Formelsammlung Mathematik: Bestimmte Integrale: Form R(x,log,cosh)

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1.1

$\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}\frac{\log ({\alpha }^2+x^2)}{\cosh \pi x}dx=4\log \left(\sqrt{2}\frac{\mathrm{\Gamma }(\frac{3}{4}+\frac{\alpha }{2})}{\mathrm{\Gamma }(\frac{1}{4}+\frac{\alpha }{2})}\right)\text{Re}(\alpha )>0$

1.2

$\underset{0}{\overset{\mathrm{\infty }}{\int }}\frac{\log x}{\cosh x+\cos \pi \alpha }dx=\frac{\pi }{\sin \pi \alpha }\log ((2\pi {)}^{\alpha }\frac{\mathrm{\Gamma }\left(\frac{1+\alpha }{2}\right)}{\mathrm{\Gamma }\left(\frac{1-\alpha }{2}\right)})0<\alpha <1$