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We explicitly compute the entropy of an extremal dyonic black hole inheterotic string theory compactified on T^6 or K3\times T^2 by taking intoaccount all the tree level four derivative corrections to the low energyeffective action. For supersymmetric black holes the result agrees with theanswer obtained earlier 1) by including only the Gauss-Bonnet corrections tothe effective action 2) by including all terms related to the curvature squaredterms via space-time supersymmetry transformation, and 3) by using generalarguments based on the assumption of AdS_3 near horizon geometry and space-timesupersymmetry. For non-supersymmetric extremal black holes the result agreeswith the one based on the assumption of AdS_3 near horizon geometry andspace-time supersymmetry of the underlying theory.Comment: LaTeX file, 18 pages; v3: some normalization conventions changed so  as to be compatible with standard conventio

α′-Corrections to extremal dyonic black holes in heterotic string theory