# Integral Calculator

Try out our best integral with steps calculator to evaluate the problems related to antiderivative, definite or indefinite integration in calculus.

## Introduction to the Integral Calculator

The general integrals solver is an online tool that is used to calculate the major concepts of integrals and integration. This calculator integral helps to calculate the area under the curve. This calculator can function with the help of some simple clicks. The integral function is very easy to use and can be easily understood. The steps mentioned here are very understandable.

It gives the proper results after doing calculations. It will help you to find the integrals step by step and make them easier to learn. The best property of integral solver with steps is that it is free of cost, easy to use, and gives you accurate results.

## How to Solve Integral Online?

To solve an integral online, you can use various online integration tools and websites that offer symbolic mathematics and calculus solutions. Here's a step-by-step guide to solving an integral online using different methods:

### Use Online Calculators

Several websites provide free tools to solve integrals. You can input your integral, and the website will return the solution. You can find these websites online simple by searching integral calculator step by step on SERP.

### Use Mathematical Software Online

Some platforms offer access to mathematical software online, where you can enter and solve complex integrals. These may include SageMathCloud or Desmos etc.

### Use Online Math Forums

If the integral is particularly complex or you need explanation and discussion, math forums can be helpful. Post your question on:

• Stack Exchange Mathematics: It is a Q&A site where you can ask for help with your integrand. Millions of experts will provide solutions or hints to you here.
• Reddit’s /r/learnmath or /r/math: Communities where you can ask math questions and get answers from a wide range of users, from students to professional mathematicians.

## What is Integration Calculator with Steps?

The word integral is used in integration to designate a number to a function. The word integral is belonging to the integration of calculus. The integral is a function, whose derivative is its function.

Finding areas of any two-dimensional objects or the volumes of three-dimensional objects. So, it is stated as finding the integrals of any function concerning the y-axis means finding the area concerning the y-axis and vice versa.

The general integrals calculator does the same job. It evaluates the integral function to give you the results accurately and quickly. By doing some smart clicks one can get the required results. It also designates a number to a function which is known as an integral.

On the other hand, the integral of complex function is called integration by partial fraction which we may calculate with integral by partial fractions calculator.

### Notation of Integral

The sign used to show integral is;

, This sign shows the integral of integration.

## Formula Used by Integral Solver

The general formula for evaluating the integral is: $$\int f'(x) dx \;=\; f(x) + C$$

Here,
f is the integral function
C is constant.

In case, if two different functions are multiplying under the integral, use ibp calculator which uses the formula of special method of integration.

## Solved Examples with Online Integration Tool

let's take a look how the online integration calculator with steps use this formula to solve integration online.

Example # 1: Consider we have a function:

$$\int_0^4 3x dx$$

Solution:

$$\int_0^4 3x dx \;=\; 3 \int_0^4 x dx$$ $$\int_0^4 3x dx \;=\; 3 \Biggr| \frac{x^2}{2} \Biggr|_0^4$$ $$\int_0^4 3x dx \;=\; 3 \Biggr[ \frac{4^2}{2} \;-\; \frac{0^2}{2} \Biggr]$$ $$\int_0^4 3x dx \;=\; 40$$

Example # 2: Consider we have a function:

$$\int (5x^2 + 9) dx$$

Solution:

$$\int (5x^2 + 9) dx \;=\; \int 5x^2 dx \;+\; \int 9 dx$$ $$\int (5x^2 + 9) dx \;=\; 5 \frac{x^3}{3} \;+\; 9x$$ $$\int (5x^2 + 9) dx \;=\; \frac{5x^3}{3} \;+\; 9x \;+\; C$$

Following are some more and general examples of integrals:

Function Integral Overview
1/x ln |x| + C The integral of 1/x w.r.t "x" is the natural log of absolute value of x.
2x 2x/ln(2) + C By using formula i.e. a^x with a = 2.
2x x2 + C By using integration power rule.
x x2/2 + C By using integration power rule.
ex ex + C ex has same derivative and antiderivative.
1/ex or e-x -e^e-x + C Using the antiderivative for ex, we adjust for the negative exponent.
1 x + C Integral of a constant is the variable of integration.
ax (where a is a constant) ax/ln(a) + C This formula generalizes the integral for any base a.
1/x2 or x-2 -1/x + C By using the integration power rule.
ln(x) xln(x) - x + C Using integration by parts technique.
sec2(x) tan(x) + C Since, derivative of the tangent function.

