prove-that-i-n-0-1-n-n-1-2-cosh-n-1-2-pi-pi-4-ii-0-1-sin-pi-x-x-x-1-x-1-x-dx-1-x-pi-4-

Question Number 163002 by mnjuly1970 last updated on 03/Jan/22

p r o v e t h a t

i : \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{(n + \frac{1}{2}) c o s h (n + \frac{1}{2}) π} = \frac{π}{4}

i i : \int_{0}^{1} \frac{s i n (π x)}{x^{x} {(1 - x)}^{1 - x}} \frac{d x}{1 + x} = \frac{π}{4}

- - -