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Integral Brain fart.

  1. Apr 1, 2004 #1
    One of my recent problems is with double integrals... and im having a brain fart on the [tex]\int ln(u) du [/tex] can you do this?
     
  2. jcsd
  3. Apr 1, 2004 #2

    NateTG

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    You can do it by parts. Consider that
    [tex]\frac{d}{dx} x \ln x = \ln x + 1[/tex]
     
  4. Apr 1, 2004 #3
    hrmm... i see what your saying..
     
  5. Apr 1, 2004 #4
    wouldn't it just be 1/u???
    unless that little dash is a negative sign mean your are integrating 1/ln(u) then I'm not sure but i think it would just be u then, but i am probably wrong
     
  6. Apr 1, 2004 #5

    ahrkron

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    iluvsr20s,

    You are probably confused with the fact that [tex]\int \frac{1}{u} du = \ln x + c[/tex]. It is not the other way around.
     
  7. Apr 1, 2004 #6
    Pfft...

    ... hehe. this ain't too bad. Can we change it to int(ln(x),dx) though? It's how I've always done it notation-wise.

    let u = ln(x), dv = dx --> du = 1/x(dx), v = x

    So, u*v -int(v,du) = int(u,dv)

    x*ln(x) - int(1,dx) = int(ln(x),dx)
    x*ln(x) - x = int(ln(x),dx)

    Et voila.
     
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