Free Online
Antiderivative Calculator
Find the primitive function in seconds. Accurate, fast, and easy to use.
Antiderivative Calculator
Enter your function using the keypad or keyboard.
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Why Use Our Antiderivative Tool?
Finding antiderivatives can be tricky. We make it simple and provide the steps.
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What is an Antiderivative?
An antiderivative of a function f(x) is a differentiable function F(x) whose derivative is equal to the original function f(x). In other words, F'(x) = f(x).
The process of finding an antiderivative is called antidifferentiation (or indefinite integration). Because the derivative of a constant is zero, any antiderivative can have an arbitrary constant added to it. This is why we write:
Where C is the constant of integration.
Common Antiderivative Rules
| Function f(x) | Antiderivative F(x) |
|---|---|
| x^n (n ≠ -1) | (x^(n+1))/(n+1) + C |
| 1/x | ln|x| + C |
| e^x | e^x + C |
| cos(x) | sin(x) + C |
| sin(x) | -cos(x) + C |
How to Use This Calculator
- 1Enter the function you want to find the antiderivative for.
- 2Select the variable (usually x).
- 3Click "Calculate Solution".
Frequently Asked Questions
Is an antiderivative the same as an integral?
Yes, an antiderivative is also known as an indefinite integral.
Why is there a + C?
Because the derivative of any constant is zero, so there are infinitely many functions that have the same derivative, differing only by a constant.
Can it find antiderivatives for all functions?
It can find antiderivatives for most standard mathematical functions. Some functions do not have an antiderivative that can be expressed in terms of elementary functions (e.g., e^(-x^2)).
Is this calculator free?
Yes, it is 100% free.