mathematical-analysis-II-prove-that-0-1-1-1-x-ln-x-2-2x-1-1-x-x-2-n-1-1-n-2-2n-n-pi-2-18-

Question Number 137610 by mnjuly1970 last updated on 04/Apr/21

\dots \dots . . m a t h e m a t i c a l a n a l y s i s (I I) \dots .

p r o v e t h a t ::

Ω = \int_{0}^{1} \frac{1}{1 + x} l n (\frac{x^{2} + 2 x + 1}{1 + x + x^{2}}) = \underset{n = 1}{\sum^{\infty}} \frac{1}{n^{2} (\begin{matrix} 2 n \\ n \end{matrix})} = \frac{π^{2}}{18} . .