Hai friends... Long time not stay in here. Let, discusse about calculus. I have not idea for solve problem bellow. Thank you for your hint...

\(\displaystyle \lim_{n \to \infty} n^4 \int_{0}^{1} \frac{ln(1-x)ln^{3} (x)}{1+x^{-n}} dx\)

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TopNewestHint : set \(x^n=t\).

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After you do the sum the integral would be : \[\int_0^1 \frac{t^{1/n} \ln(1-t^{t/n}) \ln^3(t)}{1+t} \ \mathrm{d}t\] Now, can you see the limit ?

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