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Documentation / Mathematica / Built-in Functions / Numerical Computation / Integration /

Further Examples: Integrate

Indefinite integrals

Here are three indefinite integrals that are evaluated by the (extended) Risch algorithm.

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Here are two indefinite integrals that are evaluated by special table lookup rules.

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Definite integrals

Here are some definite integrals.

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Options: Assumptions and GenerateConditions

When an integrand depends on a parameter, the indefinite integral should be considered valid for "generic" values of the parameter. For certain values the reported integral may be meaningless, as is the case here for .

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By contrast, when you ask for a definite integral, Mathematica tries to return a result that is always valid, if necessary by stating validity conditions.

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The option Assumptions lets you explicitly state conditions on the parameters. If you are only interested in real values of that are less than 0, the reported result is unconditional.

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The same unconditional result is returned if you override the default setting of the option GenerateConditions. Unless you know beforehand under what conditions the result is valid, this usage can lead to nonsense.

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This integral is a definition of the Beta function.

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Numerical integration

When a function cannot be integrated symbolically, you can usually obtain a definite integral numerically using NIntegrate.

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See the Further Examples for NIntegrate.