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We study several multiscale one-loop five-point families of Feynmanintegrals. More specifically, we employ the Simplified Differential Equationsapproach to obtain results in terms of Goncharov polylogarithms of up totranscendental weight four for families with two and three massive externallegs and massless propagators, as well as with one massive internal line and upto two massive external legs. This is the first time this computationalapproach is applied to cases involving internal masses.

One-loop Feynman integrals for $2\to3$ scattering involving many scales including internal masses