Related: To calculate the integral of an integral, use of multivariable integral calculator is a best choice.

## Significance of Integral Calculator Show Steps

There are numerous significance of this calculator like it solve integral online in no time. This online integrator uses integration techniques to evaluate the integrals. The general integrals solver solves the function step by step and gives the integral answer appropriately. The results provided are appropriate, authentic and accurate.

The integration solver with steps provides the integrals of different functions. The online tool calculates complex problems and provides accurate and reliable results. There is no need to do large complex problems of calculus. You have to do some smart clicks to get the required solution.

Also try our integral triple calculator to evaluate integral multiple times (thrice) instantly.

## How to Use Online Integration Calculator with Steps?

Calculus is the most difficult part of mathematics due to its complicated formulas and techniques. Especially, integration is so time taking and full of errors. So, to evaluate different techniques of calculus, there are specially designed calculators like long division integral calculator & many more.

These calculators help its user to get error-free results for long and complex problems of integration. The different online integration solvers provide the best reliable error-free results in no time.

By using some small easy steps one can get the free solution from these online available integration tools. The use of the integrals calculator is important that it made calculations of integral easier. It saves time and energy which is being used while solving integration problems manually.

### Steps to use Online Integration Solver:

By using the following simple steps one can easily get the solution to their desired complex problems.

Step 1: Put the Function

To evaluate the integrals, the first input you need to put in the integration solver with steps is the integrand function. This tool also offers "Examples" option. You can get example from there to calculate integral with step by step detailed solutions.

Step 2: Select the Variable

The best integral calculator with steps offers three different variables x,y,z. You can select the variable of your choice according to which you want to evaluate the integral step by step.

Step 3: Choose Definite/Indefinite Integral

This integration solver provides two different type of integral solving tools. You can select either definite integral or indefinite integral that you want to calculate.

1. For definite integrals, Select the limit integral calculator, you need to input the upper bound limit and lower bound limit in this online integral solver.
2. If you select the indefinite calculator, just hit the "CALCULATE" button to get the step by step evaluation of integrand.

## Benefits of Using Complex Integration Calculator with Steps

In the era of high tech & machinery, manual calculations seem to be very hectic. Therefore, the best integral calculator has made the solution to solve the integrals with the help of this calculator.

The online integral tool makes finding the integrals of different functions easier. It provides faster and easier solutions. The results are appropriate & reliable.

The complex integral calculator show steps is no doubt an excellent way for students to do their homework on exact date and time. Moreover, some basic benefits of this integral solver with steps are listed as:

1. It safe your precious time-consuming in solving the integrals by hand.
2. It also assists you in every step while using this integral solver.
3. It is free of cost and gives the whole steps of the results step by step.
4. This calculator also eases your calculation time and gives you authentic results.
5. The integrals solver gives you results quickly within no time.

## Reason to Choose this Integral Function Calculator?

The main reason to choose this calculator is that it has the best and easiest features to use. It gives accurate results of integrals within a short interval. It gives you authentic solutions. It gives step-by-step instructions to solve integral problems. And the results can easily be understood.

## Tips for Using Online Integrator Tool

There are some simple tips while using this integral step by step calculator. These should help you to get accurate and efficient answer from our online integration tool.

Clearly Define Integral: Make sure you enter the integral correctly, including all necessary symbols and parameters.

Specify Limits if Needed: If you're solving a definite integral, ensure you specify the limits of integration.

Check the Solution Method: Some tools offer step-by-step solutions or hints. Use these features to understand how the integral is solved, not just to get the answer.

By using these online resources and tools, you can solve almost any integral, from basic to highly complex.

## How to Find Integral Step by Step Calculator?

Finding the right integration online tool for solving complex integrals, whether for academic purposes, research or personal interest is not as much complex. To choose the best online integral calculator step by step that suits your needs, consider the following steps:

Based on your question problems, choose the tool that will match with your requirements. Keep in mind that there isn't one solution that works perfectly in every circumstance, so keeping some in a list that could be useful.

• Identify the type of integrals you want to solve. Different tools perform different calculations according to the nature of integrand, from simple indefinite integrals to more complex definite and improper integrals. Knowing your needs can help narrow down your search.
• Use SERP with keywords like "integration online", "solve integral online" or "integral step by step calculator". Explore the first few search results to compile a list of potential tools available here.
• Once you've narrowed down, test the tool with a few integrals to see how well they meet your needs in terms of solution depth, explanation clarity, and overall user experience.

