Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
Symbolic computation
Computer algebra systems |
| gptkbp:concerns |
Finding antiderivatives expressible in terms of elementary functions
|
| gptkbp:criteria |
Liouville's theorem gives necessary and sufficient conditions
|
| gptkbp:describedBy |
Liouville's theorem (1833, 1841)
|
| gptkbp:example |
∫e^{x^2} dx is not elementary
∫sin(x)/x dx is not elementary |
| gptkbp:field |
gptkb:Mathematics
gptkb:Calculus |
| https://www.w3.org/2000/01/rdf-schema#label |
Integration in Finite Terms
|
| gptkbp:involves |
gptkb:Inverse_trigonometric_functions
gptkb:Trigonometric_functions Rational functions Algebraic functions Elementary functions Exponentials Logarithms |
| gptkbp:notableAchievement |
Some elementary functions have non-elementary antiderivatives
|
| gptkbp:relatedTo |
gptkb:Liouville's_theorem_(differential_algebra)
Symbolic integration Risch algorithm Differential Galois theory Differential algebra |
| gptkbp:studiedBy |
gptkb:Joseph_Liouville
|
| gptkbp:bfsParent |
gptkb:Joseph_Fels_Ritt
|
| gptkbp:bfsLayer |
7
|