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

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0.1

$\underset{0}{\overset{1}{\int }}\log (\tan \frac{\pi x}{2})dx=0$

0.2

$\underset{0}{\overset{\pi }{\int }}{\log }^2(\tan \frac{x}{2})dx=\frac{{\pi }^3}{4}$

0.3

$\underset{0}{\overset{\pi }{\int }}{\log }^2(\tan \frac{x}{4})dx=\frac{{\pi }^3}{4}$

0.4

$\underset{\pi /4}{\overset{\pi /2}{\int }}\log \log \tan xdx=\frac{\pi }{2}\log \left(\sqrt{2\pi }\frac{\mathrm{\Gamma }\left(\frac{3}{4}\right)}{\mathrm{\Gamma }\left(\frac{1}{4}\right)}\right)$