Answer
The integral diverges.
Work Step by Step
We have
$$
\int_{1}^{\infty} \frac{e^{\sqrt{x}} d x}{\sqrt{x}}=2\int_{1}^{\infty} e^{\sqrt{x}} d {(\sqrt{x})}=2e^{\sqrt{x}}|_{1}^{\infty} =2(\infty-e)=\infty.
$$
Hence, the integral diverges.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 33
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