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().

Useful companions

Use simplify() to make an expression easier to read, subset() when extracting data for numerical work, and sum() for finite discrete accumulation. Functions such as sin() and exp() 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.