Antiderivative
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Antiderivative Calculator
Find the antiderivative of a polynomial.
Constant
+ C
Comprehensive Guide
An antiderivative is the reverse of differentiation. If a derivative tells you how fast something changes, an antiderivative reconstructs the original function up to a constant. That makes it central to calculus and mathematical modeling.
For polynomials, the rule is straightforward: increase the power by one and divide by the new power. The calculator is useful when you want to check your work quickly or see the pattern term by term.
Real-World Examples
For 3x² - 2x + 5, the antiderivative becomes x³ - x² + 5x + C. If the coefficients change, the output changes in a predictable way. That predictability is what makes polynomials a good fit for a calculator.
Because every antiderivative differs by a constant, the +C is always part of the answer.
Reference Table
| Input | Antiderivative | Why |
|---|---|---|
| 3, -2, 5 | x³ - x² + 5x + C | Power rule |
| 4, 0, 1 | x⁴ + x + C | Zero coefficients preserved |
| 1, 2 | x²/2 + 2x + C | Divide by new power |
Frequently Asked Questions
What is an antiderivative?
A function whose derivative returns the original function.
Why is +C included?
Because constants disappear when you differentiate.
Does it handle non-polynomials?
This version is focused on polynomials.
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