Answer
$\int_0^\infty \frac{dx}{e^x}$.
Work Step by Step
We compare it with $\int_0^\infty \frac{dx}{e^x}$, where $ x+e^x> e^x $ and since $\int_0^\infty \frac{dx}{e^x}$ converges, then $\int_0^\infty \frac{dx}{x+e^x}$ also converges.
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 - Preliminary Questions - Page 440: 4
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