\[\int_{0}^{\infty}\frac{\,\mathrm{d}t}{{\operatorname{Ai}}^{2}\left(t\right)+{%
\operatorname{Bi}}^{2}\left(t\right)}=\int_{0}^{\infty}\frac{t\,\mathrm{d}t}{{%
\operatorname{Ai}'}^{2}\left(t\right)+{\operatorname{Bi}'}^{2}\left(t\right)}=%
\frac{\pi^{2}}{6}.\]