What are the cohomology of the classifying space of $E_8$ group and $SU(2)$ group, $H^*(BE_8;\mathbb{Z})$ and $H^*(BSU(2);\mathbb{Z})$?

In the paper http://homepages.math.uic.edu/~bshipley/ConMcohomology1.pdf , it was given that $H^∗[BSU(2); \mathbb{Z}_2] = \mathbb{Z}_2[u_4]$. But I like to know the result for integer coefficient.

== added ==

Mike Miller answered the $BSU(2)$ part of the question. There is no torsion
in $H^*(BSU(2);\mathbb{Z})$. A motivation for me to ask the above question is to find simple *compact* and *simply connected* Lie groups $G$, such that
$H^*(BG;\mathbb{Z})$ has torsions at certain dimensions. So $SU(2)$ is out.