Introduction to Indefinite Integral Calculator:
Indefinite integral calculator is an amazing tool that is used to find the solution of given indefinite integral problems. Our tool determines the indefinite integral of different types of functions like logarithmic, exponential, trigonometric, or algebraic.
It is a beneficial tool for students, teachers, and professionals who want a reliable tool for the evaluation of indefinite integral problems that gives them accurate solutions quickly without any man-made mistakes.
What is an Indefinite Integral?
Indefinite integral is a basic process of integration in calculus in which the indefinite integral represents a family of functions F(x) whose derivative gives back the original function f(x), up to a constant C.
$$ \int f(x)\; dx \;=\; F(x) + C $$
where F(x) is an antiderivative of integral function f(x), and C is the integration constant. The above rule shows that F(x) is a set of functions that are separated by a constant in a definite integral.
How to Calculate Indefinite Integrals?
Indefinite integrals is a method that calculates the antiderivative of a function f(x) because it uses the direct rule of integration during the calculation.
Unlike definite integral where you apply the limit values after integration, you just integrate the given function only. Here are the step-by-step procedures on how to compute indefinite integrals:
Step 1: Determine the indefinite integral function f(x) that you want to integrate.
Step 2: Apply the integration rules that give an appropriate solution for the given function f(x). These common rules include:
- Power Rule:
When you have a function in exponential power you can apply the power rule where 1 is added to the exponential power and the new value is divided by that number.
$$ \int x^n\; dx \;=\; x^n + \frac{1}{n + 1}\; for\; n ≠ −1 $$
- Constant Multiple Rule:
When the given function is multiple of a constant then you can integrate the given function f(x) only, keeping the constant outside the integral.
$$ \int a . f(x)\; dx \;=\; a . \int f(x)\; dx $$
- Sum/Difference Rule:
For the sum and difference of two functions f(x) and g(x) rules, separate both the functions and then integrate them with respect to the variable of integration.
$$ \int (f(x) \pm g(x)) dx \;=\; \int f(x)\; dx \pm \int g(x)\; dx $$
- Exponential and Logarithmic Rules:
For the exponential function, integration is the same function as given in the original function as shown in the below rule. For logarithmic function, indefinite integration is the derivative of the given function.
$$ \int e^x\; dx \;=\; e^x + C,\; \; \; \int \frac{1}{x} dx \;=\; ln |x| + C $$
- Trigonometric Rules:
For trigonometric functions, integral rules are given below, the inverse trigonometric rules are also present in the rules of integration.
$$ \int sin(x)\; dx \;=\; - cos(x) + C $$
$$ \int cos(x)\; dx \;=\; sin(x) + C $$
$$ \int tan(x)\; dx \;=\; sec^2(x) + C $$
Step 3: After applying the appropriate rule the solution of antiderivative F(x): ∫f(x)dx=F(x)+C, where F(x) is the antiderivative of f(x), and C is the constant of integration.
Step 4: For more complex integrals, another method can also be used as the U substitution or integration by parts, the trigonometric substitution method to integrate the given indefinite integral function.
You can use our indefinite calculator which is the best tool in the digital world and completely free to quickly and accurately find indefinite integrals in just a few seconds.
Solved Example of Indefinite Integral:
Let's see an example of indefinite integral with solution function where the calculation process of an indefinite integrals calculator is explained.
Example: Evaluate the indefinite integral
$$ \int (5x^3 - 7x^2 + 3x + 4) dx $$
Solution:
Separate the integral for each value,
$$ \int (5x^3 - 7x^2 + 3x + 4) dx \;=\; \int 5x^3 dx - \int 7x^2 dx + \int 3x\; dx + \int 4\; dx $$
Separate the constant by using constant multiple rule,
$$ \int 5x^3 dx - \int 7x^2 dx + \int 3x\; dx + \int 4dx \;=\; 5 \int x^3 dx - 7 \int x^2 dx + 3 \int x\; dx + 4 \int 1\; dx $$
Apply the direct rule for integration of a given indefinite integral function and then simplify it in solution.
$$ \int (5x^3 - 7x^2 + 3x + 4) dx \;=\; \frac{5}{4}x^4 - \frac{7}{3}x^3 + \frac{3}{2}x^2 + 4x + C $$
How to Use the Indefinite Integration Calculator?
The indefinite calculator has a simple design that helps you to solve the given indefinite integral question instantly. You just need to put your indefinite integral problem in this indefinite integral calculator with steps only and follow some simple steps. These steps are:
- Enter the indefinite integral function in the input box.
- Choose the integration of a variable for the given indefinite integral function in the input fields.
- Check your given indefinite integral function to get the exact solution of the indefinite integral question.
- Click on the Calculate button to get the result of the given indefinite integral function problems.
- If you want to check the working procedure of the indefinite integrals calculator then you can use the given example to get a solution.
- The “Recalculate” button for the calculation of more examples of indefinite integral functions with the solution.
Final Result of Indefinite Calculator:
Indefinite Integration calculator 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 so you get the solution of your Indefinite Integral question.
Steps Box:
When you click on the steps option, you get the result of Indefinite Integral problems in a step-by-step process.
Advantages of Indefinite Integral Calculator With Steps:
Indefinite integrals calculator has many advantages when you use it to find the indefinite integral. Our tool only gets the input value and it provides a solution without doing any external effort. These advantages are:
- It is a reliable tool as it always provides you with accurate solutions to given indefinite integral problems.
- Indefinite integration calculator is an efficient tool that provides solutions to the given indefinite integral problems in a few seconds.
- It is a learning tool that provides you with complete knowledge about the concept of indefinite integral function very easily through an online platform.
- It is a handy tool that evaluate the indefinite integral problems quickly without manual calculation.
- Indefinite calculator is a free tool that allows you to use it for the calculation of indefinite integral functions without paying.
- Indefinite integral calculator with steps is an easy-to-use tool, anyone or even a beginner can easily use it for the solution of indefinite integral problems.
