求积分(3/2)∫dx/(x^2-x+1)

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/05/30 23:54:21

(3/2)∫dx/(x^2-x+1)=根号[3] ArcTan[(-1 + 2 x)/根号[3]]+c
再问：思路过程？我也知道答案是这个啊Q_Q
再答： ∫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*arctan1/[2√3/3*(x-1/2)]+C

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