Free Online
Integral Calculator
Solve definite and indefinite integrals in seconds. The most beautiful and accurate calculator on the web.
Calculate Integral
Enter your function using the keypad or keyboard.
Result will appear here
Why Students Love Us
We combine powerful mathematical engines with a design that makes calculus less intimidating.
Lightning Fast
Get solutions instantly. No waiting, no loading screens.
100% Accurate
Powered by advanced symbolic integration algorithms.
Accessible Anywhere
Fully responsive design works perfectly on mobile and tablet.
What is an Integral Calculator?
An integral calculator is an advanced mathematical tool that computes the antiderivative (indefinite integral) or the area under a curve (definite integral) of a given function. It is an essential resource for students and professionals in calculus, physics, and engineering.
Our tool uses symbolic integration algorithms to parse your input, apply integration rules (like substitution, integration by parts, and partial fractions), and simplify the result. It bridges the gap between complex manual calculations and instant, accurate solutions.
Indefinite Integrals
An indefinite integral represents a family of functions. It is the reverse process of differentiation. When you find the indefinite integral of a function f(x), you are looking for a function F(x) such that F'(x) = f(x).
Definite Integrals
A definite integral has upper and lower limits (bounds). It calculates the net signed area between the function and the x-axis over a specific interval [a, b]. The result is a number, not a function.
Common Integration Rules
| Rule Name | Formula |
|---|---|
| Power Rule | ∫ x^n dx = (x^(n+1))/(n+1) + C |
| Constant Multiple | ∫ k·f(x) dx = k · ∫ f(x) dx |
| Sum Rule | ∫ (f + g) dx = ∫ f dx + ∫ g dx |
| Exponential | ∫ e^x dx = e^x + C |
| Natural Log | ∫ (1/x) dx = ln|x| + C |
How to Use
- 1Enter the function (e.g.,
x^2 + sin(x)) using the keypad. - 2Select the variable of integration (default is
x). - 3Toggle "Definite" if you need to calculate limits.
- 4Click "Calculate Solution" to see the result.
Key Features
- Symbolic Integration Engine
- Step-by-Step Logic (Beta)
- LaTeX Math Rendering
- Scientific Keypad Support
- Dark Mode Compatible
Frequently Asked Questions
Is this integral calculator free?
Yes, our integral calculator is 100% free to use for students, teachers, and professionals. There are no hidden fees or subscriptions.
Can it solve definite integrals?
Absolutely. You can switch to 'Definite' mode and enter the upper and lower limits to calculate the area under the curve.
Does it support trigonometric functions?
Yes, we support all standard trigonometric functions including sin, cos, tan, csc, sec, cot, and their inverse functions.
How accurate is the calculator?
Our calculator uses advanced symbolic math libraries to ensure high precision and analytical accuracy for solvable integrals.