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

    and when we work it out we get:


    and then:

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

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


    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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