You enter a polynomial in x using caret notation for exponents (e.g., 3x^2 + 2x + 1). The tool parses each term into a coefficient and power, applies the power rule — ∫axⁿ dx = (a/(n+1))x^(n+1) — to each term independently, and sums the results with a constant of integration. It supports polynomials only; trigonometric, exponential, and logarithmic functions are not handled.
For any term axⁿ where n ≠ −1, the integral is (a/(n+1))x^(n+1) + C. You increase the exponent by one and divide the coefficient by the new exponent. This reverses the power rule for differentiation.
The power rule applies to terms of the form axⁿ. Functions like sin(x), eˣ, or ln(x) require different integration techniques (substitution, integration by parts, etc.) that this tool does not implement.
C is the constant of integration. Since the derivative of any constant is zero, there are infinitely many antiderivatives for a given function, all differing by a constant. You need an initial condition to find the specific value of C.
The parser supports integer exponents entered with the caret symbol (e.g., x^3, x^-2). Fractional exponents are not currently supported — enter only whole-number powers.
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.