求助∫x^2ln(X+X^2)dx - 知识问答

求助∫x^2ln(X+X^2)dx

2个回答

∫x^2ln(x+x^2)dx
=(1/3)∫ln(x+x^2)d(x^3)
=(1/3)x^3ln(x+x^2)-(1/3)∫x^3(1+2x)/(x+x^2)dx
=x^3ln(x+x^2)/3-(1/3)∫[2(x+1)x^2-(x+1)^2+2(x+1)-1]/(x+1)dx ------约分,化成分母形式,展开
=x^3ln(x+x^2)/3-(1/3)∫(2x^2-x+1)dx-(1/3)∫1/(x+1)dx
=x^3ln(x+x^2)/3-2x^3/9+x^2/6-x/3-ln|x+1|/3+c

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