FREQUENTLY ASKED QUESTIONS
What input formats does the Integrator acceptdo I have to use Mathematica notation? The Integrator is programmed to accept a wide variety of input formats and syntaxes. However, if you are having problems, Mathematica syntax will work. See How to Enter Input for more details. Instead of an answer, I got a message that says, "Mathematica could not find a formula for your integral." What can I try if the Integrator doesn't do my integral? First, try checking your input. The most common reason for the Integrator being unable to do an integral is input that it cannot understand. If you think your integral can be computed in terms of common functions, check to be sure that the integrand has been entered correctly, or try reentering it in Mathematica notation. More information on input syntax is available at the How to Enter Input page on this site. If the integrand has been entered correctly and the Integrator is still unable to do the integral, check carefully that the integral actually has a solution. There are many seemingly simple integrals that cannot be solved in closed form. If you think you have a solution to an integral that the Integrator is unable to do, we would like to hear from you. Please send us your integral and solution, and perhaps we can improve the Integrator. Instead of an answer, I got a message that says, "Sorry, the Integrator was unable to complete this example in the time alotted. Please try another function." What does that mean? The Integrator is limited to a few seconds per integral to prevent a few tough integrals from monopolizing the server. You still might be able to solve your problem by simplifying part of it by hand, or by substituting numbers for named parameters. If you are still stuck, you can try using the full version of Mathematica, which has no such time restrictions. Instead of an answer, I got a message that says, "Sorry, the Integrator cannot understand what you entered. See the How to Enter Input page for suggestions." What does that mean? This means that the Integrator was unable to interpret what you entered. Your input may have included a syntax error, a function that the Integrator does not know about, or a format that it does not recognize. See How to Enter Input for details on input syntax. What are Gamma, PolyLog, Hypergeometric2F1, etc? I've never heard of these functions. Not all integrals can be solved in terms of elementary functions such as trigonometric functions and exponentials. Mathematicians have devised many socalled "special functions" to denote solutions to frequently occurring integrals and differential equations. Although many of these functions appear unusual to nonspecialists, they all have their uses and greatly increase the number of integrals that can be evaluated. See The Wolfram Functions Site for more information on special functions. What happened to the constant of integration? In calculus classes, it is usual to require a constant of integration to indicate that indefinite integration is welldefined only up to the addition of a constant. However, Mathematica does not add a constant of integration to the end of results. A constant can easily be added to the end of the Integrator's output if desiredsimply select a text format (InputForm or OutputForm) and edit the results in your application of choice. As values for the constant of integration can differ, the Integrator's results may not quite match what you anticipate. For example, if you expect the answer Log[2 x], and the Integrator gives the answer Log[x], both answers are in fact correct due to the identity Log[2 x] = Log[2] + Log[x]. If you get an answer you were not expecting, check to see whether the discrepancy can be resolved by applying an identity or subtracting a constant quantity. The Integrator gave an answer different from what I expected. Which is correct? Often both are correct. The Integrator gives results that do not make assumptions on variable values. The expected result may be using assumptions that give rise to simplifications. Or the results might be equivalent (say, using trignonmetric identities), up to a constant. Why does the Integrator use Log instead of Ln for the natural logarithm? Log is the notation used in Mathematica, and elsewhere in mathematics. Usage that denotes a logarithm to base 10 is common in engineering (and base 2 is common in computer science), but the Integrator maintains a usage uniform with that of Mathematica.
