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January 29th, 2015, 11:37 AM   #1
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Convergence and Divergence help

Hello,

I have 2 integrals I want to proof are either diverging or converging:

The 2 are:
First: Integral of (1/(x*ln(x)))dx from 1 to infinity
Second: Integral of (1/(x*ln(x)^2))dx from 1 to infinity

Almost the same just that the second one is (ln(x))^2

I am almost sure that the first 1 diverges and the second one with ln(x)^2 converges, I just dont find which method to proove that.

Thanks

Last edited by jamesmith134; January 29th, 2015 at 11:44 AM.
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January 29th, 2015, 11:51 AM   #2
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If you sibstitute $\displaystyle \ln x = t$, you should be able to integrate them. After that, look at the limits carefully. What do they do when approaching infinity or 0 (with respect to new variable $\displaystyle t$)?
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