Integral Calculator

This integral calculator finds the indefinite integral, or antiderivative, of a function of x. Integration is the reverse of differentiation: where a derivative tells you how fast something is changing, the integral builds the original quantity back up from its rate of change, which is how you turn velocity into distance or a rate of flow into a total volume. Because the derivative of any constant is zero, an indefinite integral is never unique, so the answer always carries a constant of integration written plus C. You enter a function using x as the variable, with a star for multiplication and a caret for powers, for example 3*x^2 + 2*x or exp(2*x), and the calculator returns its antiderivative. It handles the cases that come up most in study and everyday calculus: polynomials of any degree using the power rule, one over x giving the natural logarithm, exponentials, and sine and cosine with a linear argument. For more unusual functions, where a neat antiderivative may not exist in elementary form, the companion definite integral calculator gives the numeric area under the curve between two limits instead. The result here may be shown unsimplified but is always correct, since you can differentiate it to recover your original function. Enter a function to see its integral straight away.

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Use * for multiply and ^ for powers. Handles polynomials and standard forms (powers, 1/x, exp, sin, cos with a linear argument). For other functions, try the definite integral calculator. Estimate only.