Limit of an Integral!

Calculus Level 4

lim⁡n→∞n∫1ex2(ln⁡(x))n dx\large{ \lim_{n \to \infty} n \int_1^e x^2 (\ln(x))^n \, dx}

For integer nn, let LL denote the value of the limit above. Find the value of ln⁡(L)\ln(L ) .

Satyajit Mohanty by Satyajit Mohanty
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