prove the relation ∫_0 ^1 ((li_5 ((x)^(1/5) ))/(x)^(1/5) )dx=(5/4)(((25)/(3072))−((ζ(2))/2^6 )+((ζ(3))/2^4 )−((ζ(4))/2^2 )+ζ(5))


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Question Number 85603 by M±th+et£s last updated on 23/Mar/20

$p r o v e t h e r e l a t i o n$ $\int_{0}^{1} \frac{{l i}_{5} (\sqrt[5]{x})}{\sqrt[5]{x}} d x = \frac{5}{4} (\frac{25}{3072} - \frac{ζ (2)}{2^{6}} + \frac{ζ (3)}{2^{4}} - \frac{ζ (4)}{2^{2}} + ζ (5))$
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