∫[(x^2-x+6)/(x^3+3x)]dx - 知识问答

∫[(x^2-x+6)/(x^3+3x)]dx

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1个回答

(x^2-x+6)/(x^3+3x)=2/x-(x+1)/(x^2+3).
原式=∫2/xdx-∫(x+1)/(x^2+3)dx
=2ln|x|-(1/2)ln(x^2+3)-(1/√3)arctan(x/√3)+C.

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