The Risch algorithm reference article from the English Wikipedia on 24-Apr-2004
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Risch algorithm

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The Risch algorithm is an algorithm for indefinite integration (finding antiderivatives). Part of its background theory is based on Liouville's principle from the 19th century.

The original paper was:

Risch,R.H.
The Problem of Integration in Finite Terms.
Trans. A.M.S. 139(1969) pp. 167-189.