Answer
Convergent for $p\gt 1$
Work Step by Step
$\int_{3}^{\infty}\frac{1}{xlnx[ln(lnx)]^{p}}dx=\int_{ln(ln3)}^{\infty}\frac{1}{u^{p}}du=\int_{ln(ln3)}^{\infty}u^{-p}du$
which is convergent for $p\gt 1$.
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: 30
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