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Homework Help: Some weird integral with natural logarithm

  1. Mar 2, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\displaystyle\int\left(\dfrac{\ln x}{x}\right)^2 dx[/tex]

    2. The attempt at a solution

    I tried letting [tex]u=\ln^2 x[/tex] and dv the rest and I also tried [tex]dv=\ln^2 x dx[/tex] and u the rest. It won't work out.
  2. jcsd
  3. Mar 2, 2009 #2
    Let u = ln(x), => du = 1/x dx.

    Then your integrand is [(u^2) / x]du

    Well, x = exp(u), so what you really have is (u^2)exp(-u)du

    Does that work? You should be able to handle that one...
  4. Mar 2, 2009 #3


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    Gold Member

    your dv is wrong its [tex]dv=\frac{1}{x^2} dx[/tex]
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