Integrate
 Usage
Notes
 Further Examples
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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These indefinite integrals assume x is real.
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Definite integrals Here are some definite integrals.
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The function Boole provides a convenient way to express multi-dimensional definite integrals over regions that are not rectangles or cuboids.
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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.
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