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 $p\lt -1$.
Multivariable Calculus, 7th Edition
by Stewart, James
Published by
Brooks Cole
ISBN 10:
0-53849-787-4
ISBN 13:
978-0-53849-787-9
Chapter 11 - Infinite Sequences and Series - 11.3 Exercises - Page 745: 31
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