求积分(3/2)∫dx/(x^2-x+1)

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求积分(3/2)∫dx/(x^2-x+1)
求积分(3/2)∫dx/(x^2-x+1)

求积分(3/2)∫dx/(x^2-x+1)
(3/2)∫dx/(x^2-x+1)=根号[3] ArcTan[(-1 + 2 x)/根号[3]]+c

∫1/(x²-x+1) dx=∫1/[(x-1/2)²+3/4] dx
=∫1/[(x-1/2)²+3/4] d(x-1/2)
=4/3*∫1/{[2√3/3*(x-1/2)]²+1} d(x-1/2)
=2√3/3...

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∫1/(x²-x+1) dx=∫1/[(x-1/2)²+3/4] dx
=∫1/[(x-1/2)²+3/4] d(x-1/2)
=4/3*∫1/{[2√3/3*(x-1/2)]²+1} d(x-1/2)
=2√3/3*∫1/{[2√3/3*(x-1/2)]²+1} d[2√3/3*(x-1/2)]
=2√3/3*arctan[2√3/3*(x-1/2)]+C
后面就带进去算就可以了
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