(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Natural log intergration

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