About the Integral Calculator
Find antiderivatives (indefinite integrals) of polynomials, trig, exponential and common functions, and optionally a definite integral.
Also known as: antiderivative calculator, indefinite integral, integration calculator, integrate function.
How to use this calculator
- Enter f(x), lower limit (optional), upper limit (optional).
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Review the breakdown shown under the main result.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
∫xⁿ dx = xⁿ⁺¹/(n+1) + C · ∫1/x dx = ln|x| + C · ∫sin(ax) dx = −cos(ax)/a + C
Worked example
Using the values pre-filled in the calculator above:
- f(x): 3x^2 + 2cos(2x) + 1/x
- Lower limit (optional) = 1
- Upper limit (optional) = 2
the calculator returns:
- ∫ f(x) dx: x^3 + sin(2x) + ln(abs(x)) + C
- ∫ from 1 to 2: 6.0270472584
Tips & common mistakes
- Always add the constant of integration C to indefinite integrals.
- For definite integrals of functions without a closed form (e.g. e^(−x²)) use the definite integral calculator.