It becomes child's play, part 2 (My eighth integral problem)

Calculus Level 5

\[ \int_{2}^{3} \sqrt{\left[x^{2} + x + 1 \right]-\sqrt{\left[x^{2} + x + 1\right]+\sqrt{\left[x^{2} + x + 1 \right]-\sqrt{\left[x^{2} + x + 1 \right]+\cdots}}}} \, dx \]

If the value of the integral above is \(V \), input \(10V\) as the answer.

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