Integral Calculator: Definite, Indefinite
This integral calculator finds the antiderivative of a function, or the definite integral between two limits. Type a function such as x^2, x*e^x or sin(2x), leave the limits empty for the indefinite integral, or add a lower and upper limit for a number. Common forms are integrated exactly and checked by differentiating numerically, and definite integrals fall back to adaptive numerical integration when no closed form is found. It runs in your browser with no sign-up.
Integral Calculator
Find indefinite and definite integrals of a function with a numeric check.
How to use the Integral Calculator
- Type the function you want to integrate, for example x^2 + 3x.
- Leave the limits empty for an indefinite integral, or enter a lower and upper limit.
- Change the variable if it is not x.
- Read the antiderivative and the value, then edit the function to try another.
Basic rules
∫ xโฟ dx = xโฟ⁺¹/(n+1) + C (n ≠ −1) · ∫ 1/x dx = ln|x| + C · ∫ eหฃ dx = eหฃ + C · ∫ sin x dx = −cos x + C · ∫ cos x dx = sin x + C · ∫ f dx from a to b = F(b) − F(a).
Features
- Indefinite integrals with + C
- Definite integrals between any two limits
- Polynomials, exponentials, trig, logs and roots
- Integration by parts for x·eหฃ, x·sin x and similar
- Numerical fallback for hard definite integrals
- Free and private
Frequently asked questions
How do I calculate an integral?
Type the function, then add limits if you want a definite integral. The calculator applies integration rules, then checks the result by differentiating it numerically.
What is the difference between definite and indefinite integrals?
An indefinite integral is a family of functions with a constant C. A definite integral between two limits is a single number, the signed area under the curve.
What if there is no closed form?
Some functions, such as e^(-x^2), have no elementary antiderivative. In that case, enter limits and the tool gives a numerical value accurate to about eight digits.
Does it include the constant of integration?
Yes. Indefinite results end with + C. Definite integrals do not need it.
Which functions are supported?
Polynomials, powers, 1/x, exponentials, sine, cosine, tangent, logarithms and square roots, plus common products and some forms that give arctan and arcsin.