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Antiderivative Calculator

Use Our Free Online Antiderivative Calculator For Fast & Accurate Results

Antiderivative Calculator

Enter Function

inf = ∞ , pi = π and -inf = -∞

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This will be Calculated

`cos(x)+x/2`

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Antiderivative Calculator

Calculus is often considered the most difficult section of mathematics. That explains why a majority of the students require online math help from experts when they are asked to solve a calculus problem. While dealing with integration, differentiation, logarithm, etc., can be confusing at times, you can now use our antiderivative calculator to instantly determine the antiderivative of a function.

MyAssignmenthelp.com is one of the leading academic help providers in the business. You can hire a qualified expert for math assignment help from this website. Moreover, you can now find a number of free online tools, including a math problem solver, an algebra calculator, and an antiderivative calculator. Let’s see how the antiderivative calculator works.

What Is Meant By The Antiderivative?

In math, integration is the process of finding the antiderivative of a function. It is the inverse process of differentiation. A function can have multiple antiderivatives, taking the form of the function with a constant number 'C.' Both these concepts of functional differentiation and function integration are connected with the fundamental theorem of Calculus. In simple words, the antiderivatives are used for finding the area under the curves for the variable x is denoted by ∫ f (x) dx.

When we talk about antiderivative, most confuse it with integral and use it as synonyms which are not entirely correct as there is a slight difference between both. Generally, 'integral' is a function associated with the original function usually defined by a limiting process, divided into two parts: the indefinite integral and the definite integral. Indefinite integral means integrating a function without any limit, whereas in definite integral, there are upper and lower limits, alternatively known as the interval of integration.

In contrast, an antiderivative means finding the functions whose derivative will be the original function. Even though there’s not much difference between antiderivative and definite integral, there's a clear difference between antiderivative and indefinite integral. Here’s an example:

  • f(x) = x²
  • The indefinite integral is ∫ x² dx = F(x) = ⅓ x³ + C, almost the antiderivative except ‘C’ which is a constant number. On the other hand, the definite integral, however, is ∫ x² dx from a to b = F(b) – F(a) = ⅓ (b³ – a³) by applying the second part of the Fundamental Theorem of Calculus. Since ‘C’ is an undetermined number, the indefinite integral is ⅓ x³ + C, a "family" of functions.

    Understanding the fundamentals of finding antiderivatives can be complex if you are new to the concept or have little knowledge. No wonder many rely on tools like an antiderivative calculator with steps to get accurate solutions quickly.

    If you are looking for an antiderivative calculator that generates accurate results, you can try our partial and general antiderivative calculator online. Our tool is developed with the latest programming language and follows the standard norms of finding an antiderivative.

How To Use This General Antiderivative Calculator?

Finding the antiderivative of a function is now simpler than ever. If you have a very limited idea about antiderivatives and derivatives of functions, you can finding antiderivatives calculator with the steps mentioned below. This tool is developed in such a way that even a layman with minimal knowledge of calculus can still use it and generate the antiderivative of a function. You can also use our reflection calculator online.

Here’s how the general antiderivative calculator works:

  • Step 1: Enter the function:
  • In order to find the antiderivative of a function on our calculator tool, you need to enter the function in the input field. Do check the accuracy of the input as a slight error in the function can lead to a significant difference in the results.

  • Step 2:Hit the “Solve” button:
  • Once you are done entering the function on the dedicated input field in the antiderivative calculator, you only need to click on the “Solve” button. The tool does the rest. Yes, it is that simple.

  • Step 3: Find the antiderivative:
  • Our tool transforms the mathematical function into a computable form. The algorithm then analyses that version of the function and generates the result (the antiderivative of the function). While the tool only gives you the antiderivative of the function, you can also seek a step-by-step solution from the experts at our website.

    As you can see, using our general antiderivative calculator is absolutely easy. And you won't even need a thorough understanding of integration in order to use the tool. However, having knowledge of the integration process always comes in handy. You can also use page calculator tool.

How To Calculate The Antiderivative of An Expression?

