Integral Calculator
Enter any function of x to get its symbolic antiderivative. The calculator combines linearity, the power rule, a table of standard antiderivatives, linear u-substitution and integration by parts. Provide both limits a and b to also evaluate the definite integral.
Formula and method
∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1) ∫_a^b f(x) dx = F(b) − F(a) [Fundamental Theorem] Supported: power rule, standard table, linear u-sub, integration by parts
Applies symbolic antidifferentiation in sequence: linearity (sum and constant-multiple rules) → reverse power rule → standard antiderivative table (sin, cos, tan, exp, ln, sqrt and their linear-argument forms ax + b) → linear u-substitution for f(ax + b) → integration by parts for polynomial × trig and polynomial × exp patterns. For definite integrals, F(b) − F(a) is computed once the antiderivative is found. Note: general trigonometric substitution, partial fractions and non-linear substitutions are beyond the implemented rules and will produce a clear error.
Worked examples
Frequently asked questions
Which integration techniques does it use?
Linearity (constant multiple + sum), reverse power rule, a standard antiderivative table (sin, cos, exp, ln, …), linear u-substitution and integration by parts for the common patterns.
What if it can't find an antiderivative?
Many integrals have no elementary closed form, or require techniques (general u-sub, partial fractions, trig substitution) beyond the rules implemented here. Use the Definite Integral tool for a numeric answer.
How do I get a definite integral?
Fill in both the lower limit a and the upper limit b. Leave them blank for the indefinite antiderivative + C.