  We calculate the general planar dual-conformally invariant double-pentagon
and pentabox integrals in four dimensions. Concretely, we derive one-fold
integral representations for these elliptic integrals over polylogarithms of
weight three. These integral representations allow us to determine the
respective symbols using consistency conditions alone. Together with the
previously calculated double-box integral, these integrals suffice to express
all two-loop planar scattering amplitudes in maximally supersymmetric
Yang-Mills theory in four dimensions -- which we thus calculate for any number
of particles and any helicity configuration!
