S1/(x^3+1)dx=S[1/3*1/(x+1)-1/3*(x-1/2)/(x^2-x+1)-1/2*1/(x^2-x+1)]dx=1/3*ln|x+1|-1/6*ln(x^2-x+1)-2/根3*arctan(2/根3)(x-1/2)]+c
ln(x^3+1)的导数是1/(x^3+1)