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Evaluate: int(x^3+x^2+2x+1)/(x^2-x+1)\ d...

Evaluate: `int(x^3+x^2+2x+1)/(x^2-x+1)\ dx`

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I=`int(x^3+x^2+2x+1)/(x^2-x+1)\ dx`
`I=x+2+ (3x-1)/(x^2-x+1) `
`I=x+2+ (3(2x-2/3)x+1-1)/(x^2-x+1) `
`I=x+2+3/2((2x-1)+(-2/3+1))/(x^2-x+1) `
`I=int x+int 2+3/2 int(2x-1)/(x^2-x+1) dx +3/2 1/3 dx/(x^2-x+1)`
`I=1/2 x^2+2x+3/2 log(x^2-x+1)+1/3 2/(sqrt(3)) tan^(-1)(2(x-1/2)/(sqrt(3)))+c`
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