Technical Questions How do I put my results in other documents? By default, the Integrator returns its results as a GIF. However, if you click InputForm over your output, it will return a text string that can be pasted into a Mathematica notebook or any other document. If you choose OutputForm, you will get a twodimensional ASCII version of the results. May I link to your site? Yes you may. The preferred URL for the Wolfram Mathematica Online Integrator is http://integrals.wolfram.com/ About the Integrator What's running the Integrator? The Integrator uses the power of Mathematica, the world's leading mathematical software package, to derive its results. You have at your fingertips the results of decades of development that went into one of the most powerful functions in Mathematica's considerable arsenal. The web interface is made possible by webMathematica, the easy way to put interactive mathematical content in your web pages. See Inside the Integrator for more information. How does this compare to a table of integrals? Proper use of a table of integrals requires knowledge of common forms and how to translate between the integral you are trying to solve and the integrals in the tables. This is timeconsuming, and tables are limited by reasonable space considerations. the Integrator is not constrained in these ways. It can solve thousands of integrals that do not appear in any tables. Can I get my own copy of the Integrator? the Integrator is a free online service provided by Wolfram Research. It is a demonstration of the power of Mathematica, which is the engine solving all of the Integrator's integrals. Mathematica may be cheaper than you think, and academic pricing and steeply discounted student versions are available. Also, a great many organizations provide Mathematica across some or all of their sites. Mathematica calculations are embedded into this website through webMathematica, which is also available for sale. If you are operating under a Wolfram Research site license (your school has Mathematica in its computer labs, say), contact your system administrator to see if your organization already has webMathematica. What Mathematica command is the Integrator running? The heart of the Integrator is Mathematica's builtin function Integrate. The typesetting of the output is also taken care of by Mathematica. See Inside the Integrator for more information. If the Integrator can't do it, can Mathematica? Can anything? Use of the Integrator is constrained to a few seconds per integral in order to prevent a few difficult integrals from monopolizing the server. If the Integrator returns a timeout message, it may well be possible to do the integral using Mathematica. If the full version of Mathematica cannot do the integral, it may not be known how to solve it. After decades of research and development, there are very few solvable integrals that Mathematica cannot do. If you think you have a solution to an integral that the Integrator is unable to do, we would like to hear from you. Please send us your integral and solution, and perhaps we can improve the Integrator. If the result comes out in terms of special functions, does it need to? Probably. Because the Integrator harnesses the full power of Mathematica, it has extensive abilities to automatically simplify expressions and find forms for them in terms of elementary functions. Thus, if the Integrator has not simplified a result, chances are it cannot be simplified. How much is the Integrator used? The Integrator has been available as a service to the internet community since 1996. Thousands of people visit the site every day. Usage of the Integrator tends to increase greatly during "calculus season," the time during the academic year when many universities cover calculus in their courses. Who uses the Integrator? People from all walks of life and with all levels of mathematical ability have found the Integrator useful. We get comments from calculus students, engineers, physicists, and professional mathematicians, among many others.
More
Information Can I see the steps used to compute the result? No. Computers evaluate integrals in a way that is qualitatively different from the way most humans do it with pencil and paper. With the algorithms used by computers, even simple integrals typically involve millions or billions of operations in less than a second, so it is not practical to show all of those steps. Additionally, the steps used by the computer almost always involve operations that are uninteresting or not viable for hand calculations. Many integrals are done using algebra that would be prohibitively cumbersome for hand calculations, or by invoking transformations that would be meaningful only to an expert in algorithmic integration. However, for relatively simple integrals, like those found in highschool and college calculus classes, WolframAlpha is often able to display the steps. What about definite integrals? The Integrator is not set up to handle definite integrals. Many definite integrals can be solved by first finding the indefinite integral and then substituting in the endpoints. If you have one of these, the Integrator can still be helpful. In either case, both WolframAlpha and Mathematica can solve a very wide range of definite integrals. Where can I do differentiation, power series, and other operations? Almost any mathematical operation that can be done on a computer can be done using WolframAlpha or with Mathematica, which is the program used to compute results for both the Integrator and WolframAlpha. The current version of the Integrator is intended only for making the indefinite integration capabilities of Mathematica available on the internet, but these and a vast number of other operations can still be done using Mathematica itself or WolframAlpha. I have a question about my homework. Can you help me? We are not equipped to handle individual questions about homework. There are many sites available on the web that offer these types of services. Of course, we would like to hear about any problems you encounter while using the Integrator. Please leave us a message so we can serve you better. Here are a few sites that may be helpful to you for homework: Where can I learn more about integration? One of the Integrator's sister sites, MathWorld, offers a wealth of information
about a wide range of mathematical topics. Here are some suggestions
to get started learning about integrals on MathWorld. Where can I learn more about special functions? Another of the Integrator's sister sites, The Wolfram Functions Site, has quickly established itself as the leading source of information about special functions on the web. The Mathematica Documentation Center also contains extensive information on these functions.
