$\displaystyle \int_{1}^{\infty} \frac{\ln(x)}{x^2} \, dx.$
$\displaystyle \int_{1}^{\infty} \frac{\ln(x)}{x} \, dx.$
$\displaystyle \int_{0}^{1} \frac{\ln(x)}{\sqrt{x}} \, dx.$
I'm really confused because I've been using comparison test for previous ones such as $1/x^n$ and $x/x^n$ but I don't know what to do when it's $\ln(x)/x^n$. Or any other function such as $\sin x$ in the numerator in that sense. Help on the third one would be awesome as well.
Hints: 1. $\ln x < x^{1/2}$ for large $x.$
$\ln x >1$ for $x>e.$
$|\ln x| < 1/x^{1/4}$ for small positive $x.$