Higher derivative terms including the Ramond-Ramond five-form

Superfield methods can be used to determine the precise way the self-dual fiveform couples to the metric in the first non-trivial α′ corrections to type IIB supergravity. We explicitly compute the exact tensor structure of these terms. This requires extensive use of computing algorithms to reduce the complicated expressions that appear to a surprisingly simple form. Along the way we show a new method of computing Schouten identities. With this result we clarify under which conditions one may neglect the five-form higher derivative terms. We comment on corrections to the thermodynamics of charged black holes.