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

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0.1

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

0.2

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

0.3

$\underset{0}{\overset{\pi }{\int }}{x}^2{\log }^2(2\cos \frac{x}{2})dx=\frac{11{\pi }^5}{180}$

0.4

$\underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{x^2}{x^2+{\log }^2(2\cos x)}dx=\frac{\pi }{8}(1-\gamma +\log 2\pi )$

1.1

$\underset{0}{\overset{\pi }{\int }}\log (1-2\alpha \cos x+{\alpha }^2)dx=\{\begin{array}{cc}0& |\alpha |\le 1\\ \\ 2\pi \log |\alpha |& |\alpha |>1\end{array},\alpha \in ℝ$