∫ dx/(x²+x+1)= ∫ dx/[(x+1/2)²+3/4]= ∫ d(x+1/2)/[(x+1/2)²+√(3/4)²]= 1/√(3/4) * arctan[(x+1/2)/√(3/4)] + C= (2/√3)arctan[(2x+1)/√3] + C
