How do I solve this natural log integration problem?

[efekwulsemmay]

Homework Statement

$$\int^{4}_{2} \frac{dx}{x\left(lnx\right)^{2}}$$

Homework Equations

Let $$u=lnx$$
$$du=\frac{1}{x}dx$$
$$x=2 \rightarrow u=ln2$$
$$x=4 \rightarrow u=ln4$$

The Attempt at a Solution

so with the u substitution we have:

$$\int^{ln4}_{ln2} \frac{1}{u^{2}}du$$

which goes to:

$$lnu^{2}\right|^{ln4}_{ln2}$$

then:

$$2\cdot lnu\right|^{ln4}_{ln2}$$

and when we work it out we get:

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

and then:

$$2\cdot ln\left(\frac{ln4}{ln2}\right)$$

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

$$\frac{1}{ln4}$$

and I have no idea how they got that. Any help would be appreciated.

 

[Samuelb88]

then integral of 1/u^2 evaluates to -1/u.