求∫[1/(x²+x+1)]dx=（2/√3）arctan[(2x+1)/ √3]+C详细推导过程

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/08/31 11:14:18

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

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