## Introduction to Integral Calculator With Steps:

Integral calculator is an online tool that helps you evaluate the **solution of integral** for trigonometry, exponential, algebraic, or polynomial expression, and so on. It can also be used to integrate definite or indefinite functions.

When you calculate the integrals manually, you get stuck in getting the result as it has complex structure. To get rid from the calculations, you can try our integration calculator that easily gives you solutions to your integral questions, allowing you to integrate online and streamline your problem-solving experience.

## What is an Integral?

Integral is a fundamental concept of calculus. It is a process of finding the infinitesimal data from the given function under a curve or a graph. This process is known as the **inverse derivative process**. It can be represented as “∫” in calculus.

Integral calculation is very important for performing complex tasks in daily life because it is used in physics, engineering, science, and mathematical fields. It has two main categories: definite integral and indefinite integral.

### Indefinite Integral:

Indefinite integral is sometimes called a derivative function because it does not **involve a limit**. To calculate indefinite integral, following formula is used.

$$ \int f(x)\; dx \;=\; F(x) + C $$

### Definite Integral:

Definite integral is the area that is present in a **closed interval**. Here a and b denote the lower and the upper limit respectively.

$$ \int_a^b f(x)\; dx $$

## How to Calculate Integrals?

To **calculate the integral** you should know the basic integral rules that are used to solve various types of integral problems.

Let's see how to calculate the definite and indefinite integral with the help of an example so that you get clarity about the integral concept.

### Definite Integral Calculation:

To **calculate the definite integral**, you need to follow these steps to be clear while solving the definite integral.

- Identify the function f(x) and the limits of integration a and b.
- Find the indefinite integral with respect to the given function F(x) to f(x).
- Evaluate the indefinite integral at the Limits, after solving the upper limit b and the lower limit a onto the antiderivative function, $$ \int ab^f(x)\; dx \;=\; F(b) − F(a) $$

Let's see an example of a definite integral with steps.

**Example**:

Calculate the definite integral:

$$ \int_0^2 (3x^2 + 2x + 1)\; dx $$

**Solution:**

Take the integration of the given integral question,

$$ \int (3x^2 + 2x + 1)\; dx \;=\; x^3 + x^2 + x + C $$

Apply limits on the above result of an integral question,

$$ \int_0^2 (3x^2 + 2x + 1)\; dx \;=\; [x^3 + x^2 + x]_0^2 $$

$$ =\; (2^3 + 2^2 + 2) - (0^3 + 0^2 + 0) $$

$$ =\; (8 + 4 + 2) - (0 + 0 + 0) $$

$$ =\; 14 $$

Therefore the solution of the given definite problem is 14.

## Indefinite Integrals Calculation:

To **calculate an indefinite integral**, follow these steps:

Identify the function f(x) to be integrated from the given integral problems. After knowing the type of integral, use standard rules to integrate common functions. These rules are:

### Power Rule:

$$ \int x^n\; dx \;=\; \frac{x^{n+1}}{n+1} + C (for\; n≠−1) $$

### Exponential Rule:

$$ \int e^x\; dx \;=\; e^x + C $$

### Trigonometric Rules:

$$ \int sin(x)\; dx \;=\; -cos(x) + C $$

$$ \int cos(x)\; dx \;=\; sin(x) + C $$

$$ \int sec^2(x)\; dx \;=\; tan(x) + C $$

### Substitution Method:

For more complex functions, you can use the **substitution method** to solve the integral problem.

Let u = g(x)(the given function) and change the integral in terms of u to make the integration process easy. Integrate with respect to u and again change u with x in the result of the given integral function.

### Integrate by Parts

When you have an integration that has the products of functions, then you can use **integration by parts method**. The formula to solve the integration by parts related problems is,

$$ \int u dv \;=\; uv - \int v\;du $$

Choose u and dv such that the integral of vdu

Let's see an example of an indefinite integral with a solution so find the example of an indefinite integral function which is:

$$ \int (4x^3 - 2x + 5)\; dx $$

**Solution:**

Takes the integration of a given function,

$$ \int 4x^3 dx \;=\; 4 \int x^3 dx $$

The integral of x^{n} is,

$$ \frac{x^{n+1}}{n+1} \; \; \; n ≠ -1 $$

$$ \int x^3 dx \;=\; \frac{x^4}{4} $$

## How to Use the Integration Calculator?

Integration solver has a simple design that helps you solve the given integral function question immediately. You just need to put your problem in it and follow some important instructions to get integration results without any trouble.

These steps ensure that integration online is easy and makes problem-solving straightforward. These instructions are:

- Choose the type of integral from the input box of integral calculator.
- Enter the function of the integral that you want to evaluate the integration solution in the input fields.
- Recheck your given input value to get the exact solution of the integral question.
- The
**Calculate button**provides you with solutions to given integral problems. - If you want to check the accuracy of our integrals calculator, you can use the load example and get its solution.
- Click the “Recalculate” button for the evaluation of more examples of the integrals with the solution.

## Outcome of Integral Solver With Steps:

Integral online provides you with a **solution** as per your input problem when you click on the calculate button. It may include as:

**In the Result Box,**

Click on the result button for the solution of the integration question.

**Steps Box**

When you click on the steps option, you get the solution of integral questions in a step-by-step process.

## Benefits of Integration Solver:

Integrals calculator has several benefits that you get whenever you use it to get the solution of integral questions. These benefits are:

- Our integral calculator with steps is a
**trustworthy tool**as it always provides you with accurate solutions of given integral problems. - It is an efficient tool that provides solutions in a step by step process of the given integral problems.
- Integration calculator is a learning tool that helps you to easily grab the concept of integration very easily through an online platform.
- It is a handy tool that solves integral problems with the help of different rules as per the given problems and you do not put any type of external effort.
- Integral solver with steps is a free tool that allows you to use it for the calculation of integral problems without spending.
- It is an easy-to-use tool, anyone, even a beginner can easily use it for the solution of integral problems.
- Integral online can save you tons of time that you use in finding the solution to integral questions as it provides you results in a run of time.