I have to determine using the comparison theorem if the following integral rather converges or diverges:

$$ int_0 ^ infty frac { ln {x}} {x ^ 2} dx $$

It is evident that this tintegral is improper because the upper limit goes to infinity and is asymptotic in $ x = 0 $. Then I split it into two parts:

$$ int_0 ^ infty frac { ln {x}} {x ^ 2} dx = int_0 ^ 1 frac { ln {x}} {x ^ 2} dx + int_1 ^ infty frac { ln {x}} {x ^ 2} dx $$

Of course, the first part has a negative sign and the second, a positive sign.

So, is it possible to determine with the comparison theorem the nature of the integral? In that case, what are the functions to compare?

Also, is it possible that the negative area can be canceled by the positive area?