Calculate definite and indefinite integrals quickly and easily. Enter a mathematical function, choose your integral type, and get a clear result with useful formulas and explanations.
Enter your function and select the calculation type.
Integration is the reverse process of differentiation. The basic power rule can be used to integrate many polynomial functions.
The power rule applies when n is not equal to −1. The constant C represents the arbitrary constant of integration.
∫xⁿ dx = xⁿ⁺¹/(n+1) + C
∫sin(x) dx = −cos(x) + C
∫cos(x) dx = sin(x) + C
∫eˣ dx = eˣ + C
∫1/x dx = ln|x| + C
∫k dx = kx + C
This Integral Calculator uses common integration rules to provide an antiderivative for supported functions. For definite integrals, it numerically evaluates the function between the selected limits.
Type a mathematical function such as x^2, sin(x), or e^x.
Choose an indefinite integral or provide lower and upper limits for a definite integral.
Click the calculate button to instantly view the result and supporting information.
These examples show some frequently used indefinite integrals.
An integral is a fundamental concept in calculus used to measure accumulation, area, displacement, and other quantities that change continuously. Integration is closely connected to differentiation.
An indefinite integral gives a family of antiderivatives, while a definite integral evaluates accumulated change between two limits and produces a numerical value.
An indefinite integral does not have specified boundaries. Its answer includes the constant of integration C because different functions can have the same derivative.
A definite integral has a lower and upper limit. It is commonly used to calculate the signed area under a curve or total accumulation over an interval.