求ln(x-1)乘x的原函数

分部积分法：∫xln(x-1)dx=(x^2/2)ln(x-1)-∫(x^2/2)/(x-1)dx=(x^2/2)ln(x-1)-1/2∫(x^2-x+x-1+1)/(x-1)dx=(x^2/2)ln(x-1)-1/2∫[x+1+1/(x-1)]dx=(x^2/2)ln(x-1)-1/2[x^2/2+x+ln|x-1|]+C