prove-that-0-1-t-2p-1-ln-t-t-2-1-dt-pi-2-24-1-4-k-1-p-1-k-2-

Question Number 40886 by prof Abdo imad last updated on 28/Jul/18

p r o v e t h a t

\int_{0}^{1} \frac{t^{2 p + 1} l n (t)}{t^{2} - 1} d t = \frac{π^{2}}{24} - \frac{1}{4} \sum_{k = 1}^{p} \frac{1}{k^{2}}