Monthly Archives: July 2017

Real integral evaluation via the residue theorem with two branch points and a log-squared term

Every so often there comes an integral that I see as a major teaching opportunity in complex integration applications. This integral represents one such opportunity. Problem: Evaluate the definite integral $$\int_0^{\infty} dx \, \frac{\log^2{x} \, \log{(1+x)}}{1+x^2} $$ This integral may be evaluated using the residue theorem. The analysis involves two branch points with respective branch […]