I would like to know the group cohomology of orthogonal groups $SO(n)$, which is the topological cohomology of the classifying space of the group: $H^*(BSO(n);\mathbb{Z}) = $ ? (for example for $n=10$)

I also like to know $H^*(BPSU(n);\mathbb{Z})$ (say for $n=3$), where $PSU(n)=SU(n)/Z_n$ and $Z_n$ is the center of $SU(n)$.

Thanks!