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Integral Calculator

Symbolic integral calculator for indefinite and definite polynomial integrals. See antiderivative steps, parse diagnostics, and export integral reports with bound evaluation.

Function

Supports polynomials like 4x^3 - 2x + 7. Use x as the variable and ^ for powers.
Examples
Uses power rule ∫ a x^n dx = a x^(n+1)/(n+1)Shows antiderivative and definite integral

Definite integral bounds

Leave one bound blank for only the indefinite integral.

Result

∫ f(x) dx

x^3 + x^2 − 5x + C

∫01 f(x) dx

-3

Step‑by‑step working

  1. For 3x^2, use power rule for integrals: ∫ a x^n dx = a x^(n+1)/(n+1). Here a = 3, n = 2, so the antiderivative term is 1x^3.
  2. For 2x, use power rule for integrals: ∫ a x^n dx = a x^(n+1)/(n+1). Here a = 2, n = 1, so the antiderivative term is 1x^2.
  3. For −-5, use power rule for integrals: ∫ a x^n dx = a x^(n+1)/(n+1). Here a = -5, n = 0, so the antiderivative term is -5x^1.

How to use this tool

  1. Write your integrand as a polynomial in x using powers with ^, or choose an example expression.
  2. Review the symbolic antiderivative F(x) + C and the power-rule step breakdown.
  3. Optionally set bounds a and b, then copy or download the integral report.

Ideal online integral calculator for early calculus

  • Practice turning derivatives back into antiderivatives using a friendly integral calculator.
  • See exactly how each exponent increases by one in the power rule ∫ a x^n dx = a x^(n+1)/(n+1).
  • Use definite integrals to compute the exact area under simple polynomial curves.

What this integral calculator supports

  • Polynomials in x with real coefficients and whole-number powers using the power rule.
  • Indefinite integrals with + C as well as optional definite integrals between two bounds.
  • Readable step-by-step integral explanations plus parse diagnostics for unsupported terms.

FAQ

Can this step-by-step integral calculator integrate 1/x or trig functions?
This mode focuses on polynomial power-rule integrals. Terms like 1/x, trig functions, exponentials, or roots require additional rules and are flagged in diagnostics.
Does order of terms matter in the integrand?
No. The calculator will parse your sum of terms and present the antiderivative in a cleaned, highest-power-first form.
Is numeric integration or approximation available?
For polynomials, the exact definite integral is computed via the antiderivative, which is more accurate and reliable than approximate numerical methods for these functions.

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