# integrate() Function & Examples

Use the integrate() math function in Calcul.io. Review its syntax, edit working examples, understand the result, and explore related math functions.

Try it yourself:

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## integrate(): find an antiderivative

**integrate(expr, variable)** symbolically integrates an expression. It finds a function whose derivative is the input; for example, integrating `x^2` with respect to x gives `x^3 / 3`, up to an arbitrary constant.

## Definite and indefinite work

An indefinite integral represents a family of functions, so remember the constant of integration when applying it outside the calculator. A definite integral uses bounds and represents accumulated signed area. Check a symbolic answer by applying [derivative()](https://calcul.io/function/derivative/index.md).

## Useful companions

Use [simplify()](https://calcul.io/function/simplify/index.md) to make an expression easier to read, [subset()](https://calcul.io/function/subset/index.md) when extracting data for numerical work, and [sum()](https://calcul.io/function/sum/index.md) for finite discrete accumulation. Functions such as [sin()](https://calcul.io/function/sin/index.md) and [exp()](https://calcul.io/function/exp/index.md) commonly appear in integrands.

## Limits

Not every elementary expression has an elementary antiderivative. State the variable explicitly in multivariable expressions and inspect assumptions about constants, units, and singularities.

[All functions](https://calcul.io/functions/index.md)