  Computing leading higher curvature contributions to thermodynamic quantities
of AdS black hole is drastically simplified once the higher curvature terms are
expressed in terms of powers of Weyl tensor by applying proper field
redefinitions, avoiding the usual complications caused by higher derivative
Gibbons-Hawking-York (GHY) term or surface counterterms. We establish the
method by computing the Euclidean action of general rotating AdS black holes in
five dimensional quadratic curvature theories with or without supersymmetry and
verifying the results numerically. Our result is the state of the art for
charged rotating AdS black holes in five dimensional minimal gauged
supergravity including corrections from all three supersymmetric curvature
squared terms. Our approach facilitates precision tests in the AdS/CFT
correspondence and should be applicable in diverse dimensions.