An antiderivative is the opposite of a derivative, used to find the total and growth in things between a specific timeframe. Some of the antiderivative formulas are as follows:

  • ∫xn dx = (1/(n + 1))xn + 1) + C
  • ∫ex dx = ex + C
  • ∫1/x dx = log |x| + C

One must consider the following rules to find an antiderivative without a calculator:

  1. ∫xndx = xn+1 + c as long as n does not equal -1. This is a vital rule for derivatives in reverse.
  2. ∫cf (x)dx = c∫f (x)dx, which states that a scalar can be pulled out of the integral.
  3. ∫(f (x) + g(x))dx =∫f (x)dx +∫g(x)dx. The antiderivative of a sum is the total of the antiderivatives.
  4. ∫sin(x)dx = - cos(x) + c
  5. ∫cos(x)dx = sin(x) + c
  6. ∫sec2(x)dx = tan(x) + c

Finding antiderivatives without an antiderivative calculator online depends on the function complexity. However, here are the step-by-step guidelines to find antiderivatives without calculators:

  • Check the integral type. If the integrals are manageable, you can solve them using direct integration rules.
  • You can use the substitution method to calculate some integrals.
  • To solve functions expressed as a product, you can use integration by parts.
  • As for definite integrals, check the antiderivative first and then use the ∫ab f(x)dx = F(b) - F(a) formula for the final answer.

An antiderivative solver or a particular, partial, or general antiderivative calculator online is an excellent option for students with limited knowledge of the formulas and the guidelines for finding an antiderivative. In addition, you can use MyAssignmenthelp.com’s antiderivative calculator online for 100% accurate results with steps.

Besides our antiderivative calculator, you can avail of the customised tutoring sessions by our math tutors. We have over 5000 PhD-qualified subject matter experts from top-tier universities around the globe to help students with their math lessons. Share your requirements right away for instant support.

Why Should You Use Our Antiderivative Calculator?

If you look for an antiderivative calculator on the internet, you will find several options, including Symbolab antiderivative calculator, Wolfram Alpha antiderivative calculator with conditions, and more. Then why should you use the calculator for antiderivative generation from MyAssignmenthelp.com?

Well, here are some factors that give our tool an edge over the most general antiderivative calculators in the market?

  • Accurate Answers:

    You should always expect accurate results from our tool. Whether you are looking for partial fraction decomposition for rational functions or integration by parts for products of certain functions – the tool offers the correct antiderivative of the submitted function on every occasion.

  • Instant Results:

    Unlike some of the other antiderivative calculators available online, our tool takes minimal time to generate the results. You only need to submit the function whose antiderivative you want to determine and click on the “Solve” button. The tool does not even require registration.

  • Clean User Interface:

    You will find the partial antiderivative calculator at our website easy to use, thanks to the clean and user-friendly interface. You won’t have to look around to find the input field on the tool. As soon as you land on our page, you can easily spot the necessary fields on the tool.

  • 24x7 Customer Support:

    If you have any query regarding our tool or having difficulty finding the right results for your calculus problem, you can get in touch with the customer support team at the website. The executives remain active throughout the day to respond to your queries and requests almost instantly.

While there are some antiderivative calculators which have a few of these aforementioned features, only our tool offers all these features under one umbrella. So, it is quite obvious why a lot of students prefer to tool over the antiderivative calculator by Symbolab, Wolfram, or others. If you want to use our algebra calculator then visit us.

What Are The Examples Of An Antiderivative?

If F(x)F(x) is a function with F′(x)=f(x)F′(x)=f(x), then F(x)F(x) is an antiderivative of f(x)f(x).

Here’s an example:

Question:

To solve ∫2x cos (x2) dx, assume x2 = u ⇒ 2x dx = du.

Substitute this into the integral to get

∫2x cos (x2) dx = ∫cos u du

= sin u + C

= sin (x2) + C

Find the antiderivatives of these functions:

  1.  ∫4x3xdx
  2. ∫13x2xdx
  3. ∫(4x2–2x+5)xdx
  4. ∫(sin⁡x–cos⁡x)xdx

Solution:

Each of these functions requires two or more integration rules. So let’s start!

