Answer
The integral diverges.
Work Step by Step
We have
$$
\int_{0}^{\infty} (x+5)^{-1/3} dx=\int_{0}^{\infty} (x+5)^{-1/3} d(x+5)\\
=\frac{1}{2/3}(x+5)^{2/3}|_0^{\infty}=\frac{3}{2}(\infty-5^{2/3})=\infty
$$
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 - Chapter Review Exercises - Page 461: 83
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