Problem Examples
Finding an elementary antiderivative is very sensitive to details. For instance, the following function has an elementary antiderivative:
namely:
(Some computer algebra systems may here return an antiderivative in terms of non-elementary functions (i.e. elliptic integrals), which however are outside the scope of the Risch algorithm.) But if 71 is changed to 72, it is not possible to represent the antiderivative using elementary functions.
The following function is a more complex example:
In fact, the antiderivative of this function has a fairly short form:
Read more about this topic: Risch Algorithm
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