We use a recently derived integral representation of the one-loop effective action in Einstein-Maxwell theory for an explicit calculation of the part of the effective action containing the information on the low energy limit of the five-point amplitudes involving one graviton, four photons and either a scalar or spinor loop. All available identities are used to get the result into a relatively compact form.
@article{arxiv.0912.2384,
title = {Effective action for Einstein-Maxwell theory at order RF**4},
author = {Jose Manuel Davila and Christian Schubert},
journal= {arXiv preprint arXiv:0912.2384},
year = {2010}
}