Antiderivative Calculator

Author: Henrick Yau
- 5 August 2026
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Calculators

This calculator helps you find the antiderivative (indefinite integral) of a function. Enter your function and see the step-by-step integration process.

Input Function

Display Options

About Antiderivatives

An antiderivative, also known as an indefinite integral, is a function F whose derivative is equal to the original function f. In other words, if F'(x) = f(x), then F(x) is an antiderivative of f(x).

Key Integration Rules
  • Power Rule: ∫xⁿ dx = (x^(n+1))/(n+1) + C, for n ≠ -1
  • Exponential Rule: ∫e^x dx = e^x + C
  • Logarithmic Rule: ∫(1/x) dx = ln|x| + C
  • Sine Rule: ∫sin(x) dx = -cos(x) + C
  • Cosine Rule: ∫cos(x) dx = sin(x) + C
  • Tangent Rule: ∫tan(x) dx = -ln|cos(x)| + C
Applications of Antiderivatives

Antiderivatives are fundamental in calculus and have various applications in:

  • Physics (calculating displacement from velocity, work from force)
  • Economics (determining total cost or revenue from marginal functions)
  • Engineering (analysing physical systems and signal processing)
  • Probability (working with probability density functions)
  • Computer graphics (curves and parametric equations)

What the antiderivative calculator does

The Antiderivative Calculator is a helpful tool designed for students and anyone interested in mathematics. It allows you to find the antiderivative, also known as the indefinite integral, of a function. By entering any function, you can see the results and follow the step-by-step integration process. This makes learning about antiderivatives easier and more interactive.

What is an Antiderivative?

An antiderivative is a function that, when differentiated, gives you the original function. For example, if the derivative of F(x) equals f(x), then F(x) is the antiderivative of f(x). This relationship helps in understanding how functions behave and is a key concept in calculus.

Entering a function and choosing options

Using this calculator is straightforward. You simply enter the function you want to integrate and specify the variable. You can choose to see the integration steps or graph the function. This flexibility helps you to learn at your own pace, whether you're looking for quick answers or deeper insights.

Step-by-step solutions and graphing

  • Step-by-Step Solutions: It shows how the antiderivative is calculated.
  • Graphical Representation: Visualize the original function and its antiderivative on a graph.
  • Custom Integration Variable: You can choose a variable other than the default 'x'.
  • User-Friendly Interface: The layout is simple, making it easy to navigate.

Integration Rules to Know

Understanding integration rules can enhance your use of the calculator. Here are some important rules:

  • Power Rule: ∫xⁿ dx = (x^(n+1))/(n+1) + C, for n ≠ -1
  • Exponential Rule: ∫e^x dx = e^x + C
  • Logarithmic Rule: ∫(1/x) dx = ln|x| + C
  • Sine Rule: ∫sin(x) dx = -cos(x) + C

Applications of Antiderivatives

Antiderivatives play a vital role in various fields. They are used in:

Benefits of Learning Antiderivatives

Learning about antiderivatives helps build a strong foundation in calculus. By using the Antiderivative Calculator, you can improve your understanding of integration, which is essential for advanced mathematics. The interactive nature of the calculator encourages practice and enhances problem-solving skills.

Why this tool helps with calculus

The Antiderivative Calculator is an excellent resource for anyone studying calculus. Its features and ease of use make it ideal for learning. Whether you are a student or just curious about mathematics, this tool can aid your understanding and enjoyment of the subject.

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