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Indefinite Integral Calculator + Online Solver with Free Steps
The Indefinite Integral Calculator is an online calculator that is used to evaluate the indefinite integrals of various functions f(x) with respect to various variables. The Indefinite Integral Calculator provides quick and accurate solutions.
The Indefinite Integral Calculator is the most effective calculator available online because it instantly provides the results without taking much time for proceeding. It also provides a detailed solution so the user can instantly grasp the concept.
The Indefinite Integral Calculator is also super easy to use as it allows the user to conveniently navigate through the interface. It also caters to one of the most fundamental concepts of calculus.
What is the Indefinite Integral Calculator?
The Indefinite Integral Calculator is a free online calculator that is used to solve indefinite integrals with respect to a certain variable. This calculator can deal with all sorts of functions and provides quick results.
The Indefinite Integral Calculator is only used to evaluate indefinite integrals. Indefinite integrals are a crucial concept in calculus as these are the integrals that are not bounded by any specified limits.
The solution of these indefinite integrals always yields a function f(x) along with a constant c. The general formula which the Indefinite Integral Calculator makes use of is given below:
\[ \int f(x) dx = F(x) + c \]
Where $c$ is the constant obtained after evaluating the indefinite integral.
Manually, the indefinite integrals are solved through various methods such as substitution method, integration by parts method, etc, but the Indefinite Integral Calculator makes this job easy by presenting the solution in a matter of a few seconds.
The best feature of the Indefinite Integral Calculator is that it allows users to enter any kind of function, be it a complex polynomial or a trigonometric function.
How To Use the Indefinite Integral Calculator?
You can use the Indefinite Integral Calculator by directly entering the function to be integrated. It is fairly easy to use due to its simple interface which is also quite user-friendly. The interface of the Indefinite Integral Calculator consists of 2 simple input boxes which prompt the user to enter the input values.
The first input box of the Indefinite Integral Calculator is labeled with “Integrate” which prompts the user to enter the function that they wish to integrate. So in other words, the function f(x) goes into this first input box.
The second input box of the Indefinite Integral Calculator has the title “with respect to” which allows the user to enter the variable. This variable is the variable which the function is integrated with.
After the two input boxes, the last prominent label of the Indefinite Integral Calculator is the button that says Calculate. After the inputs have been added by the user, all the user has to do is click on this button to obtain the desired solution.
For a detailed understanding of the working of the Indefinite Integral Calculator, consider the step-by-step guide given below:
Step 1
Before moving on to using the Indefinite Integral Calculator for the evaluation of indefinite integrals, the first step is to analyze the given function and the variable. There is no restriction on the type of function or variable. You can choose any function f(x) for calculating the indefinite integral.
Step 2
After you have analyzed your function f(x), the next step is entering the inputs. Firstly, move on to the first input box with the title “Integrate” and enter your function f(x) into this input box.
Step 3
After filling the first input box, move on to the second input box. This input has the title “With Respect To” and enter your variable into this input box. This variable is the one according to which the function f(x) is integrated.
Step 4
Now that both the input boxes have been filled, the last step is to click on the button that says Calculate. By doing so, the Indefinite Integral Calculator will begin its processing and will present the solution in a few seconds.
Output of the Indefinite Integral Calculator
After the calculator has finished its processing, it presents the output. The output presented by the Indefinite Integral Calculator consists of the solution of the indefinite integral along with the input interpretation of the indefinite integral with the function f(x) and the variable.
How Does the Indefinite Integral Calculator Work?
The Indefinite Integral Calculator works by calculating the indefinite integrals for functions f(x). The working of this calculator is based on one of the most crucial concepts of calculus, which is solving the indefinite integrals.
To get a clear understanding of the working of the Indefinite Integral Calculator, let’s take a quick recap of the previous topics to strengthen our understanding of the working.
What Are Indefinite Integrals?
Indefinite integrals are the integrals that are evaluated without specifying the limits. In other words, these integrals are not enclosed by any upper or lower limits.
Since integration is the reverse process of differentiation, hence, the function being integrated is a derivative, and its integration will yield the original function f(x).
The solution of indefinite integrals besides producing the original function f(x), also produces a constant value which is termed c. This constant term c serves to be the main differentiating factor between definite and indefinite integrals.
This is because definite integrals will always produce a definite answer since these integrals are bounded by limits. Whereas, indefinite integrals are not enclosed within limits which is why they produce an uncertain answer which is presented as the constant of integration c.
Solved Examples
To further enhance your understanding regarding the working of the Indefinite Integral Calculator, a few examples are given below.
Example 1
For the following function, calculate the indefinite integral:
\[ x^{\frac{2}{3}} \]
Solution
Before moving on to determining the solution for this function f(x), let’s first analyze the function f(x). The function is given below:
\[ x^{\frac{2}{3}} \]
Upon analyzing, the function f(x) appears to be a simple polynomial function. Since the function is expressed in the variable x, hence we will integrate this function f(x) with respect to x.
The next step is to fill the input boxes. We already have our function f(x) so simply insert this function f(x) into the first input box. Next up, enter the variable in the second input box. The variable is also specified and it is x.
After entering the two input values, simply move on to the button that says “Calculate” and click on it. The Indefinite Integral Calculator will begin processing the solution.
After a few seconds, the following output along with the solution will be displayed:
\[ \int x^{\frac{2}{3}} dx = \frac {3x^{\frac{5}{3}}}{5} + constant \]
Hence, this is the solution to the indefinite integral of $x^{\frac{2}{3}}$, presented along with the integration constant c.
Example 2
Evaluate the indefinite integral for the following function:
\[ f(x) = x e^{x} \]
Solution
Before using the Indefinite Integral Calculator for solving this function f(x), the first step is to analyze the function f(x).
The function f(x) is given below:
\[ f(x) = x e^{x} \]
Since there is no restriction on the type of function to be used as input for the Indefinite Integral Calculator, hence this function f(x) perfectly qualifies.
This function f(x) will act as our first input and will go into the first input box with the title “Integrate.”
The next step is to fill the second input box, which needs to be filled with the variable. Upon analyzing the function, it is evident that the only plausible variable which can be used to integrate this function is x so insert x in the second input box with the label “With Respect To.”
Now that both the input boxes have been filled, we can proceed toward the last step which is simply obtaining the solution by clicking on the button that says “Calculate.”
Clicking on this button will trigger the Indefinite Integral Calculator and it will begin processing the solution. After a few seconds, the following solution in the form of the output will be presented by the Indefinite Integral Calculator:
\[ \int xe^{x} dx = e^{x} (x-1) + constant \]
Hence, this is the solution of the indefinite integral obtained for the function $xe^{x}$.
Example 3
Calculate the indefinite integral for the following trigonometric function:
f(x) = sin(2x)
Solution
First, let’s analyze our function f(x). It is evident that the function f(x) is a trigonometric function. The function is given below:
f(x) = sin(2x)
Next up, for the variable for integration. Upon analyzing the function f(x), since the function is expressed in terms of x, so let the variable of integration be x.
Now that we have both our function and variable, enter them in the first and second input respectively.
Once the input values have been inserted, click on the button that says “Calculate.” The calculator will present the following solution:
\[ \int sin(2x) dx = -\frac{1}{2} cos(2x) + constant \]