∫(1-lnx)/(x-lnx)^2 dx
=∫[(x-lnx)+(1-x)]/(x-lnx)^2 dx
=∫1/(x-lnx) dx+∫(1-x)/(x-lnx)^2 dx
=x*1/(x-lnx)-∫ xd[1/(x-lnx)]+∫(1-x)/(x-lnx)^2 dx→第一部分分部积分法
=x/(x-lnx)-∫x(1-x)/[x(x-lnx)^2] dx+∫(1-x)/(x-lnx)^2 dx
=x/(x-lnx)-∫(1-x)/(x-lnx)^2 dx+∫(1-x)/(x-lnx)^2 dx,第二项和第三项可抵消
=x/(x-lnx)+C