# Displaying the solution step by step in Wolfram Mathematica

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### yar...@gmail.com

Nov 21, 2008, 5:33:18 AM11/21/08
to
Hi

I have such a question: Is it possible to display in Mathematica the
solution for example of integral equation step by step? Not only the
this in Documentation Center unless I missed it.

cheers

### Dave Oracle News

Nov 22, 2008, 6:09:16 AM11/22/08
to
perhaps..but bear in mind the
algorithms employed by the system to do many processes including
integration and factorization for ex. utilise entirely different methods
than what you would have learnt through your regular calculus course.

### David Bailey

Nov 22, 2008, 6:11:13 AM11/22/08
to
Unfortunately, I think Mathematica uses extremely general methods to
solve integrals, integral equations, etc. and a trace of what it had
done would be incomprehensible, and not resemble a human calculation in
any way.

David Bailey
http://www.dbaileyconsultancy.co.uk

### Nikolaus Rath

Nov 22, 2008, 6:11:45 AM11/22/08
to

It is probably possible ("evaluation tracing" is the keyword to look
for) but most likely this is not what you want:

Mathematica usually solves problems in a way that differs very much
from the way that a human would solve them. With integrals, for
example, Mathematica may start by differentiating a very long and
complex expression and just try to match coefficients. Hence looking
at the individual steps is not going to tell you much unless you want
to debug/optimize Mathematica internals.

Best,

-Nikolaus

--
=C2=BBIt is not worth an intelligent man's time to be in the majority.
By definition, there are already enough people to do that.=C2=AB
-J.H. Hardy

PGP fingerprint: 5B93 61F8 4EA2 E279 ABF6 02CF A9AD B7F8 AE4E 425C

### dimitris

Nov 22, 2008, 6:11:55 AM11/22/08
to

Unless you are a computer algebra guru I think you will not
be able to follow the way that Mathematica follows in order
to solve one problem, say an integration.
CAS algorithms are completely different than "by hand" evaluations.

Execute for example the following command to take a glance...

Trace[Integrate[x, {x, 0, 2*Pi}], TraceInternal -> True]

### app...@att.net

Nov 22, 2008, 6:12:49 AM11/22/08
to
Here is the information from Wolfram's website:

"Q: I'm searching for a program that will show step by step how my
equations are solved. Does Mathematica for Students have this capability?
Unfortunately, Mathematica will not provide step-by-step explanations
for your solutions. However, a program could be written in
Mathematica's high-level programming language to provide this feature.
Calculus WIZ, an interactive homework helper based on the most widely
used calculus textbooks, will show you the steps for each calculus
problem. Calculus WIZ is a stand-alone product that can be purchased
at your local campus bookstore or directly from Wolfram Research. "

You can find it at the following link:

http://www.wolfram.com/products/student/mathforstudents/qa.html#previous

### Sergio Miguel Terrazas Porras

Nov 24, 2008, 4:06:27 AM11/24/08
to
Hi!
I remember there was an example or demo in version 3 or 4 where
Diferentiation was shown step by step. It was obviously written by
someone at Wolfram.
Something similar could be written for integration, writting your own
rules.

Greetings

Sergio Terrazas

-----Mensaje original-----
De: David Bailey [mailto:da...@removedbailey.co.uk]
Para: math...@smc.vnet.net
Asunto: Re: Displaying the solution step by step in Wolfram
Mathematica

### David Park

Nov 24, 2008, 4:06:38 AM11/24/08
to
I didn't immediately answer this because if it is about actually solving
general integral equations it is beyond what I have experience with. But
some of the responses referred to the straight evaluation of integrals and
that I can say something about.

The Presentations package has a subsection called Student's Integral that
allows the step by step evaluation of definite or indefinite integrals. This
contains commands for operating on an integral expression. It doesn't just
show the steps that Mathematica might (or might not) use but allows the
student (or researcher) to specify the steps to be used. The sub-package
comes with a BasicIntegralTable, such as students might use, or allows users
to construct their own integral table. Alternatively at any point an
integral can be turned over to the regular Mathematica Integrate or
NIntegrate command.

The user writes an integrate command (with a small i) that keeps it in an
unevaluated form, and then operates on it by various commands. The user can
operate on the integrand, say by using Apart or CompletTheSquare. Integral
sums can be broken our and constants taken outside of the integral. The user
can use change of variable, integration by parts or trigonometric
substitution. Integration by parts throws off a panel of information showing
the internal substitutions. Trigonometric substitution throws off a triangle
diagram showing the expressions on each side. Definite integrals return a
LimitsBracket expression such as is usually seen in textbooks that can then
be evaluated.

Peter Lindsay at the Mathematical Institute in the University of St Andrews
[ www.mcs.st-and.ac.uk ] has kindly undertaken to maintain an archive that
solutions that have appeared on MathGroup.

A Step by Step Integration example for the volume of a surface of revolution
using integration by parts will be shown there.

Mathematica does many things automatically and most users prefer it that
way. For teaching purposes this is often a problem. Nevertheless, it is
possible to work around it and create definitions and possibly formatting
that allows students to work conveniently at a more basic level. The
developers of Mathematica can't get every convenient thing, for every field,
in there. But that doesn't mean that Mathematica doesn't have the capability
to tackle these kinds of applications. It is just that users and third party
developers have to develop some of these applications.

