Question Number 225861 by fantastic2 last updated on 15/Nov/25
$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{{ln}^{\mathrm{12}} \left(\mathrm{1}−{x}\right)}{\:\sqrt{\frac{{ln}^{\mathrm{12}} \left(\mathrm{1}−{x}\right)}{\:\sqrt{\frac{{ln}^{\mathrm{12}} \left(\mathrm{1}−{x}\right)}{\:\sqrt{\frac{{ln}^{\mathrm{12}} \left(\mathrm{1}−{x}\right)}{...}}}}}}}}{dx}=? \\ $$