The set of local unitary invariants of a system of multiple qubits, whose group of local unitary transformations is given by a cartesian product of the unitary groups, associated with individual qubits, provides the most detailed meaure of their entanglement. We study algebraic invariants of the (Liouville) space of mixed states of multiple qubits, as well as its subspace of so-called X-states, the latter naturally arising in quantum light (entangled photon) spectroscopy. Using basic techniques of the Geomterical Invariant Theory (GIT), we explicitly compute the fields of rational invariants in both cases, and show that they are purely rational over the field of complex numbers, i.e., generated by finite sets of invariants with no algebraic relations between them. The field extension of the rational invariants of mixed states over its X-state counterpart is also briefly addressed.