prove-that-0-tanhx-x-3-sech-2-x-x-2-dx-7-pi-2-3-where-3-apery-s-constant-

Question Number 112369 by mathdave last updated on 07/Sep/20

p r o v e t h a t

\int_{0}^{\infty} (\frac{\tanh x}{x^{3}} - \frac{{sech}^{2} x}{x^{2}}) d x = \frac{7}{π^{2}} ζ (3)

w h e r e ζ (3) = {a p e r y}^{'} s c o n s t a n t