# Introduction in the Indefinite Integrals

The **indefinite integral** represents a function which will describe an area under the function chart between 2 points arbitrarily chosen. Practically, it is the family of all functions whose derivative is f(x). There is a possibly finite set of exceptions.

## Indefinite Integral Definition

The **indefinite integrals** are integrals without limits. The process of integration is useful in two different ways:

- To find the function you have the derivative for.

- To find the area under the function chart between 2 points arbitrarily chosen.

The **definition of indefinite integral** is the following:

Let f(x) be the derivative of the function F(x) with respect to x on an interval. Then, the family of all antiderivatives of f(x) is called the indefinite integral of f(x) with respect to x: 'c' - represents the constants of integration.

### Evaluate the indefinite integral

The **table of Indefinite Integrals** contains a series of **indefinite integrals formulas**. These formulas are hard to prove, but easy to remember , this is why the table must be treated very carefully and with responsibility. Basically, it is a general **list of indefinite integrals**, the most important ones, which will show you how to **evaluate the indefinite integral**.

### Indefinite integral table

Any **indefinite integral formula** from above can be used in problems or exercises to ease your process of **evaluating indefinite integrals**.

## Indefinite integral examples

After we saw the **indefinite integral definition** and how to **evaluate indefinite integral**, it's time we offer you a short series of **indefinite integral examples**.

First **indefinite integral example** of solved exercise:

The second one:

Those from above were practical **indefinite integrals examples**. It would be very beneficial if you would have a look over them too, in order to make an idea of how exercises like that should be approached and to improve your skills.

Next, we will offer you a few tips, just to make sure you understood our today lesson.

1. ∫(Symbol for integration) *f*(*x*)(Integrand) *dx*(Differential of x) =*F*(*x*)(Antiderivative or indefinite integral of *f*(*x*)) + *C*(Constant of integration).

2. The integral of a function is not unique. The constant different the integrals of the same function.

3. Integration is the inverse of differentiation.

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