# Antiderivative Calculator

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

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## 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 = 6x2/2 = 3x2

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

= 3x2 + 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 3x2/2 + C Antiderivative of x x2/2 + 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 ex ex + C