  • First function – ∫4x3xdx:

    Factor out 4 from the integral expression using the integral property, ∫kf(x)xdx=k∫f(x)xdx and integrate the expression, ∫x3xdx, using the power rule: ∫xnxdx=xn+1n+1+C.

    4x3xdx=4∫x3xdx=4⋅x3+13+1+C=4⋅x44+C=x4+C

  • For the third function, apply the sum and difference properties first and integrate each term using the constant multiple and power rules.
  • Factor out 4 and 2 out of the integrands and apply the antiderivative formula, ∫xnxdx=xn+1n+1+C.

Integrate the third expression using the integration rule, ∫kxdx=kx+C.

∫(4x2−2x+5)xdx=∫4x2xdx–∫2xxdx+∫5xdx=4∫x2xdx–2∫xxdx+∫5xdx=4⋅x2+12+1–2⋅x1+11+1+∫5xdx=43x3–x2+5x+C

Before heading to the fourth function, remember that ∫sin⁡xxdx=–cos⁡x and ∫cos⁡xxdx=sin⁡x. So, use these two formulas to find the antiderivative of the function.

∫(cos⁡x–sin⁡x)xdx=∫cos⁡xxdx–∫sin⁡xxdx=(−sin⁡x)–(cos⁡x)+C=−sin⁡x–cos⁡x+C

Thus, leaving you with the final antiderivatives:

  • ∫4x3xdx=x4+C
  • ∫13x2xdx=−13x+C
  • ∫(4x2–2x+5)xdx=43x3–x2+5x+C
  • ∫(sin x–cos x) dx= - sin x – cos x + C

For more examples of finding antiderivatives without a calculator, visit our site today. Our sample repository is well-stocked with hundreds of antiderivative examples. If not, our partial and general antiderivative calculator is always available online for your easy use.

Enjoy Additional Features With Our Antiderivative Calculator

Apart from the aforementioned features of our antiderivative calculator, you can actually enjoy plenty of other additional benefits while using this tool. Every time you use this tool to determine the antiderivative of a function, you get the following benefits –

  • Ease of access through any browser on your laptop, PC, and tablet
  • No hidden cost involved; available for free
  • Free access to hundreds of sample solutions for reference
  • Expert guidance from qualified individuals on request
  • Ad-free experience

So, why are you still waiting? Choose our antiderivative calculator today and get accurate results in seconds.

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Frequently Asked Questions By Students

The antiderivative calculator lets you determine the antiderivative of a given function with a simple click. All you have to do is enter the function as mentioned in the space provided in the tool. You can also provide the variable of integration and integration bounds in the tool. Once done, click on the ‘Calculate’ button for instant solutions.

An antiderivative is the opposite of a function. Here are some common formulas for basic antiderivatives:

Power rule

F (x)=xn+1/n+1+CF

Difference rule

F(x)=G(x)−H(x)+C

Sum rule

F(x)=G(x)+H(x)+C

Product rule

F(x)=k⋅F(x)+C

As you can see, in the case of antiderivatives, you can take the derivative of the function to get the original function.

Here’s how to solve antiderivatives using a TI-84:
  • Press Y.
  • Move the cursor o the Y= area.
  • Note that this area will be Y1 if there are no other equations present.
  • Press the Math button.
  • Press 9 and choose fnInt, the command to find integral.
  • Enter the appropriate values and get your answer.

The antiderivative of 1 is:

x + C.

You can also say that the integral of 1 is x + C and write it as ∫1 dx = x + C.

The definite integral is what we apply to the second part of the Fundamental Theorem of Calculus. An antiderivative, on the other hand, is a function, and it is applicable to the first part of the Fundamental Theorem of Calculus. It is important to know how to find antiderivatives to calculate integrals.

Integration of 2x:

∫2x dx = x2 + C

Where C is the constant.

Using the Power Rule of Integration and Antiderivative Rule for Scalar Multiple of Function, we get:

∫2x dx = 2 ∫x dx

= 2 ∫x1 dx

= 2 [x1+1/(1 + 1)] + C

= 2 x2/2 + C

= x2 + C 

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