Question Number 127839 by mnjuly1970 last updated on 02/Jan/21
$$\:\:\: \\ $$$${if}\:\:\Omega\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}−{x}\right)\Gamma\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)}{\Gamma\left(\mathrm{2}−\frac{{x}}{\mathrm{2}}\right)\left(\frac{{x}}{\mathrm{2}}−\mathrm{1}\right)}\right){dx} \\ $$$$\:\:{find}\:\:\:\:\frac{{Re}\left(\Omega\right)}{{Im}\left(\Omega\right)}=? \\ $$