Calxsolver
Calculus

Polynomial Integral

Enter a polynomial in x. The calculator finds the antiderivative with the reverse power rule ∫ c·xⁿ dx = c/(n+1)·xⁿ⁺¹ + C. Supply both limits a and b to also evaluate the definite integral as F(b) − F(a).

Polynomial Integral

Integrate a polynomial — indefinite or definite.

Try:
Answer∫ f(x) dx = 2x³ − 2x² + 3x + C
  1. Integrandf(x) = 6x² − 4x + 3
  2. Reverse power rule∫ 3x dx = 3x¹
  3. Reverse power rule∫ -4x dx = -2x²
  4. Reverse power rule∫ 6x² dx = 2x³
  5. Indefinite integral∫ f(x) dx = 2x³ − 2x² + 3x + C
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Worked examples

Find ∫ (2x + 3) dx Apply the reverse power rule to compute an indefinite integral. Find ∫₀³ x² dx Compute a definite integral with the fundamental theorem of calculus.

Key terms

Integral The accumulation of a function — the signed area under its graph between two points. Antiderivative A function whose derivative is the given function.

Frequently asked questions

How do I get a definite integral?

Fill in both the lower limit a and the upper limit b. Leave them blank for the indefinite integral.

Why is there a + C?

Indefinite integrals are determined only up to an arbitrary constant, written + C.

Is the result exact?

Yes. Polynomial integration is symbolic and exact, including the definite-integral evaluation.

Related solvers

Polynomial Derivative Differentiate a polynomial exactly with the power rule. Derivative Calculator Symbolic derivative of any function — chain, product and quotient rules. Integral Calculator Symbolic antiderivative — indefinite or definite — with full working. Derivative at a Point Numeric derivative of any function of x at a point. Definite Integral Numeric definite integral of any function of x. Limit Calculator Estimate the limit of a function as x approaches a value. Tangent Line Calculator Equation of the tangent line to a curve at a point.