  We apply numerical and analytic techniques to the study of Yang-Mills
integrals with orthogonal, symplectic and exceptional gauge symmetries. The
main focus is on the supersymmetric integrals, which correspond essentially to
the bulk part of the Witten index for susy quantum mechanical gauge theory. We
evaluate these integrals for D=4 and group rank up to three, using Monte Carlo
methods. Our results are at variance with previous findings. We further compute
the integrals with the deformation technique of Moore, Nekrasov and
Shatashvili, which we adapt to the groups under study. Excellent agreement with
all our numerical calculations is obtained. We also discuss the convergence
properties of the purely bosonic integrals.
