x/(x^2-x+1) = (x -1/2) /(x^2-x+1) + (1/2) /(x^2-x+1)
∫(x -1/2) /(x^2-x+1) dx 凑微分,u = (x^2-x+1)
= (1/2)∫du / u = (1/2) lnu + C = (1/2) ln (x^2-x+1) + C
∫(1/2) /(x^2-x+1) dx = (1/2)∫dx / [(x-1/2)² + 3/4] 凑微分,v=(x-1/2)
= (1/2) ∫dv / (v² + 3/4) = (1/2) * (2 /√3) arctan(2v /√3) + C
= 1/√3 * arctan[(2x-1) /√3] + C
原式 = (1/2) ln (x^2-x+1) + (1 /√3) * arctan[(2x-1) /√3] + C
