Find-in-closed-form-n-N-0-1-ln-1-x-2-ln-n-1-x-dx-

Question Number 150121 by mathdanisur last updated on 09/Aug/21

Find in closed form : n \in N^{*}

\underset{0}{\int^{1}} \ln (1 - x^{2}) \ln^{n} (1 - x) dx = ?

Answered by Kamel last updated on 09/Aug/21

2 {(- 1)}^{n} n! (\underset{k = 2}{\sum^{n + 1}} {L i}_{k} (\frac{1}{2}) + L n (2) - n - 1)

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