Answer
Convergent for $p\lt -1$.
Work Step by Step
$\int_{1}^{\infty}x(1+x^{2})dx=\int_{2}^{\infty}\frac{1}{2}u^{p}du=\frac{1}{2}(\infty^{p}-2^{p})$
which is convergent for $p\lt -1$.
Calculus: Early Transcendentals 9th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1337613924
ISBN 13:
978-1-33761-392-7
Chapter 11 - Section 11.3 - The Integral Test and Estimates of Sums - 11.3 Exercises - Page 759: 33
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