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Integrating indefinitely: (ln x)/x^3

  1. Jun 8, 2008 #1
    edit: Nevermind, I realized a way to find the answer after posting it. Though I still don't know about the thing involving the notes, can someone confirm if what I have written down as my teacher doing is true?

    1. The problem statement, all variables and given/known data
    note: I'll use this S as an integral symbol.

    S(ln x)/x^3

    2. Relevant equations

    3. The attempt at a solution
    With a ln x type function being divided by a power of x, I did the obvious and made u = ln x and du = 1/x dx, but that still leaves x^-2. I don't know how to get from here.

    I just saw this problem in my notes and am not sure if I made an error when writing, but what my teacher appears to have done is made the same substitution I did, and then wrote
    S(ln x)/x^3 = Se^(-2u) du.

    I don't know how one makes that, and when I plug back the substitution I don't arrive at the original equation. I get e^(-2 ln x)*dx/x = (x^2)/x * dx (I split e^-2 ln x into (e^-ln x)(e^-ln x) = -x^2. So I think I just wrote something down wrong, but in any case, I still do not know how to go beyond that simple substitution I made earlier.

    edit: I just needed to integrate by parts with ln x = u and dv = 1/x^3
    Last edited: Jun 8, 2008
  2. jcsd
  3. Jun 8, 2008 #2


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    Homework Helper

    Yes integration by parts would work,but the substitution of u=lnx works as well,though longer


    and [itex]u=lnx \Rightarrow x=e^u[/itex]

    so you can find [itex]x^{-2}[/itex] from that and you'll get what he did.
  4. Jun 8, 2008 #3
    Thank you. :p
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