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Question Number 118081 by bemath last updated on 15/Oct/20

$$\int \mathrm{arc}\cos \left(\frac{\cos \mathrm{x}}{1+2\cos \mathrm{x}}\right)\mathrm{dx}=?$$

Commented by MJS_new last updated on 15/Oct/20

$$\mathrm{seems}\mathrm{impossible}\mathrm{to}\mathrm{solve}$$

Commented by MJS_new last updated on 16/Oct/20

$$\mathrm{this}\mathrm{is}\mathrm{one}\mathrm{version}\mathrm{of}\mathrm{the}\mathrm{Coxeter}\mathrm{Integral}$$$$\mathrm{but}\mathrm{it}\mathrm{needs}\mathrm{borders}$$$$\underset{0}{\stackrel{\frac{\pi }{2}}{\int }}\arccos \frac{\cos x}{1+2\cos x}dx=\frac{5{\pi }^2}{24}$$$$\mathrm{see}\mathrm{the}\mathrm{video}\mathrm{or}\mathrm{search}\mathrm{the}\mathrm{web}$$

Commented by bemath last updated on 16/Oct/20

$$thanksir$$

Answered by AbduraufKodiriy last updated on 15/Oct/20

$$\mathit{S}\mathit{o}\mathit{l}\mathit{u}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{t}\mathit{o}\mathit{t}\mathit{h}\mathit{i}\mathit{s}\mathit{i}\mathit{n}\mathit{Y}\mathit{o}\mathit{u}\mathit{T}\mathit{u}\mathit{b}\mathit{e}\mathit{c}\mathit{h}\mathit{a}\mathit{n}\mathit{n}\mathit{e}\mathit{l}$$$$\mathit{w}\mathit{h}\mathit{i}\mathit{c}\mathit{h}\mathit{i}\mathit{s}{}^{\prime }\mathit{F}\mathit{l}\mathit{a}\mathit{m}\mathit{m}\mathit{a}\mathit{b}\mathit{l}\mathit{e}{\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{s}}^{\prime }$$

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