分三项分部积分,详解参考下图
∫(x^2-x+1)lnx dx= ∫lnx d(x^3/3 - x^2/2 + x)= (x^3/3 - x^2/2 + x)lnx - ∫(x^3/3 - x^2/2 + x) dlnx= (x^3/3 - x^2/2 + x)lnx - ∫(x^2/3 - x/2 + 1) dx= (x^3/3 - x^2/2 + x)lnx - (x^3/9 - x^2/4 + x) +C