  The long-time behavior of solutions to the initial value problem for the
Korteweg-de Vries equation on the whole line, with general initial conditions
has been described uniformly using five different asymptotic forms. Four of
these asymptotic forms were expected: the quiescent behavior (for |x| very
large), a soliton region (in which the solution behaves as a collection of
isolated solitary waves), a self-similar region (in which the solution is
described via a Painlev\'e transcendent), and a similarity region (where the
solution behaves as a simple trigonometric function of the quantities t and
x/t). A fifth asymptotic form, lying between the self-similar (Painlev\'e) and
the similarity one, has been described in terms of classical elliptic
functions. An integral of elliptic type, giving an explicit representation of
the phase, has appeared in this context. The same integral has appeared in the
table of integrals by Gradshteyn and Ryzhik. Our goal here is to confirm the
validity of this entry.
