∫(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