Integral Calculator

The Integral Calculator finds antiderivatives and evaluates definite integrals, naming the technique at every step. Direct antiderivatives. u-substitution with the substitution and du written out. Integration by parts with u and dv chosen and the reason stated. Partial fractions with the decomposition shown. Trigonometric integrals and substitutions. Improper integrals with the limit taken explicitly. Definite integrals include the evaluation at the bounds. Area between curves and volumes of revolution are handled when you describe the region. Integrals that need a reduction formula, a trigonometric substitution with the triangle described, or repeated integration by parts are walked through one pass at a time.

Type the integrand and the bounds or photograph the problem. "integral of x e^x dx" or "integral from 0 to pi of sin^2(x) dx". If the assignment requires a technique, say so: "using integration by parts". Include the differential so the variable is unambiguous. Use e^(2x), ln(x), sqrt(x), sec(x)^2. Set Answer form to exact for symbolic results, decimal for a numeric value of a definite integral. For area, volume, arc length, or average value problems, describe the region or the interval in words and the solver writes the setup integral before evaluating it. If the integrand is a product, say which factor should be u if your course has a rule for it.

Output: the antiderivative with + C, or the numeric value of a definite integral, first. Then the technique, the intermediate integrals, and the back-substitution. Definite integrals show F(b) - F(a) with each evaluation written. Improper integrals show the limit and whether it converges. The working is shown so you can check it, and differentiating the result is the fastest check. For the derivative, use the Derivative Calculator. For a series representation, use the Series & Sequences Solver. A follow-up can re-evaluate the integral with a different technique for comparison, or approximate a definite integral by the trapezoid or Simpson's rule with the table of sample points shown. The antiderivative check by differentiation is included on request.