### What is the Integral of ex?

The integral of ex is ex + C. Where C represents the constants. And its symbolical representation is:

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

You can get the solution of this type of tricky problems with our calculator integral online.

### What is an Improper Integral?

The word improper in integration refers to infinity. The improper integral is the definite integral which may have or may not have infinite integral or poses integrand having undefined values such as infinity.

One can solve improper integral on this website by using our improper integral calculator with steps.

For Example

$$\int_0^∞ f(x) dx \;=\; \lim \limits_{t \to ∞} \int_a^t f(x) dx$$

$$\int_{-∞}^b f(x) dx \;=\; \lim \limits_{t \to -∞} \int_t^b f(x) dx$$

$$\int_{-∞}^∞ f(x) dx \;=\; \lim \limits_{t \to -∞} \int_t^a f(x) dx \;+\; \lim \limits_{t \to ∞} \int_a^t f(x) dx$$

One can also perform such calculations online using this integral online calculator.

### How do you Calculate the Integral of e(-x2)?

We don't calculate this integral as this is known as Reimann-Integrals. It does not have antiderivative so do not solve it down.

But can calculate integral online for Riemann integral, if we use this riemann sum limit calculator available on our calculator integral website.

### What is the Integral of lnx?

The Integral of lnx may evaluate as:

$$\int_1^e ln(x) dx \;=\; xln(x) - x \Biggr]_1^e$$

$$=\; (e ln(e) - e) - (1 ln(1) - 1)$$

$$(e-e) - (0-1)$$

$$(e-e) - (0-1)$$

$$=\; 1$$

### What is the Integral of tanx

The integral of tanx concerning x is:

$$\int \tan(x) dx \;=\; \ln | sec(x) | + C$$

Where c is representing the constant of integration. The derivation of finding the integral of tanx is,

$$\tan(x) \;=\; \frac{sin (x)}{cos (x)}$$

Therefore,

$$\int \tan(x) dx \;=\; \int \frac{sin(x)}{cos(x)} dx$$

Apply the substitution method and assuming the value of t

$$t \;=\; cos(x) \;so\; dt \;=\; - sin(x) \; dx$$

$$sin(x) dx \;=\; -dt$$

So the answer is given, such questions can also be integrate online.

### What is the Integral of 0

When integrating a constant value such as 0 which is given, the result is simply the constant times x, plus a constant of integration of C. The integrate calculator gives results in the form of,

$$\int 0\;dx \;=\; C$$

In simple words, the integral of zero is a constant function. It's independent on the value of x, the results will always be the same constant.

### What is the Integral of e^x^2

The integral of ex2 with respect to x is difficult as it does not have a solution in terms of elementary functions. It means you cannot express the integral using the basic algebraic functions but this can be solved in the integral calculus calculator.

However, the integral can be expressed as the power series or by using the special functions. The integral of the above functions can be represented as,

$$\int e^{x^2} dx \;=\; sum_{n=0}^{\infty} \frac{x^{2n+1}}{n!(2n+1)} + C$$

Here C is the constant of integration.

### What is the Integral of 1/x

The integral of 1/x with respect to x is a natural logarithm of the absolute value of x and a constant of integration C which can be represented by calculator integrals as,

$$\biggr[ \int \frac{1}{x} dx \;=\; ln |x| + C \biggr]$$

This type of integral is generally important because it represents the antiderivative of the function which is 1/x.

### What is the Integral of a Constant

The integral of a constant let's suppose k with respect to x is the constant multiplied by x with the constant of integration which is shown on the integrator online as,

$$\int k \;dx \;=\; kx \;C$$

It’s because the derivative of kx with respect to x is k means that the antiderivative of k with respect to x is kx. The constant of integration here is because the derivative of a constant is zero so any constant could be shown in the original function before differentiation.

### What is the Integral of 1/x^2

The integral of 1/x2 is the same as x-2. The integral or antiderivative of xn, where n ≠ -1 so the integration with steps is,

$$\frac{x^{n+1}}{n+1}$$

Applying this rule, the integral of 1/x2is,

$$x^{-2} dx \;=\; \frac{x^{-2+1}}{-2+1} + C \;=\; \frac{x^{-1}}{-1} + C \;=\; -\frac{1}{x} + C$$

So the integral is,

$$-\frac{1}{x} + C$$