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Question Number 125034 by mathmax by abdo last updated on 07/Dec/20

$$\mathrm{find}{\int }_0^{\frac{\pi }{2}}\frac{\mathrm{x}}{\mathrm{sinx}}\mathrm{dx}$$

Commented by Olaf last updated on 07/Dec/20

$$\mathrm{The}\mathrm{Catalan}\mathrm{constant}\mathrm{K}\mathrm{has}\mathrm{many}$$$$\mathrm{expressions}.\mathrm{One}\mathrm{of}\mathrm{them}\mathrm{is}:$$$$\mathrm{K}=\frac{1}{2}{\int }_0^{\frac{\pi }{2}}\frac{x}{\sin x}dx$$$$\Rightarrow {\int }_0^{\frac{\pi }{2}}\frac{x}{\sin x}dx=2\mathrm{K}\approx 1,831931188$$

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