  A unitary matrix integral that appears in the low-energy limit of QCD-like
theories with quarks in real representations of the gauge group at finite
chemical potential is analytically evaluated and expressed as a pfaffian. Its
application to the GOE-GUE crossover in random matrix theory is discussed. An
analogous unitary integral for QCD-like theories with quarks in pseudoreal
representations of the gauge group is also evaluated.
