Antiderivative & Definite Integral Calculator
Antiderivative & Definite Integral ∫ f(x) dx
Find antiderivative F(x) + C or compute definite integral. Results display exact fractions, logarithms, or decimals.
The calculator above finds an antiderivative F(x) and evaluates the definite integral from a to b with the Newton–Leibniz formula.
Formulas used
∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C (n ≠ −1)
∫ₐᵇ f(x) dx = F(b) − F(a)
- ∫ 1/x dx = ln|x| + C, ∫ eˣ dx = eˣ + C, ∫ cos x dx = sin x + C.
- Do not forget the constant C for indefinite integrals.
Worked example
Evaluate the integral of 2x + 1 from 0 to 2:
∫₀² (2x + 1) dx = [x² + x]₀² = 6
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Type the integrand f(x) and, for a definite integral, the limits a and b.
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.