∫xdx/(x^3-3x+2)求解∫xdx/(x^3-3x+2)哪位好心人帮我解下

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∫xdx/(x^3-3x+2)求解∫xdx/(x^3-3x+2)哪位好心人帮我解下

∫xdx/(x^3-3x+2)求解∫xdx/(x^3-3x+2)哪位好心人帮我解下
∫xdx/(x^3-3x+2)求解
∫xdx/(x^3-3x+2)哪位好心人帮我解下

∫xdx/(x^3-3x+2)求解∫xdx/(x^3-3x+2)哪位好心人帮我解下
请看图:

∫xdx/(x^3-3x+2)
=ʃxdx/[(x-1)(x-2)]
=ʃx[1/(x-2)-1/(x-1)]dx
=ʃ[x/(x-2)-x/(x-1)]dx
=ʃ[2/(x-2)-1/(x-1)]dx
=2ʃd(x-2)/(x-2)-ʃd(x-1)/(x-1)
=2ln|x-2|-ln|x-1|+C