- #1

- 42

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[itex]

\int_2^\infty \left(\frac{1}{x\log^2x}\right)^p \, dx

[/itex]

converges for p=1, but does it diverge for p>1? How do you show this?

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- Thread starter tjkubo
- Start date

- #1

- 42

- 0

[itex]

\int_2^\infty \left(\frac{1}{x\log^2x}\right)^p \, dx

[/itex]

converges for p=1, but does it diverge for p>1? How do you show this?

- #2

mathman

Science Advisor

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It will converge for p > 1, since it is dominated by p=1 integrand. It will diverge for p < 1, since integrand > 1/x.

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- #3

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Mathman, the integrand is not always > 1/x on (2,∞) for all p<1. For p=0.9, for example, it's < 1/x for the most part.

- #4

mathman

Science Advisor

- 7,924

- 467

To be precise, there will be some X so that for all x > X, the integrand is > 1/x. (That is for the most part).

Mathman, the integrand is not always > 1/x on (2,∞) for all p<1. For p=0.9, for example, it's < 1/x for the most part.

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