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 $p\gt 1$.
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 11 - Infinite Sequences and Series - 11.3 The Integral Test and Estimates of Sums - 11.3 Exercises - Page 766: 30
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