  We introduce an integrable Hamiltonian which is an extended d+id-wave pairing
model. The integrability is deduced from a duality relation with the
Richardson-Gaudin (s-wave) pairing model, and associated to this there exists
an exact Bethe ansatz solution. We study this system using the continuum limit
approach and solve the corresponding singular integral equation obtained from
the Bethe ansatz solution. We also conduct a mean-field analysis and show that
results from these two approaches coincide for the ground state in the
continuum limit. We identify instances of the integrable system where the
excitation spectrum is gapless, and discuss connections to non-integrable
models with d+id-wave pairing interactions through the mean-field analysis.
