原式=不定积分（x^2）/(x^2-3x+2)dx
=不定积分（x^2-3x+2+3x-2）/(x^2-3x+2)dx
=不定积分1dx+不定积分[3(x-1)+1]/(x-2)(x-1)dx
=x+不定积分3/(x-2)dx+不定积分1/(x-2)(x-1)dx
=x+3ln(x-2)+ln[(x-2)/(x-1)]+C
=x+ln[(x-2)^4/(x-1)]+C