∫Inx/(1-x)^2dx=-∫Inx/(1-x)^2d(1-x)=∫Inxd1/(1-x)=lnx/(1-x)-∫x/(1-x)dx=lnx/(1-x)+∫(1-x+1)/(1-x)dx=lnx/(1-x)+∫[1+1/(1-x)]dx=lnx/(1-x)+x-ln(1-x)+C
用分部积分即可原式=∫lnxd1/(1-x)=lnx/(1-x)+∫1/x(x-1)dx=lnx/(1-x)+ln[x/(x-1)]+c