Symbolic integration

Symbolic integration is the application of computer software to solving problems in mathematics of find the integral of an expression, but finding an expression rather than a value.

Example:

$\int x^{2}\,dx=1/3*x^{3}$ is a symbolic result rather than a numerical value for the answer.

Finding the derivative of an expression is a straight forward process for which it is easy to determine an algorithm. The reverse question of finding the integral (of finding the expression who's derivative is a specified expression) is much more difficult. Many expressions that are relatively easy to state do not even have integrals that can be expressed in closed form.

A procedure called the Risch algorithm exists which is capacble of determining if an integral exists and returning it if it does, for many expressions. Such algorithms are still being expanded.

References

Symbolic Integration 1 (transcendental functions) by Manuel Bronstein, 1997 by Springer-Verlag, ISBN 3540605215

External links

Mapworld on the Risch Algorithm