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Homework Help: Natural log intergration

  1. Feb 6, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]\int^{4}_{2} \frac{dx}{x\left(lnx\right)^{2}}[/tex]

    2. Relevant equations
    Let [tex]u=lnx[/tex]
    [tex]du=\frac{1}{x}dx[/tex]
    [tex]x=2 \rightarrow u=ln2[/tex]
    [tex]x=4 \rightarrow u=ln4[/tex]

    3. The attempt at a solution
    so with the u substitution we have:

    [tex]\int^{ln4}_{ln2} \frac{1}{u^{2}}du[/tex]

    which goes to:

    [tex]lnu^{2}\right|^{ln4}_{ln2}[/tex]

    then:

    [tex]2\cdot lnu\right|^{ln4}_{ln2}[/tex]

    and when we work it out we get:

    [tex]2\cdot\left[ln\left(ln4\right)-ln\left(ln2\right)\right][/tex]

    and then:

    [tex]2\cdot ln\left(\frac{ln4}{ln2}\right)[/tex]

    This is where I am stuck. I am supposed to get:

    [tex]\frac{1}{ln4}[/tex]

    and I have no idea how they got that. Any help would be appreciated.
     
  2. jcsd
  3. Feb 6, 2010 #2
    then integral of 1/u^2 evaluates to -1/u.
     
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