Indefinite Integral Calculator
Find a symbolic antiderivative for sums, monomials, constant factors and supported elementary functions of linear expressions, with a constant of integration.
Description
Find a supported elementary symbolic primitive and return its indefinite integral with + C.
An indefinite integral describes a family of primitives whose derivative recovers the integrand on an appropriate connected domain. This tool finds one primitive using supported symbolic rules and returns it both with and without an arbitrary constant.
When to use this tool
Find a supported elementary symbolic primitive and return its indefinite integral with + C. Use it when the input measurements and conventions below match the operation you need.
- Prepare expression, variable, respecting the measurement basis and boundaries below.
- Compare the worked example with your intended operation before reusing its result.
How to use the tool and how it works
- Enter expression with explicit multiplication, choose variable or keep its x default, and supply finite integration bounds if shown.
- Run the tool. Correct input errors before interpreting an output.
- Read the named output fields below. Check the symbolic domain or the numerical-method limitations before using the answer.
Enter an explicitly multiplied expression and the case-sensitive integration variable, default x. After parsing and constant-domain checks, the rule engine handles sums, constant factors, monomials and supported elementary functions whose inner derivative is a nonzero numerical constant. It renders antiderivative and appends + C for integral; reciprocal powers use ln(abs(...)) where applicable.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| expression | Explicit multiplication, e.g. x^2, 1/x or sin(2*x+1); unmatched integration rules return a structured error. | Nonempty expression text, at most 4,096 characters; explicit multiplication |
| variable | Case-sensitive integration variable; other symbols are constant parameters. | Text; optional, default "x" |
| Output field | Interpretation |
|---|---|
| antiderivative | One elementary primitive, valid on connected real domains where the original expression is defined; no arbitrary constant included. |
| integral | Antiderivative with + C; C denotes an arbitrary constant independently of input symbol names. |
{
"input": {
"expression": "x^2",
"variable": "x"
},
"output": {
"antiderivative": "(x ^ 3) / 3",
"integral": "(x ^ 3) / 3 + C"
}
}Limitations and assumptions
- No matching rule produces a structured error, not a numerical guess. The engine does not implement general integration by parts or arbitrary substitution. Results apply on connected real domains where the original expression is defined; C is an arbitrary integration constant independent of input symbol names.
- The expression must use explicit multiplication, such as 2*x, and supported function calls. Variable names are case-sensitive ASCII letters followed by letters or digits; constants and function names are reserved. Only variable is optional, defaulting to x.
- Expressions are limited to 4,096 characters and bounded nesting and operation counts. Constant-domain errors are rejected; symbolic results do not certify every variable-dependent domain constraint.
Alternative or Complementary methods
Use symbolic differentiation to check a proposed primitive where supported, or numerical quadrature to compare values over a regular finite interval. Sample-based integration requires its own smoothness and domain checks. Compare the scope of the nearby tools below before substituting one.
References
Similar or alternative tools
- Symbolic Derivative
Differentiate real arithmetic and supported elementary functions with product, quotient, power and chain rules where differentiable; other symbols are held constant.
- Definite Integral Calculator
Approximate a finite real expression integral with 256-panel composite Simpson quadrature; the refinement error estimate assumes a smooth integrand and is not a certified bound or improper integral solver.