Question Number 84726 by M±th+et£s last updated on 15/Mar/20
$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left({y}^{{y}} \right)^{\left({y}^{{y}} \right)^{\left({y}^{{y}} \right)^{.^{.^{.} } } } } {dy}=\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$