计算∫(4x-6)/(x^2-3x+9)dx,

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计算∫(4x-6)/(x^2-3x+9)dx,
计算∫(4x-6)/(x^2-3x+9)dx,

计算∫(4x-6)/(x^2-3x+9)dx,
∫(4x-6)/(x²-3x+9)dx
=2∫(2x-3)/(x²-3x+9)dx
=2∫1/(x²-3x+9)d(x²-3x)
令x²-3x=t
则
=2∫1/(t+9)dt
=2∫1/(t+9)d(t+9)
=2ln(t+9)+c
=2ln(x²-3x+9)+c

∫(4x-6)/(x^2-3x+9)dx,
=4ʃ（x-3/2)/[(x-3/2)²+27/4] dx
=2ʃ d[（x-3/2)²+27/4]/[(x-3/2)²+27/4]
=2ln|(x-3/2)²+27/4|+C
=2ln(x^2-3x+9)+C

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