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

Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy