We collect explicit and user-friendly expressions for one-point densities of the real eigenvalues \λᵢ\ of N× N Wishart-Laguerre and Jacobi random matrices with orthogonal, unitary and symplectic symmetry. Using these formulae, we compute integer moments τₙ=<∑ᵢ₌₁Nλᵢⁿ> for all symmetry classes without any large N approximation. In particular, our results provide exact expressions for moments of transmission eigenvalues in chaotic cavities with time-reversal or spin-flip symmetry and supporting a finite and arbitrary number of electronic channels in the two incoming leads.