Mathematics & algebra calculator
Antiderivative Calculator
Find general antiderivatives, particular antiderivatives from conditions, repeated antiderivatives, and optional graphs with step-by-step solutions.
Antiderivative result
Antiderivative Calculator results
Your antiderivative will appear here
Enter your function and click Calculate. Results are not shown before you run the calculator.
Antiderivative
Symbolic integration is handled by a browser-based math engine. Review syntax and assumptions for coursework or formal use, especially for difficult integrals.
Calculator overview
Quick Antiderivative Calculator Overview
Use this antiderivative calculator to find indefinite integrals, apply common integration rules, and review step-by-step work. It is focused on symbolic calculus practice rather than graphing or numeric approximation.
Enter a function to calculate its antiderivative and review the integration steps.
Guide
Antiderivative Calculator Guide
Use this guide to understand general antiderivatives, particular solutions, repeated antiderivatives, evaluation, and graphing without turning the page into a full integration-techniques textbook.
What This Calculator Does
This antiderivative calculator finds symbolic antiderivatives and indefinite integrals. It can return the most general antiderivative with + C, solve a particular antiderivative from a condition, and calculate a second or higher repeated antiderivative.
The calculator is designed as an anti derivative solver with steps. It also supports optional graphing and point evaluation for a representative antiderivative.
What an Antiderivative Is
An antiderivative of f(x) is a function F(x) whose derivative is f(x). Because adding a constant does not change the derivative, the general answer includes + C.
Antiderivative idea
If F'(x) = f(x), then an antiderivative of f(x) is F(x) + C f(x)The function you enter
F(x)One function whose derivative is f(x)
CThe arbitrary constant for the family
variableThe symbol used for antidifferentiation
General vs Particular Antiderivatives
The most general antiderivative describes a full family of functions. A particular antiderivative uses a condition such as F(2) = 7 to choose one member of that family.
General family
Include an arbitrary constant after integration.
Specific condition
Use a point condition to solve for C.
Repeated constants
Repeated integration introduces more constants.
Graph preview
Use one representative graph when no condition is given.
Indefinite Integral Notation
Indefinite integral notation is another way to write the antiderivative family. In plain text, the idea is:
Indefinite integral
int f(x) dx = F(x) + C Common Rules Used
Many antiderivatives use the power rule, sum rule, constant multiple rule, and standard trig, exponential, and logarithmic patterns. Substitution appears when the integrand looks like the reverse of a chain rule, such as x*cos(x^2).
Second and Repeated Antiderivatives
A second antiderivative means integrating twice. The first integration adds C1, and the second integration adds another constant, so repeated antiderivatives naturally include C1, C2, and more for higher orders.
Graphing an Antiderivative
Graphing one antiderivative requires choosing a specific constant. When no condition is given, this calculator graphs a representative antiderivative with C = 0. If a particular condition is supplied, the graph uses that specific antiderivative instead.
How to Use
Choose the mode
Use general, particular, or repeated antiderivative mode.
Enter the function
Use standard syntax such as x^2, sin(x), or e^(2*x).
Choose the variable
Select the variable of integration when more than one symbol appears.
Add details
Add a condition, repeated order, point value, or graph option if needed.
Click Calculate
Review the symbolic result, verification, steps, and optional graph.
Tips / Notes
- Always include + C for a general antiderivative.
- Use a condition to determine a particular antiderivative.
- Repeated integration introduces additional constants.
- If extra symbols are present, choose the variable of integration carefully so the remaining symbols are treated as constants.
- Verification is useful because differentiating the antiderivative should return the original function.
- Check the symbolic result and syntax before relying on an optional graph or point value.
FAQ
Frequently Asked Questions
Clear answers about antiderivatives, indefinite integrals, constants, graphs, and point values.
What does the Antiderivative Calculator do?
It finds symbolic antiderivatives and indefinite integrals, including general antiderivatives, particular antiderivatives from conditions, repeated antiderivatives, steps, graphs, and point evaluation.
How do I find the general antiderivative of a function?
Choose General Antiderivative, enter the function, select the variable of integration, and click Calculate. The calculator returns a representative antiderivative and the family with + C.
What is the difference between an antiderivative and an indefinite integral?
An antiderivative is a function whose derivative gives the original function. An indefinite integral is the notation used to describe the full family of those antiderivatives, usually written with + C.
How do I find the particular antiderivative that satisfies a given condition?
Use Particular Antiderivative mode, enter the function, then enter a condition such as F(2) = 7. The calculator solves for C and returns the specific antiderivative.
What is a second antiderivative?
A second antiderivative is found by integrating a function twice. It introduces two constants because each integration adds a new arbitrary constant.
Can this calculator graph an antiderivative or evaluate it at a point?
Yes. Graphing is optional and uses one representative antiderivative, usually with C = 0 unless a particular condition is supplied. General mode can also evaluate the representative antiderivative at a point.