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

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#### Coxeter Integrale

##### 0.1
${\displaystyle \int _{0}^{\frac {\pi }{2}}\arccos \left({\frac {\cos x}{1+2\cos x}}\right)dx={\frac {5\pi ^{2}}{24}}}$

##### 0.2
${\displaystyle \int _{0}^{\frac {\pi }{3}}\arccos \left({\frac {\cos x}{1+2\cos x}}\right)dx={\frac {2\pi ^{2}}{15}}}$

##### 0.3
${\displaystyle \int _{0}^{\frac {\pi }{2}}\arccos \left({\frac {1}{1+2\cos x}}\right)dx={\frac {\pi ^{2}}{6}}}$

##### 0.4
${\displaystyle \int _{0}^{\frac {\pi }{3}}\arccos \left({\frac {1}{1+2\cos x}}\right)dx={\frac {\pi ^{2}}{8}}}$

##### 0.5
${\displaystyle \int _{0}^{\arccos \left({\frac {1}{3}}\right)}\arccos \left({\frac {1-\cos x}{2\cos x}}\right)dx={\frac {\pi ^{2}}{6}}}$

##### 0.6
${\displaystyle \int _{0}^{\frac {\pi }{3}}\arccos \left({\frac {1-\cos x}{2\cos x}}\right)dx={\frac {11\pi ^{2}}{72}}}$

##### 0.7
${\displaystyle \int _{0}^{\frac {\pi }{2}}\arccos {\sqrt {\frac {\cos x}{1+2\cos x}}}\,dx={\frac {\pi ^{2}}{6}}}$

##### 0.8
${\displaystyle \int _{0}^{\frac {\pi }{3}}\arccos {\sqrt {\frac {\cos x}{1+2\cos x}}}\,dx={\frac {5\pi ^{2}}{48}}}$