Integrate the function $\frac{\large 1}{\large x+x\;log x}$

Question

$\begin{array}{1 1} \log\;|(1+\log x)|+c. \\ \log\;|(1-\log x)|+c. \\ \log\;|(x+\log x)|+c. \\ \log\;|(x-\log x)|+c.\end{array} $