Introduction to Indefinite Integral Calculator:
Indefinite integral calculator with steps is an amazing tool that is used to find the 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 integral calculator with steps helps to 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 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 finding the trigonometric functions, the indefinite integral calculator uses integral rules. Nevertheless, 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,solve the integral 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, some other methods can also be used that are the U substitution or integration by parts method, and the trigonometric substitution method to integrate the given indefinite integral function.
You can use our indefinite calculator which is the best and completely free tool in the digital world to find indefinite integrals quickly.
Solved Example of Indefinite Integral:
Let's see an example of indefinite integral with solution function which will help us to understand the working process of indefinite integrals calculator.
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 on the given indefinite integral function and then simplify it to get 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 only and follow some simple steps. These steps are:
- Enter the indefinite integral function in the input box of indefinite integral calculator.
- Choose the integration of a variable for the given indefinite integral function.
- 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 process of the indefinite integrals calculator then you can use the load example option.
- Use the “Recalculate” button for more calculations of indefinite integral functions.
Final Result of Indefinite Calculator:
Indefinite Integration calculator provides you with a solution as per your input when you click on the calculate button. It may include as:
Result Box:
Click on the result button so you can get the solution of your Indefinite Integral question.
Steps Box:
When you click on the steps option, you get the step by step solution of indefinite integral problems.
Advantages of Indefinite Integral Calculator With Steps:
Our indefinite integrals calculator only take the input value and provides a solution. It has many advantages when you use it to find the indefinite integral. These advantages are:
- It is a reliable tool as it always provides you with accurate solutions of 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.
- It is an easy-to-use tool, so a beginner can easily use it to get the solution of indefinite integral problems.
