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Editor: mcd
Time: 2009/06/26 00:20:27 GMT-7
Note: solvin

added:

From mcd Fri Jun 26 00:20:27 -0700 2009
From: mcd
Date: Fri, 26 Jun 2009 00:20:27 -0700
Subject: solvin
Message-ID: <20090626002027-0700@axiom-wiki.newsynthesis.org>

int(sqrt(x), x);

Errors in symbolic integration

AXIOM Examples

1)

axiom
integrate(sin(x)+sqrt(1-x^3),x)
>> Error detected within library code: failed - cannot handle that integrand

int(sin(x)+sqrt(1-x^3),x);
reduce
LatexWiki Image 

2)

axiom
integrate(sqrt(1-log(sin(x)^2)),x)
>> Error detected within library code: integrate: implementation incomplete (constant residues)

int(sqrt(1-log(sin(x)^2)),x);
reduce
LatexWiki Image 

3)

axiom
integrate(sqrt(sin(1/x)),x)
>> Error detected within library code: integrate: implementation incomplete (constant residues)

That seems strange given the claims about the "completeness" of Axiom's integration algorithm! But to be fair, Maple also returns this integral unevaluated.

int(sqrt(sin(1/x)),x);
reduce
LatexWiki Image 

4)

axiom
integrate(sqrt(sin(x)),x)
LatexWiki Image(1)
Type: Union(Expression Integer,...)

int(sqrt(sin(x)),x);
reduce
LatexWiki Image 

For this Maple 9 gives the following result:

LatexWiki Image(2)

And Mathematica 4 gives:

LatexWiki Image(3)

symbolic integration
Tue, 22 Mar 2005 11:48:00 -0600 reply
axiom
integrate(exp(-x^2),x)
LatexWiki Image(4)
Type: Union(Expression Integer,...)
Errorfunction
Wed, 23 Mar 2005 08:23:21 -0600 reply
axiom
integrate(exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)
LatexWiki Image(5)
Type: Union(f1: OrderedCompletion? Expression Integer,...)

axiom
int(x,x)
There are no exposed library operations named int but there are 5 unexposed operations with that name. Use HyperDoc Browse or issue )display op int to learn more about the available operations.
Cannot find a definition or applicable library operation named int with argument type(s) Variable x Variable x
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

axiom
integrate(x,x)
LatexWiki Image(6)
Type: Polynomial Fraction Integer

axiom
axiomintegrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)
There are no library operations named axiomintegrate Use HyperDoc Browse or issue )what op axiomintegrate to learn if there is any operation containing " axiomintegrate " in its name.
Cannot find a definition or applicable library operation named axiomintegrate with argument type(s) Expression Integer SegmentBinding OrderedCompletion Integer
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

axiom
integrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)
LatexWiki Image(7)
Type: Union(fail: failed,...)

The answer should be:

LatexWiki Image(8)

integrate(exp(x)/x^2) --unknown, Thu, 25 Aug 2005 05:57:53 -0500 reply
Axiom does not perform the integration (while it perform the integration of exp(x)/x ), but the integration can be given in terms of Ei(x)

integrate(exp(x)/x^2,x) --> Ei(x)-exp(x)/x

int(sqrt(x), x)

int(sqrt(x), x);