January 29th, 2015, 11:37 AM  #1 
Newbie Joined: Oct 2014 From: Here Posts: 17 Thanks: 0  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. 
January 29th, 2015, 11:51 AM  #2 
Senior Member Joined: Dec 2013 From: some subspace Posts: 212 Thanks: 72 Math Focus: real analysis, vector analysis, numerical analysis, discrete mathematics 
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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convergence, divergence 
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