(x눀-x+1)lnxdx不定积分

2025-04-14 18:54:14
推荐回答(2个)
回答1:

分三项分部积分,详解参考下图

回答2:

∫(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