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0-log-sinh-x-log-tanh-x-dx-7-3-8-pi-2-8-ln-2-




Question Number 155849 by mnjuly1970 last updated on 05/Oct/21
      Ω=∫_0 ^( ∞) log(sinh(x)).log(tanh(x))dx=((7ζ(3))/8) +(π^( 2) /8)ln^  (2)
$$ \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} {log}\left({sinh}\left({x}\right)\right).{log}\left({tanh}\left({x}\right)\right){dx}=\frac{\mathrm{7}\zeta\left(\mathrm{3}\right)}{\mathrm{8}}\:+\frac{\pi^{\:\mathrm{2}} }{\mathrm{8}}{ln}^{\:} \left(\mathrm{2}\right) \\ $$

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