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limn→∞n∫1ex2(ln(x))n dx\large{ \lim_{n \to \infty} n \int_1^e x^2 (\ln(x))^n \, dx}n→∞limn∫1ex2(ln(x))ndx
For integer nnn, let LL L denote the value of the limit above. Find the value of ln(L)\ln(L ) ln(L).
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