Integral Calculator • With Steps!
Calculate integrals and antiderivatives of functions online — for free! Check your solutions to calculus exercises with full working steps. Supports definite and indefinite integrals, multiple variables, and all common integration techniques. Interactive graphs help visualize functions. For step-by-step solutions.
How the Integral Calculator Works
First, a parser analyzes the mathematical function. It transforms it into a form understandable by a computer — a syntax tree. The Integral Calculator detects implicit multiplication (e.g. 5x → 5*x) and respects order of operations. The parser is implemented in JavaScript and provides real-time LaTeX preview via MathJax as you type.
When Go! is clicked, the function is passed to the symbolic math engine Nerdamer.js, which computes the antiderivative using the Risch algorithm, integration by parts, substitution, partial fractions, and other techniques. For definite integrals, numerical integration (adaptive Simpson's rule with 10,000 subdivisions) computes the result to high precision.
For step-by-step solutions, the calculator calls the Claude AI API which explains each integration step in clear, human-readable form. The interactive function graph is computed in-browser using the HTML5 Canvas element, plotting both f(x) and its antiderivative F(x), with singularity detection and pan/zoom support via touch gestures.
The Check Answer feature verifies equivalence by evaluating both expressions at multiple random points and checking if their numerical derivatives match — the same probabilistic approach used by professional CAS systems.