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

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0.1

$\underset{0}{\overset{\frac{\pi }{2}}{\int }}\log (2\sin \frac{x}{2})dx=-G$

0.2

$\underset{0}{\overset{\frac{\pi }{3}}{\int }}{\log }^2(2\sin \frac{x}{2})dx=\frac{7{\pi }^3}{108}$

0.3

$\underset{0}{\overset{\pi }{\int }}{\log }^2(2\sin \frac{x}{2})dx=\frac{{\pi }^3}{12}$

0.4

$\underset{0}{\overset{\frac{\pi }{3}}{\int }}x{\log }^2(2\sin \frac{x}{2})dx=\frac{17{\pi }^4}{6480}$