Free antiderivative calculator: sum of a·x^n terms (integer n), optional 1/x → ln|x|, symbolic F(x)+C, numeric check at x₀, scenario sensitivity rows, and a full guide—also for “rantiderivative” searches—not a full CAS.
Antiderivative (indefinite integral) means “a function whose derivative is the integrand,” up to + C. This helper integrates a finite sum of power termsa xⁿ with integer exponents n ≠ −1, plus optional n = −1 terms that become a ln|x|. It is not a full computer algebra system—no substitution chain rule wizardry—just transparent power-rule arithmetic and a small scenario table for sensitivity.
Summary: Enter coefficients and exponents for each term of f(x) (the integrand). Like terms merge automatically. You get a readable F(x) + C, a numeric check F(x₀) with C = 0 at a chosen x₀ > 0 (required when ln|x| appears), and rows that nudge coefficients—same spirit as the mortgage calculator’s stress checks.
Antiderivative calculator (polynomial + 1/x)
Typo note: people sometimes search rantiderivative calculator; they mean antiderivative. This page is built for that intent.
Rules used (transparent)
For n ≠ −1: ∫a xⁿdx = a/(n+1) · xn+1 + C.
For n = −1: ∫a x−1dx = a ln|x| + C (on intervals where x ≠ 0).
Exponents are treated as integers between −8 and 12; coefficients as decimals in a modest range.
