This formula, which is quite old, is recorded in various tables of definite integrals.
It appears as formula 865.5 in [4], where a reference is given to Nouvelles Tables
d’Int´egrales D´efinies, by B. de Haan: P. Engels, Leyden, 1867, and it also appears,
in thin disguise, as entry 4.293(8) of [6]. We include below a proof for the sake of
completeness. We have,