原式=∫(x^3-2x^2+3x+2x^2-4x+6+x-6)/(x^2-2x+3)dx=∫xdx+∫2dx+∫(x+6)/((x-1)^2+2)dx=1/2x^2+2x+∫(x-1+7)/((x-1)^2+2)d(x-1)=1/2x^2+2x+1/2∫1/((x-1)^2+2)d(x-1)^2+7√2/2∫1/(((x-1)/√2)^2+1)d((x-1)/√2)=1/2...