Every function has infinitely many antiderivatives that differ by a constant; +C represents all of them.

What if there is no elementary antiderivative?

Some functions (like e^(−x²)) have none. For definite integrals the calculator still returns an accurate numerical value.

Integral Calculator

Find antiderivatives and evaluate definite or improper integrals. The calculator identifies the technique (power rule, u-substitution, integration by parts, partial fractions) and verifies the answer by differentiating it back or comparing with numerical integration.

How to use the integral calculator

Enter the integrand.
Leave the bounds empty for an indefinite integral (+C), or enter both for a definite integral (use inf for ∞).
Review the technique, the antiderivative and the verification.

Examples

∫ x² sin x dx

Answer: −x² cos x + 2x sin x + 2cos x + C

Integration by parts (twice)

∫₀³ 2x dx

Answer: 9

∫ 1/(x² − 1) dx

Answer: ½ ln|x − 1| − ½ ln|x + 1| + C

Partial fractions

Formulas

Fundamental Theorem of Calculus

\int_{a}^{b} f (x) d x = F (b) - F (a), F^{'} = f

Integration by Parts

\int u d v = uv - \int v d u