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

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0.1

${\int }_0^{\frac{\pi }{2}}\log (2\sin \frac{x}{2})dx=-G$

0.2

${\int }_0^{\frac{\pi }{3}}{\log }^2(2\sin \frac{x}{2})dx=\frac{7{\pi }^3}{108}$

0.3

${\int }_0^{\pi }{\log }^2(2\sin \frac{x}{2})dx=\frac{{\pi }^3}{12}$

0.4

${\int }_0^{\frac{\pi }{3}}x{\log }^2(2\sin \frac{x}{2})dx=\frac{17{\pi }^4}{6480}$