求下列不定积分：∫xln(x一1)dx
∫xln(x-1)dx=1/2x2ln(x-1)-1/2∫x2/(x-1)dx=1/2x2ln(x-1)-1/2∫[x+1+1/(x-1)]dx=x2/2ln(x-1)-x2/4-x/2-1/2ln(x-1)+c=(x2-1)/2ln(x-1)-x/4(x+2)+c．
求下列不定积分：∫xln(x一1)dx
∫xln(x-1)dx=1/2x2ln(x-1)-1/2∫x2/(x-1)dx=1/2x2ln(x-1)-1/2∫[x+1+1/(x-1)]dx=x2/2ln(x-1)-x2/4-x/2-1/2ln(x-1)+c=(x2-1)/2ln(x-1)-x/4(x+2)+c．