Mathematica is not so much a tool for doing mathematics as a meta-tool for
making the tools to conveniently do mathematics on specific applications.

### anz...@gmail.com

Dec 9, 2012, 10:58:06 AM12/9/12
to
Hi. By way of response to other posters, both Wolfram alpha (the web app) and Wolfram student assistant (ipad app) will show integration steps. It is frustrating this is not in Mathematica, per se. Although Mathematica may occassionally employ integration solutions that are obscure, many of the problems I have done in student assistant have yeilded useful solutions.

### Šerých Jakub

Dec 9, 2012, 11:29:57 PM12/9/12
to
It is possible (in version 8 and above) using Alpha. Just enter for example:

==integrate sin(k \[Omega] t) dt

and than click on the Step by step solution. It has the advantage over Alpha, that you can uncover steps one by one, which is good for learning purposes.

And you can also easily copy and paste the steps into the Mathematica notebook. What more do you need?

Jakub Serych

> -----Original Message-----
> From: anz...@gmail.com [mailto:anz...@gmail.com]
> Sent: Sunday, December 09, 2012 5:00 PM
> To: math...@smc.vnet.net
> Subject: Re: Displaying the solution step by step in Wolfram
> Mathematica
>

### mayi...@gmail.com

Dec 9, 2012, 11:30:13 PM12/9/12
to
Well, Wolfram Mathematica does not always take the best decisions solving integrals.But, when you are writing you can select how you enter the input. There, you can choose Wolfram | Alpha query, a little wolfram logo will appear, next to it you can write the integral, then you evaluate the cell, the answer will appear (same appereance that the online integrals wolfram solver,that shows the solution,the plot of the integrals, alternate forms etc. .), then on the right part of the top you must click: "Step-by-step-solution">show all steps. That's all!, hope it helps. For doing it you'll need internet connection.

### Bob Hanlon

Dec 9, 2012, 11:30:40 PM12/9/12
to
Within Mathematica you can call WolframAlpha

WolframAlpha["e^2 x cos(3x)", IncludePods -> {"Indefinite Integral"},
PodStates -> {"Step-by-step solution", "Show all steps"}]

Compare with

Integrate[E^2 x Cos[3 x], x] // Simplify

Bob Hanlon

### Šerých Jakub

Dec 9, 2012, 11:32:11 PM12/9/12
to
It is possible (in version 8 and above) using Alpha. Just enter for example:

==integrate sin(k \[Omega] t) dt

and than click on the Step by step solution. It has the advantage over Alpha, that you can uncover steps one by one, which is good for learning purposes.

And you can also easily copy and paste the steps into the Mathematica notebook. What more do you need?

Jakub Serych

> -----Original Message-----
> From: anz...@gmail.com [mailto:anz...@gmail.com]
> Sent: Sunday, December 09, 2012 5:00 PM
> To: math...@smc.vnet.net
> Subject: Re: Displaying the solution step by step in Wolfram
> Mathematica
>

### Murray Eisenberg

Dec 9, 2012, 11:32:22 PM12/9/12
to
Mathematica itself is using state-of-the-art integration methods, which
are often not the methods taught in calculus. Often, seeing the steps
that Mathematica takes would be uninformative.

On Dec 9, 2012, at 10:59 AM, anz...@gmail.com wrote:

> Hi. By way of response to other posters, both Wolfram alpha (the web
app) and Wolfram student assistant (ipad app) will show integration
steps. It is frustrating this is not in Mathematica, per se. Although
Mathematica may occassionally employ integration solutions that are
obscure, many of the problems I have done in student assistant have
yeilded useful solutions.

---
Murray Eisenberg
mur...@math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2838 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305

### mayi...@gmail.com

Dec 9, 2012, 11:32:27 PM12/9/12
to

### Bob Hanlon

Dec 9, 2012, 11:32:53 PM12/9/12
to
Within Mathematica you can call WolframAlpha

WolframAlpha["e^2 x cos(3x)", IncludePods -> {"Indefinite Integral"},
PodStates -> {"Step-by-step solution", "Show all steps"}]

Compare with

Integrate[E^2 x Cos[3 x], x] // Simplify

Bob Hanlon

### Murray Eisenberg

Dec 9, 2012, 11:30:08 PM12/9/12
to
Mathematica itself is using state-of-the-art integration methods, which
are often not the methods taught in calculus. Often, seeing the steps
that Mathematica takes would be uninformative.

On Dec 9, 2012, at 10:59 AM, anz...@gmail.com wrote:

> Hi. By way of response to other posters, both Wolfram alpha (the web
app) and Wolfram student assistant (ipad app) will show integration
steps. It is frustrating this is not in Mathematica, per se. Although
Mathematica may occassionally employ integration solutions that are
obscure, many of the problems I have done in student assistant have
yeilded useful solutions.

### leand...@hotmail.com

Dec 15, 2013, 5:26:47 AM12/15/13
to
OH MAN THX SOOOO MUCH