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Line 18: There are expressions in radicals for all solutions of [[cubic equation]]s (degree 3) and [[quartic equation]]s (degree 4). The size of these expressions increases significantly with the degree, limiting their usefulness. In higher degrees, [[Abel–Ruffini theorem]] states that there are equations whose solutions cannot be expressed in radicals, and, thus, have no closed forms ~~as a solution in radicals~~.~~<ref group=note>See [[Bring radical]], for larger collections of basic functions that allow the solutions of all quintics equations to have closed form in that modified sense of the word.</ref>~~ The simplest example is the equation <math>x^5-x+1.</math> [[Galois theory]] provides an [[algorithmic method]] for deciding whether a particular polynomial equation can be solved in radicals. == Symbolic integration ==

Closed-form expression: Difference between revisions