(lnx/x)'=-lnx/x^2+1/x^2∫lnx/x^2dx=∫(lnx/x^2-1/x^2+1/x^2)dx=∫d(-lnx/x)+∫1/x^2dx=-lnx/x-1/x=-(1+lnx)/x |(1,+∞)=0+(1+0)/1=1
