设1/[x(x+1)(x^2+x+1)=A/x+B/(x+1)+(C+Dx)/(x^2+x+1),A=1,B=-1C=-1,D=0,∴原式=∫[1/x-1/(x+1)-1/(x^2+x+1)]dx=∫dx/x-∫dx/(x+1)-∫d（x+1/2）/[(x+1/2)^2+3/4]=ln|x/（x+1)|-2√3/3arctan[2(x+1/2)/√3]+C
