Integral Calculator

Indefinite integrals (antiderivatives) found symbolically and verified by differentiation before they are shown.

Your result will appear here

Fill in the fields and press Integrate, or pick one of the examples.

About the Integral Calculator

Finds an antiderivative of the integrand symbolically. Before the result is displayed it is differentiated numerically and compared with the integrand at several points; an antiderivative that fails this check is never shown.

Many elementary functions have no elementary antiderivative ( $e^{-x^2}$ , $\sin x / x$ , $x^x$ ). In that case the calculator says so — use the Definite Integral Calculator to get a numerical value over an interval.

Limitations

Coverage depends on the symbolic engine: polynomials, exponentials, logarithms, common trigonometric integrands, and many products handled by parts or substitution.
No derivation is shown: the engine returns only the final antiderivative.
Results involving special functions (erf, Si, …) are not displayed.

How to use it

Type the integrand, e.g. x * cos(x).
Set the variable of integration.
Press Integrate.

Example

∫ 2x dx

→ x^2 + C

Formulas used

\int x^{n}\,dx = \frac{x^{n+1}}{n+1} + C,\quad n \ne -1

Power rule for integrals.

\int u\,dv = uv - \int v\,du

Integration by parts.

Definite Integral CalculatorEvaluate definite and improper integrals: analytically when an antiderivative exists, otherwise by adaptive quadrature.Derivative CalculatorDifferentiate functions symbolically — first, second and higher derivatives — with the rules used and a numerical verification.Numerical Integration CalculatorApproximate integrals with the trapezoidal, midpoint and Simpson’s rules and compare them with an adaptive reference value.

About the Integral Calculator

Limitations

How to use it

Formulas used

Related tools

About the Integral Calculator

Limitations

How to use it

Formulas used