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

Explanation

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

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

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

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

Equating coefficient

`2 lambda=1 `

`Rightarrow lambda=frac{1}{2}`

And

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