  We present analytic results for the two tennis-court integral families
relevant to $2\to2$ scattering processes involving one massive external
particle and massless propagators in terms of Goncharov polylogarithms of up to
transcendental weight six. We also present analytic results for physical
kinematics for the ladder-box family and the two tennis-court families in terms
of real-valued polylogarithmic functions, making our solutions well-suited for
phenomenological applications.
