For the path integral in phase space, we have assumed that the \(P \mathrm{~s}\) are always on the left of the \(X \mathrm{~s}\) in the Hamiltonian. Consider a case where this is not true, for instance having an extra term in the Hamiltonian of the type \(\alpha\left(\hat{P} \hat{X}^{2}+\hat{X} \hat{P} \hat{X}+\hat{X}^{2} P\right)\). Redo the calculation, and see what you obtain for the path integral in phase space.