  In this note, we use a basic identity, derived from the generalized doubling
integrals of \cite{C-F-G-K1}, in order to explain the existence of various
global Rankin-Selberg integrals for certain $L$-functions. To derive these
global integrals, we use the identities relating Eisenstein series in
\cite{G-S}, together with the process of exchanging roots. We concentrate on
several well known examples, and explain how to obtain them from the basic
identity. Using these ideas, we also show how to derive a new global integral.
