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...

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

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...

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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestHint : set \(x^n=t\). – Haroun Meghaichi · 2 years, 5 months ago

Log in to reply

– Pebrudal Zanu · 2 years, 5 months ago

Next hint...Log in to reply

– Haroun Meghaichi · 2 years, 5 months ago

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 ?Log in to reply