求不定积分∫xln(x-1)dx．
利用分部积分公式．∫xln(x-1)dx=∫ln(x-1)d(x2/2)=(x2/2)ln(x-1)-∫x2/2•[1/(x-1)]dx=(x2/2)ln(x-1)-1/2∫[x+1+1/(x-1)]dx=(x2/2)ln(x-1)-x2/4-x/2-(1/2)ln(x-1)+C．
求不定积分∫xln(x-1)dx．
利用分部积分公式．∫xln(x-1)dx=∫ln(x-1)d(x2/2)=(x2/2)ln(x-1)-∫x2/2•[1/(x-1)]dx=(x2/2)ln(x-1)-1/2∫[x+1+1/(x-1)]dx=(x2/2)ln(x-1)-x2/4-x/2-(1/2)ln(x-1)+C．
