  We have computed alpha^2F's for the hole-doped cuprates within the framework
of the one-band Hubbard model, where the full magnetic response of the system
is treated properly. The d-wave pairing weight alpha^2F_d is found to contain
not only a low energy peak due to excitations near (pi,pi) expected from
neutron scattering data, but to also display substantial spectral weight at
higher energies due to contributions from other parts of the Brillouin zone as
well as pairbreaking ferromagnetic excitations at low energies. The resulting
solutions of the Eliashberg equations yield transition temperatures and gaps
comparable to the experimentally observed values, suggesting that magnetic
excitations of both high and low energies play an important role in providing
the pairing glue in the cuprates.
