  We derive integral representations for the Rankin-Selberg L-functions on
GL(3) x GL(1) and GL(3) x GL(2) by a process of unipotent averaging at
archimedean places. A key feature of our result is that it allows one to fix
the choice of test vector at finite places, irrespective of ramification. This
enables a new proof of the functional equation for GL(3) x GL(2) Rankin-Selberg
L-functions in many cases.
