Every application of integration by parts can be done with a tabular method. The trick is to identify and consider each new integral in the table before deciding how to proceed. This paper supplements a classic introduction to integration by parts with a particular tabular method called Row Integration by Parts (RIP). Approaches to tabular methods found online and in the literature often fail to clearly identify new integrals since the focus is on constructing columns, thus new integrals are ignored. With RIP, each integral is identified with a row and tables are built one row at a time. This allows RIP to be an efficient bookkeeping method and to apply to a much wider range of functions than those typically considered with other tabular methods.