# Antiderivative Calculator

**Derivatives** are defined as finding the rate of change of a function with respect to other variables. It deals with the variables such as x and y, functions f(x), and the corresponding changes in the variables x and y. The derivative of a function is represented by f '(x).

## What is Antiderivative Calculator?

'Cuemath's Antiderivative Calculator' is an online tool that helps to calculate the value of the anti-derivatives. Cuemath's online Antiderivative Calculator helps you to calculate the value of the anti-derivatives in a few seconds.

## How to Use Antiderivative Calculator?

Please follow the below steps to find the value of the anti-derivatives:

**Step 1:**Enter the function with respect to x in the given input boxes.**Step 2:**Click on the**"Calculate"**button to find the value of the anti-derivatives.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the different functions.

## How to Find an Antiderivative Calculator?

The** antiderivative** is defined as the reverse process of differentiation which is also known as integration. The integration is represented by** ' ∫ '**

'Let's see an example to understand briefly.

Cosider a function f(x) = x^{2}

We know that d / dx ( x^{2}) = 2x <----(1)

Here we say, x^{2} is the integral of 2x

In fact, there exist infinite integrals of this function because the derivative of any real constant CC is zero and we can write equation(1) as:

d / dx( x^{2} + c) = 2x.

There are common functions and rules we follow to find the integration.

**Solved Example:**

Find the anti-derivative value of 5x^{3} + 2x^{2}

**Solution:**

= ∫( 5x^{3} + 2x^{2})

= ∫( 5x^{3}) + ∫(2x^{2})

Using multiplication by constant and power rule,

= [5 × (x^{3}^{ + 1} / 3 + 1)] + [2 × x^{2}^{ + 1} / 2 + 1]

= 5x^{4} / 4 + 2x^{3} / 3

Therefore, the anti-derivative value of 5x^{3} + 2x^{2 }is 5x^{4} / 4 + 2x^{3} / 3

Similarly, you can use the calculator to find the value of anti-derivatives for the following:

- x
^{3}/ 2 - 5x
^{2}+ 6x