Computer algebra
Symbolic integration
Finding an expression whose derivative matches a given expression.
Definition
Symbolic integration
Symbolic integration searches for an antiderivative or an exact value for a definite integral.
Integration is generally harder than differentiation because an antiderivative may require a larger expression language or may not have an elementary form. Differentiating a proposed antiderivative provides a direct check in many cases.
01
Example
An antiderivative of 2x is x² + C because differentiating x² + C returns 2x.
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Important distinction
A verified derivative equality does not by itself settle endpoint behavior or convergence for every definite integral.
After reading this article, you should be able to
- Define Symbolic integration in the sense used on this site.
- Verify a proposed antiderivative and state any remaining conditions for a definite integral.