Answer:
It diverges.
Step-by-step explanation:
We are given the inetegral: [tex]\int\limits^{\infty}_2 \frac{1}{x} (\ln x)^2 dx[/tex]
[tex]\int\limits^{\infty}_2 \frac{1}{x} (\ln x)^2 dx=\int\limits^{\infty}_2 (\ln x)^2 d(\ln x)=\\\\=\lim_{t \to \infty} \int\limits^t_2 (\ln x)^2d(\ln x)=\lim_{t \to \infty} \frac{(\ln t)^3}{3} |^t_2=\infty-\frac{(\ln 2)^3}{3} =\infty[/tex]
So it is divergent.
