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