Function reference · Calculus

`integrate`

Computes a symbolic antiderivative with respect to a variable when Nerdamer has a supported integration path.

Integration handles linear combinations, constant factors, common elementary functions, scaled arguments, and a broader set of algebraic and trigonometric forms through Nerdamer's integration routines.

When an antiderivative is not available, Nerdamer can leave the integral unevaluated instead of inventing a result.

Examples

These examples use Nerdamer Notation.

Integrate a polynomial term by term.

integrate(x^2+3*x+1,x)
// → x+(3/2)*x^2+(1/3)*x^3

Use linearity across elementary functions.

integrate(sin(x)+cos(x),x)
// → -cos(x)+sin(x)

Account for a scaled inner argument.

integrate(sec(2*x)^2,x)
// → (1/2)*tan(2*x)

Interfaces

The same operation is available through the interfaces below.

Nerdamer Notation · nerdamer API · Direct API

Nerdamer Notation

Use this form inside input passed to nerdamer(...).

integrate(expression[, variable])

Parameters

expression — Expression to integrate.
variable — Optional integration variable.

`nerdamer.integrate`

Call the operation through the default nerdamer import.

nerdamer.integrate(expr: ExpressionInput, dx: ExpressionInput, depth: number): Expression

Parameters

Name	Type	Description
`expr`	`ExpressionInput`	Integrand to normalize and integrate.
`dx`	`ExpressionInput`	Plain integration variable.
`depth`	`number`	Internal recursion depth. Defaults to zero.

Returns

Expression — A symbolic antiderivative without an integration constant, or an unevaluated `integrate(...)` Expression.

Browse the nerdamer API →

Direct JavaScript / TypeScript API

Import the operation directly from its package entry point.

import { integrate } from 'nerdamer/calculus';

integrate(expr: ExpressionInput, dx: ExpressionInput, depth: number): Expression

Parameters

Name	Type	Description
`expr`	`ExpressionInput`	Integrand to normalize and integrate.
`dx`	`ExpressionInput`	Plain integration variable.
`depth`	`number`	Internal recursion depth. Defaults to zero.

Returns

Expression — A symbolic antiderivative without an integration constant, or an unevaluated `integrate(...)` Expression.

Browse nerdamer/calculus →

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