Relationship between the Fransén–Robinson constant, e, pi, and logarithm

Theorem

The following formula holds: $$F=e+\displaystyle\int_0^{\infty} \dfrac{e^{-x}}{\pi^2+\log(x)^2} \mathrm{d}x,$$ where $F$ denotes the Fransén–Robinson constant, $e$ denotes E, $\pi$ denotes pi, and $\log$ denotes the logarithm.