设3\(x^3+1)=a\(x+1)+(bx+c)\(x^2-x+1)
得a=1,b=-1,c=2
3\(x^3+1)=1\(x+1)-(2x-1)\2(x^2-x+1)+3\2[(x-1\2)^2+3\4]
∴∫3/(x∧3+1)dx =In|x+1|-(1\2)*In(x^2-x+1)
+3^(1\2)arctan[(2x-1)\3^(1\2)]+C