Evaluate: `int(x+1)\ sqrt(x^2+x+1)\ dx`

Explanation

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Let `{I}=int(x+1) sqrt{x^{2}+x+1} d x `

`x+1=lambda frac{d}{d x}(x^{2}+x+1)+mu `

`Rightarrow x+1=lambda(2 x+1)+mu `

`Rightarrow x+1=(2 lambda) x+lambda+mu`

Equating coefficient

`2 lambda=1 `

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