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: indefinite integral'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

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:
indefinite integral example

The second one:
indefinite integral examples

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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