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Evaluate: int1/(x^2+x+1)dx...

Evaluate: `int1/(x^2+x+1)dx`

Text Solution

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`int(1)/(x^(2)-x+1)dx`
`=int(1)/((x-1//2)^(2)+3//4)dx`
`=int(1)/((x-1//2)^(2)+(sqrt(3)//2)^(2))dx`
`=(1)/(sqrt(3)//2)tan^(-1)((x-1//2)/(sqrt(3)//2))+C`
`=(2)/(sqrt(3))tan^(-1)((2x-1)/(sqrt(3)))+C`
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