∫ (1-lnx)/(x-lnx)^2 dx
=∫ [ (x-lnx) - x(1-1/x) ] /(x-lnx)^2 dx
=∫ [ (x)'(x-lnx) - x(x-lnx)' ] /(x-lnx)^2 dx
= x/(x-lnx) + C