  A recently introduced approach to the classical gravitational dynamics of
binary systems involves intricate integrals (linked to a combination of
nonlocal-in-time interactions with iterated $\frac1r$-potential scattering)
which have so far resisted attempts at their analytical evaluation. By using
computing techniques developed for the evaluation of multi-loop Feynman
integrals (notably Harmonic Polylogarithms and Mellin transform) we show how to
analytically compute all the integrals entering the nonlocal-in-time
contribution to the classical scattering angle at the sixth post-Newtonian
accuracy, and at the seventh order in Newton's constant, $G$ (corresponding to
six-loop graphs in the diagrammatic representation of the classical scattering
angle).
