求解:y的三阶导数等于ln x
- 培训职业
- 2025-05-04 23:03:32
∫lnx dx = xlnx - ∫xdlnx = xlnx -x +C1
∫xlnx -x +C1dx = ∫xlnx dx -x^2/2 +c1x = ∫lnx dx^2/2 -x^2/2 +c1x
= 0.5x^2lnx - x^2/2 +c1x - x^2/4 +C2= 0.5 x^2 lnx -3x^2/4 +c1x +c2
∫0.5 x^2 lnx -3x^2/4 +c1x +c2dx =∫0.5x^2lnx dx - x^3/4 +c1x^2 +c2x
= ∫lnx dx^3/6 dx- x^3/4 +c1x^2 +c2x = x^3lnx/6 - x^3/18 - x^3/4 +c1x^2 +c2x +C3
这就是答案，没有难度，只是繁琐
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