19.1 Introduction to Integration

Maxima has several routines for handling integration. The integrate function makes use of most of them. There is also the antid package, which handles an unspecified function (and its derivatives, of course). For numerical uses, there is a set of adaptive integrators from QUADPACK, named quad_qag, quad_qags, etc., which are described under the heading QUADPACK. Hypergeometric functions are being worked on, see specint for details. Generally speaking, Maxima only handles integrals which are integrable in terms of the "elementary functions" (rational functions, trigonometrics, logs, exponentials, radicals, etc.) and a few extensions (error function, dilogarithm). It does not handle integrals in terms of unknown functions such as g(x) and h(x).