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Integrate[f, x] gives the indefinite integral  .
Integrate[f, {x, xmin, xmax}] gives the definite integral  .
Integrate[f, {x, xmin, xmax}, {y, ymin, ymax}] gives the multiple integral  .

Integrate can be used to find the area under a curve or the accumulated total of a continuous function.
Integrate[f, x] can be entered as  .
 can be entered as AliasIndicatorintAliasIndicator or \[Integral].
 is not an ordinary d; it is entered as AliasIndicatorddAliasIndicator or \[DifferentialD].
Integrate[f, {x, xmin, xmax}] can be entered with xmin as a subscript and xmax as a superscript to  .
• Multiple integrals use a variant of the standard iterator notation. The first variable given corresponds to the outermost integral, and is done last.
Integrate can evaluate integrals of rational functions. It can also evaluate integrals that involve exponential, logarithmic, trigonometric, and inverse trigonometric functions, so long as the result comes out in terms of the same set of functions.
Integrate can give results in terms of many special functions.
Integrate carries out some simplifications on integrals it cannot explicitly do.
• The integration variable can be any expression. However, Integrate uses only its literal form. The object  , for example, is not converted to  .
• For indefinite integrals, Integrate tries to find results that are correct for almost all values of parameters.
Integrate can evaluate essentially all indefinite integrals and most definite integrals listed in standard books of tables.
Integrate[f, x] is output as  .
• See also:
NIntegrate, NSum, SolveODE.


Using InstantCalculators

Here are the InstantCalculators for the Integrate function. Enter the parameters for your calculation and click Calculate to see the result.

Entering Commands Directly

You can paste a template for this command via the Text Input button on the Integrate Function Controller.

Indefinite integrals

Here are two indefinite integrals.

Here is an indefinite integral that is evaluated by special table lookup rules.

Definite integrals

Here are two definite integrals.

Ordinary Mathematical Notation

Indefinite integral

This also gives the indefinite integral of  .

Definite integral

This also gives the definite integral of  from -1 to 1.