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Question Number 124591 by mohammad17 last updated on 04/Dec/20

Commented by mohammad17 last updated on 05/Dec/20

$$whoiscansolvethis?$$

Answered by mindispower last updated on 05/Dec/20

$$let\mathrm{\Delta }beethisintegralebysymetri={\int }_0^{1}ln\left(\mathrm{\Gamma }(1-x)\right){cos}^2\left(\pi (1-x)\right)dx$$$$={\int }_0^{1}ln\left(\mathrm{\Gamma }(1-x)\right){cos}^2\left(\pi x\right)dx$$$$2\mathrm{\Delta }={\int }_0^{1}ln\mathrm{\Gamma }(1-x)\mathrm{\Gamma }\left(x\right)){cos}^2\left(\pi x\right)dx$$$$={\int }_0^{1}ln\left(\frac{\pi }{sin\left(\pi x\right)}\right){cos}^2\left(\pi x\right)$$$$={\int }_0^{1}ln\left(\pi \right){cos}^2\left(\pi x\right)-\int ln\left(sin\left(\pi x\right)\right){cos}^2\left(\pi x\right)dx$$$$A-B,Aeasy,Bbypart$$

Commented by mohammad17 last updated on 05/Dec/20

$$canyoucompletethesolutionpleasesir?$$

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