The keyword is: Haar Measure. See for example this http://gemma.ujf.cas.cz/~brauner/files/Haar_measure.pdf" [Broken].
Sorry for the short answer, I'm in a hurry.
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I passed over a discussion which shows that integrating over SU(2) is similar to that over a sphere S^3. I want a similar discussion for integration over SU(3).
Can someone please specify a reference that gives a good explanation of SU(3) (like finding generators, etc..)?