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I Unsure of solution to improper integral

  1. Apr 24, 2016 #1
    I've been trying to solve this improper integral ∫[∞][1] ln(x) x^-1 dx. I couldn't find any way to use the comparison test to find divergence, so I used substitution and got ∞-∞ which I was pretty sure was divergence until I noticed I put 0 instead of 1 making my answer ∞. Do I need to prove divergence with a comparison test or is an answer of ∞ enough to prove it.
  2. jcsd
  3. Apr 24, 2016 #2


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    Hi T, :welcome:
    You could work out $$\int_1^Y {\ln x\over x} dx $$ (As I think you did already) and take ##\lim Y\rightarrow \infty## to show the integral does not exist.
  4. Apr 24, 2016 #3


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    Hi,this integral has simple antiderivative (after substituting ##\ln##), after you can take the limit of the result for ##Y\rightarrow +\infty## (as suggested by @BvU ).
  5. Apr 24, 2016 #4
    Thanks for your help and the warm welcome.
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