  The pairing symmetry in infinite-layer nickelate superconductors has been an
intriguing problem under heated debates. In this work, we study a two-orbital
Hubbard model with one strongly correlated $3d$ orbital and one more itinerant
$5d$ orbital, by using an eight-site cellular dynamic mean field theory study.
We establish a superconducting phase diagram with $d_{x^{2}-y^{2}}$, $s_{\pm}$
and $d+is$ wave pairing symmetries, based on which we clarify the roles of
various relevant parameters including hybridization $V$, itinerant carrier
density $\langle n_{c}\rangle$ and interaction $U_{c}$. We show that the
inclusion of a less correlated $5d$ band in general suppresses the
$d_{x^{2}-y^{2}}$ wave pairing. We demonstrate that the $d+is$ wave is
maximized when the $5d$ orbital has a large Coulomb repulsion with intermediate
hybridization parameter. We perform fluctuation diagnostics to show that the
driving force behind the $d_{x^{2}-y^{2}}$ wave is the intraband
antiferromagnetic fluctuations in the $3d$ orbital, while for the $s_{\pm}$
wave, the pairing is mainly from the antiferromagnetic correlations residing on
the local $3d$-$5d$ bond in real space.
