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