d t=\int u^{1/2}du\\
=\frac{1}{3/2} u^{3/2}+c=\frac{2}{3}(e^t+1)^{3/2}+c
$$
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: 86
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