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
Famous quotes containing the words problem and/or examples:
“The thinking person has the strange characteristic to like to create a fantasy in the place of the unsolved problem, a fantasy that stays with the person even when the problem has been solved and truth made its appearance.”
—Johann Wolfgang Von Goethe (1749–1832)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)