Question Number 165097 by abdullahhhhh last updated on 26/Jan/22
Answered by Eulerian last updated on 26/Jan/22
$$\: \\ $$$$\:\mathrm{By}\:\mathrm{using}\:\mathrm{King}\:\mathrm{rule}\:\mathrm{of}\:\mathrm{integration}: \\ $$$$\:\int_{\frac{\pi}{\mathrm{6}}\:} ^{\:\frac{\pi}{\mathrm{3}}} \:\left(\mathrm{cot}\:\mathrm{x}\right)^{\left(\mathrm{tan}\:\mathrm{x}\right)^{\left(\mathrm{cot}\:\mathrm{x}\right)} } \:−\:\left(\mathrm{tan}\:\mathrm{x}\right)^{\left(\mathrm{cot}\:\mathrm{x}\right)^{\left(\mathrm{tan}\:\mathrm{x}\right)} } \:\mathrm{dx}\:=\:\mathrm{0} \\ $$