(maxima.info)Introduction to Integration

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19.1 Introduction to Integration
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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)'.