Integration using Schwinger Parametrization

This paper draws attention to an underappreciated method for evaluating certain types of definite integrals. The method relies on a substitution in the Eulerian integral for the Legendre gamma function, and has become known in some quarters as a Schwinger parametrization. We present some examples to illustrate the utility of this technique in the hope that by doing so we may convince the reader that it makes a valuable addition to one's integration toolkit.