$\displaystyle \int_e^{\infty} \frac{1}{x(\ln x)^3} dx$

First i made a u-substitution by making u = ln x.

After which i got $\displaystyle -\frac{1}{2(\ln x)^2}$

Then i went back to compute the improper integral again , but couldn't solve it.

Did i made any wrong move?

Thanks