Answer
$2e^{\sqrt x}+c $
Work Step by Step
Recall that $(e^x)'=e^x$
Let $ u= \sqrt x $, then $ du=\frac{1}{2\sqrt x} dx $ and hence we have
$$
\int \frac{e^{\sqrt x}}{\sqrt x} dx=2\int e^{u} du\\
=2e^u+c=2e^{\sqrt x}+c
.
$$
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: 85
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