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# Antiderivative Calculator

Select definite or indefinite integral option, enter the function, and Hit the ** submit **button to find the antiderivative using antiderivative calculator.

Table of Contents:

## Antiderivative Calculator With Steps

Antiderivative calculator is a tool that **evaluates the integral** of a given function with respect to a variable. This antidifferentiation calculator also calculates the definite as well as indefinite integral for the given function.

This integral calculator also shows the steps of integration for every calculation.

## What is an integral?

An integral can be defined as,

**“**An **integral **assigns numbers to functions in a way that can define volume, area displacement, and even probability. Integral is an inverse function of derivative, which is why, it is generally referred to as antiderivative.**”**

The process of finding integral is known as **integration**. It is used to find the area under the curve. The symbol of **integration **or **antiderivative **is** **∫**.**

## How to evaluate an integral?

*Example: *

Evaluate the following integral.

**∫ (6x + 2) dx**

**Solution:**

**Step 1: **Apply linearity to the function.

**=** **6** **∫ x dx + 2 ∫ 1 dx** ------- **1**

**Step 2: **Solve **6** ** ∫ x dx **and

**2** ∫ 1

dx separately and place the values in the above equation (**1**).

**6 ∫ x dx**

Apply power rule.

**6 ∫ ****x dx ****= 6****x**^{2}/**2** **= 3x ^{2}**

**2** **∫** 1 dx

Apply constant rule `∫a dx = ax + C`

.

**2 ∫ 1 dx = 2x + C**

**Step 3: **Put the solved integrals in equation (**1**).

**= 6 ∫ x dx + 2 ∫ 1 dx**

**= 3****x ^{2} + **

**2x + C**

The** integral solver** above performs all of these steps and shows you the complete calculation for your ease.

Below are some other examples of antiderivative

Function f(x) | Antiderivative F(x) |

Antiderivative of 3x | 3x^{2}/2 + C |

Antiderivative of x | x^{2}/2 + C |

Antiderivative of 1/x | ln|x| + C |

Antiderivative of sinx | -cos(x) + C |

Antiderivative of cosx | sin(x) + C |

Antiderivative of secxtanx | sec(x) + C |

Antiderivative of tanx | -ln|cos(x)| + C |

Antiderivative of e^{x} | e^{x} + C |