  The approximate renormalized one-loop effective action of the quantized
massive scalar, spinor and vector field in a large mass limit, i.e., the lowest
order of the DeWitt-Schwinger expansion involves the coincidence limit of the
Hadamard-DeWitt coefficient a3. Building on this and using Wald's approach we
shall construct the general expression describing entropy of the
spherically-symmetric static black hole being the solution of the
semi-classical field equations. For the concrete case of the quantum-corrected
Reissner-Nordstrom black hole this result coincides, as expected, with the
entropy obtained by integration of the first law of black hole thermodynamics
with a suitable choice of the integration constant. The case of the extremal
quantum corrected black hole is briefly considered.
