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∫ Integral Calculator

Find indefinite and definite integrals of polynomial functions in x. See the antiderivative F(x) + C and compute ∫ from a to b with clear, step-by-step explanations.

Integral Calculator

Integrate single‑variable polynomial functions symbolically. See the antiderivative F(x) with + C, and optionally compute a definite integral by evaluating F(b) − F(a).

Function

f(x)

Supports polynomials like 4x^3 - 2x + 7. Use x as the variable and ^ for powers.

Uses power rule ∫ a x^n dx = a x^(n+1)/(n+1)Shows antiderivative and definite integral

Definite integral bounds

Lower limit (a)

Upper limit (b)

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

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.
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.
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

Write your integrand as a polynomial in x using powers with ^.
Review the symbolic antiderivative F(x) + C produced by the power‑rule integral calculator.
Add bounds a and b to compute the definite integral value F(b) − F(a).

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 tailored for students revising calculus.

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 more advanced rules and are not fully shown step by step here.
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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