Integral Calculator
Antiderivatives with the technique spelled out step by step: powers and linear substitutions, trig, exponentials, ln, and integration by parts.
Runs entirely on your device - nothing is ever uploaded.
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How to use the integral calculator
- Type the integrand with x as the variable, for example x*cos(2x) or 1/(3x+2).
- Fill the bounds into the boxes on the integral sign for a definite integral, or leave them blank for an antiderivative with + C.
- Follow the listed technique behind each step.
What it is for
Integrals measure accumulated change: areas, distances from speed, total growth from a rate. Textbook answers rarely show the chosen technique, so this tool spells out which rule produced each antiderivative.
How it works
The integrand is matched against the standard antiderivative families - powers and their linear substitutions, trig functions, exponentials, 1/x, and integration by parts for x times sin, cos, or e^(kx) - with every applied rule recorded as a step. A definite integral is a numerical estimate: adaptive Simpson quadrature is applied directly to the integrand between the two bounds.
Worked example: substitution
Integrate 2x·cos(x²): the 2x is (up to a constant) the derivative of the inside function x², so substitute u = x² and the integral becomes ∫cos(u)du = sin(u) + C, hence sin(x²) + C. The same page estimates a definite integral numerically. From 0 to 2, the integral of x comes out to 2, the triangular area under y = x. Substitution, parts, and power-rule steps are each labeled as they fire.