这题要采用分部积分法
xln(x-1)dx = ln(x-1)d(x²)
∫xln(x－1)dx
=∫ln(x－1)d(x²)
=x²ln(x-1)- ∫x²*[1/(x-1)]dx
∫x²*[1/(x-1)]dx = ∫[x+1+1/(x-1)]dx = 1/2x²+x+ln|x-1| + C
仅供参考~