Online Indefinite Integral Calculator

An indefinite integral calculator helps you find the antiderivative of a function. This tool is essential for calculus students, engineers, and anyone working with integrals in mathematics, physics, or engineering. The calculator provides step-by-step solutions and supports a wide range of functions.

What is an Indefinite Integral?

An indefinite integral, also known as an antiderivative, represents a family of functions whose derivative is the original function. It is written as ∫f(x)dx and includes a constant of integration, C. The general solution is F(x) + C, where F'(x) = f(x).

Indefinite Integral Formula

∫f(x)dx = F(x) + C, where F'(x) = f(x)

Indefinite integrals are used to find areas under curves, solve differential equations, and analyze functions. They are fundamental in calculus and have applications in physics, engineering, and economics.

How to Use the Calculator

Using the online indefinite integral calculator is straightforward. Follow these steps:

Enter the function you want to integrate in the input field.
Select the variable of integration (usually x).
Click the "Calculate" button to compute the integral.
Review the result and explanation provided.

Tip

For complex functions, ensure you enter the correct syntax. The calculator supports basic arithmetic operations, trigonometric functions, exponentials, and logarithms.

Basic Integral Rules

Here are some fundamental rules for computing indefinite integrals:

Power Rule: ∫x^n 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
Trigonometric Rules:
- ∫sin(x) dx = -cos(x) + C
- ∫cos(x) dx = sin(x) + C
- ∫sec²(x) dx = tan(x) + C

Example

∫3x² dx = x³ + C

Common Integral Examples

Here are some examples of indefinite integrals and their solutions:

Function	Integral
x²	x³/3 + C
sin(x)	-cos(x) + C
e^x	e^x + C
1/x	ln\|x\| + C

Note

The constant of integration, C, is added to the result to represent the family of possible antiderivatives.

Limitations of the Calculator

While the online indefinite integral calculator is powerful, it has some limitations:

It does not solve definite integrals (with limits).
It may not handle all types of special functions.
Complex integrals may require manual computation.

For Advanced Cases

For complex integrals, consider using symbolic computation software like Mathematica or Wolfram Alpha.

Frequently Asked Questions

What is the difference between definite and indefinite integrals?

An indefinite integral represents a family of functions (including a constant of integration), while a definite integral computes a specific area under the curve between two limits.

Can the calculator solve integrals with multiple variables?

This calculator is designed for single-variable functions. For multivariate integrals, specialized tools are required.

How accurate are the results from this calculator?

The calculator provides accurate results based on standard integral rules. For complex functions, manual verification may be necessary.