Calculus Of the day

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...

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

#Calculus

Easy Math Editor

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Comments

Hint : set $x^n=t$ .

Haroun Meghaichi - 6 years, 10 months ago

Next hint...

pebrudal zanu - 6 years, 10 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 ?

Haroun Meghaichi - 6 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$