Integral of natural log function using substitution

Integral of natural log function using substitution

$$\int_{2} ^{4}\dfrac{dx}{x(lnx)^2}$$
Here is what I did:
$$u=lnx, du=\dfrac{dx}{x}$$
$$\int_{2} ^{4}u^{-2}du$$
$$(-1)u^{-1} |_{2}^{4}$$
$$-\dfrac{1}{lnx}|_{2}^{4}$$
$$-\dfrac{1}{ln4} + \dfrac{1}{ln2}$$
However the answer in the back of my textbook says that the answer is
$\dfrac{1}{ln4}$. I have went over my work a couple of times and I cannot
see what I did wrong. Could someone please explain what's wrong here?
Thank you.