we know that $$ \ln(x)=\frac{1}{x} \int_{0}^{1}dt \frac{1}{1+xt} $$
then given a cuadrature formula inside $(0,1)$ is that true
$$ \ln(x)= \frac{1}{x}\sum_{i}\frac{w_{i}}{1+xt_{i}} $$
wht other rational approximations of logarithm are useful based on rational functions ?? $ R(x)$