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Indefinite Integral Calculator

Work out indefinite integral instantly with clear inputs, formula shown and shareable results.

About Indefinite Integral Calculator

Integrating a polynomial applies the reverse power rule term by term: xⁿ becomes x^(n+1)/(n+1). Every antiderivative differs by a constant, which is why C appears.

Formula

Reverse power rule

∫a·xⁿ dx = a·x^(n+1)/(n+1) + C, for n ≠ −1

Worked example

With the default values below, Indefinite Integral Calculator returns Indefinite integral of 1.5x^4 - 1.333333x^3 + 3x + 5 + C. Change any input above and every figure here is recalculated in your browser.

Inputs used

Polynomial coefficients, highest power first
6, -4, 0, 3
Constant of integration C
5

Results

Indefinite integral
1.5x^4 - 1.333333x^3 + 3x + 5 + C
Differentiating back
6x^3 - 4x^2 + 3
Degree of the antiderivative
4
Antiderivative at x = 1
8.166667

Step by step

  1. 1Values used
  2. 2Reverse power rule
  3. 3Indefinite integral= 1.5x^4 - 1.333333x^3 + 3x + 5 + C
  4. 4Differentiating back= 6x^3 - 4x^2 + 3
  5. 5Degree of the antiderivative= 4
  6. 6Antiderivative at x = 1= 8.166667

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Integrate 6x³ − 4x² + 3.

1.5x⁴ − (4/3)x³ + 3x + C, and differentiating returns the original.

Why is C necessary?

Because the derivative of any constant is zero, so infinitely many functions share the same derivative.

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