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

$$provethat$$$${\int }_0^{\mathrm{\infty }}(\frac{\tanh x}{x^3}-\frac{{\mathrm{sech}}^{2}x}{x^2})dx=\frac{7}{{\pi }^2}\zeta \left(3\right)$$$$where\zeta \left(3\right)={apery}^{\prime }sconstant$$

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