sqrt(…)root(n, …)pi for π,
alpha for α, …
Use parentheses, if necessary. Also see "Examples". Change integration variable and order in "Options". Click Go! to compute the integral.
Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step integration). All common integration techniques and even special functions are supported.
This calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. You can also check your answers!
Powered by Maxima CAS — the same engine used by integral-calculator.com — for accurate symbolic results, with SymPy generating detailed step-by-step solutions.
And now: Happy integrating!
Enter the function into the input field. Skip the f(x)=
part and the dx.
Use parentheses if necessary, e.g. a/(b+c).
Write decimals with a period, e.g. 3.141.
Click Go! to compute. Set bounds and variable in Options.
Supported formats:
x^2
for x²sqrt(x)
for √xln(x)
for natural loge^x
for eˣsin(x), cos(x), tan(x)
arcsin(x), arctan(x)
abs(x)
for |x|pi
for π, e
for Euler's numberClick an example to load it:
For those with a technical background, the following section explains how the Integral Calculator works.
First, a parser analyzes the mathematical function you enter. It transforms it into a form better understood
by
a computer — a syntax tree. The parser handles cases like implicit multiplication (e.g. 5x
instead of 5*x)
and respects the correct order of operations. As you type, the tree is converted into LaTeX code and rendered
live in the preview box using MathJax.
When you click Go!, the function and settings are sent to the server where the computer algebra system Maxima CAS computes the exact symbolic answer. Maxima is a powerful open-source CAS used by mathematicians, engineers, and researchers worldwide. In many cases the antiderivative is found using the Risch algorithm — a systematic method for symbolic integration.
The step-by-step solution is generated separately using SymPy — a Python mathematics library. It applies the same integration techniques a student would use: u-substitution, integration by parts, partial fractions, trigonometric identities, and more. When the integrand matches a known form, it applies fixed rules. Otherwise it tries different substitutions and transformations until the integral is solved.
The Check Answer feature determines whether your antiderivative is equivalent to the computed result. It differentiates your input and compares it to the original function at multiple test points — if they match, your answer is correct.
The interactive graph is computed directly in the browser using Plotly.js. It evaluates the function in small steps across the visible range and plots the curve, detecting singularities and discontinuities automatically.