What is the integral of lim n→∞ 1/n ∑top: n bottom: i=1 Sqrt[(ln(1+i/n)]?

Question

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What is the integral of lim n→∞ 1/n ∑top: n bottom: i=1 Sqrt[(ln(1+i/n)]?

Answer 1

lim n→ ∞ 1/n∑₁ⁿsqrt[ln(1 + i/n)] = ∫₁²sqrt(lnx)dx