∫（x-4）╱（x的平方-3x+2）dx - 知识问答

∫（x-4）╱（x的平方-3x+2）dx

1个回答

答：
∫[(x-4)/(x^2-3x+2)]dx
=∫{(x-4)/[(x-2)(x-1)]}dx
=∫{(x-4)[1/(x-2)-1/(x-1)]}dx
=∫[(x-4)/(x-2)]dx-∫[(x-4)/(x-1)]dx
=∫[1-2/(x-2)]dx-∫[1-3/(x-1)]dx
=x-2ln|x-2|-x+3ln|x-1|+C
=3ln|x-1|-2ln|x-2|+C

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