解：∵3x^2-8x-1=(3x^2-6x+3)-(2x+4)=3(x-1)^2-2(x+2)，∴原式=3∫dx/[(x-1)(x+2)]-2∫dx/(x-1)^3。而，3∫dx/[(x-1)(x+2)]=∫[1/(x-1)-1/(x+2)]dx=ln丨(x-1)/(x+2)丨+c1；-2∫dx/(x-1)^3=1/(x-1)^2+c2，∴原式=ln丨(x-1)/(x+2)丨+1/(x-1)^2+C。供参考。
