Integral Calculator
Find antiderivatives, evaluate definite integrals, and estimate average value over an interval
Enter one single-variable expression. Use ^ for powers, log(x) or ln(x) for natural log, and pi for pi.
Integrate with respect to this symbol.
Used only for definite integrals.
Used only for definite integrals.
Digits used for decimal results.
Try an example
Integral Result
Antiderivative of 3x^2 - 4x + 5
Antiderivative
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Definite Value
Enter bounds in definite mode.
Interval Width
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Average Value
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Variable
x
Calculation Steps
- Enter a function to integrate.
How This Integral Calculator Works
The calculator parses your expression, finds an antiderivative, and optionally evaluates accumulated area over an interval.
1. Parse the expression
Keep the function to one variable and use common notation such as powers, roots, trig functions, exponentials, and logarithms.
2. Find an antiderivative
The symbolic engine applies common calculus rules and shows the antiderivative with + C for indefinite integrals.
3. Evaluate bounds
Definite mode evaluates the integral between two bounds and estimates the average function value on that interval.
Integral Calculator Examples
Common calculus cases and how to enter them.
Polynomial antiderivative
Enter 3x^2 - 4x + 5 to get an equivalent antiderivative such as x^3 - 2x^2 + 5x + C.
Area under sine
Enter sin(x), choose definite mode, and use bounds 0 to pi for an area of 2.
Integral Calculator FAQ
Answers about antiderivatives, definite integrals, bounds, and symbolic results.
What is the difference between indefinite and definite integrals?
An indefinite integral finds an antiderivative plus a constant of integration. A definite integral evaluates accumulated area or net change between two bounds.
Can this calculator show exact answers?
Yes. For many common expressions it shows an exact symbolic antiderivative and exact definite-integral value, plus a decimal approximation when bounds are entered.
Does log mean natural logarithm?
Yes. In calculus notation, log is treated as the natural logarithm. You can also type ln(x), which is normalized to log(x).
Why does the calculator sometimes return integrate(...)?
Some integrals do not have an elementary antiderivative or are outside the symbolic engine's supported patterns. Definite mode may still provide a numerical estimate.
What should I check before using a definite integral result?
Check the function's domain and discontinuities. Reciprocal, logarithmic, tangent, and square-root expressions may be undefined over parts of an interval.