Answer
$\frac{2}{3}(e^t+1)^{3/2}+c $
Work Step by Step
Let $ u= e^t $, then $ du=e^{t}dt $ and hence we have
$$
\int e^t\sqrt{e^t+1}dt= \int \sqrt{u+1}du= \int (u+1)^{1/2}du\\
=\frac{1}{3/2} (u+1)^{3/2}+c=\frac{2}{3}(e^t+1)^{3/2}+c
.
$$
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 - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 328: 79
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