  The field equation with the cosmological constant term is derived and the
energy of the general 4-dimensional stationary axisymmetric spacetime is
studied in the context of the hamiltonian formulation of the teleparallel
equivalent of general relativity (TEGR). We find that, by means of the integral
form of the constraints equations of the formalism naturally without any
restriction on the metric parameters, the energy for the asymptotically flat/de
Sitter/Anti-de Sitter stationary spacetimes in the Boyer-Lindquist coordinate
can be expressed as $E=\frac{1}{8\pi}\int_S d\theta d\phi(sin\theta
\sqrt{g_{\theta\theta}}+\sqrt{g_{\phi\phi}}-(1/\sqrt{g_{rr}})(\partial{\sqrt{g_
{\theta\theta} g_{\phi\phi}}}/\partial r))$. It is surprised to learn that the
energy expression is relevant to the metric components $g_{rr}$,
$g_{\theta\theta}$ and $g_{\phi\phi}$ only. As examples, by using this formula
we calculate the energies of the Kerr-Newman (KN), Kerr-Newman Anti-de Sitter
(KN-AdS), Kaluza-Klein, and Cveti\v{c}-Youm spacetimes.
