1÷(x^2+x+1)dx
=ʃdx/[(x+1/2)^2+3/4]
=ʃ4/3*dx/[(2x/√3+1/√3)^2+1]
=4/3*√3/2ʃd(2x/√3+1/√3)/[(2x/√3+1/√3)^2+1]
=2√3arctan(2x/√3+1/√3)+C
∴ʃ(-∞,+∞)1÷(x^2+x+1)dx
=2√3arctan(2x/√3)|(-∞,+∞)
=2√3π
1÷(x^2+x+1)dx
=ʃdx/[(x+1/2)^2+3/4]
=ʃ4/3*dx/[(2x/√3+1/√3)^2+1]
=4/3*√3/2ʃd(2x/√3+1/√3)/[(2x/√3+1/√3)^2+1]
=2√3arctan(2x/√3+1/√3)+C
∴ʃ(-∞,+∞)1÷(x^2+x+1)dx
=2√3arctan(2x/√3)|(-∞,+∞)
=2√3π