login  home  contents  what's new  discussion  bug reports help  links  subscribe  changes  refresh  edit

# Edit detail for Symbolic Integration revision 4 of 12

 1 2 3 4 5 6 7 8 9 10 11 12 Editor: test1 Time: 2013/04/11 17:45:59 GMT+0 Note:

removed:
-
-From unknown Sat May 21 12:49:39 -0500 2005
-From: unknown
-Date: Sat, 21 May 2005 12:49:39 -0500
-Subject:
-Message-ID: <20050521124939-0500@page.axiom-developer.org>
-
-\begin{axiom}
-int(x,x)
-\end{axiom}

removed:
-
-From unknown Sat May 21 12:51:59 -0500 2005
-From: unknown
-Date: Sat, 21 May 2005 12:51:59 -0500
-Subject:
-Message-ID: <20050521125159-0500@page.axiom-developer.org>
-
-\begin{axiom}
-axiomintegrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)
-\end{axiom}

removed:
-From unknown Sat Oct 22 19:04:53 -0500 2005
-From: unknown
-Date: Sat, 22 Oct 2005 19:04:53 -0500
-Subject:
-Message-ID: <20051022190453-0500@page.axiom-developer.org>
-
-int(sqrt(x), x)

changed:
-int(sqrt(x), x);
\begin{axiom}
integrate(sqrt(x), x)
\end{axiom}

changed:
-integrate(a*x,x);
integrate(a*x,x)


## Errors in symbolic integration

AXIOM Examples

1)

axiom
integrate(sin(x)+sqrt(1-x^3),x)
 (1)
Type: Union(Expression(Integer),...)

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

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

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

4)

axiom
integrate(sqrt(sin(x)),x)
 (2)
Type: Union(Expression(Integer),...)

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

For this Maple 9 gives the following result:

 (3)

And Mathematica 4 gives:

 (4)

symbolic integration
Tue, 22 Mar 2005 11:48:00 -0600 reply
axiom
integrate(exp(-x^2),x)
 (5)
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)
 (6)
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

axiom
integrate(x,x)
 (7)
Type: Polynomial(Fraction(Integer))

axiom
integrate(x^6*exp(-x^2/2)/sqrt(%pi*2),x=%minusInfinity..%plusInfinity)
 (8)
Type: Union(fail: failed,...)

 (9)

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

axiom
integrate(sqrt(x), x)
 (10)
Type: Union(Expression(Integer),...)

axiom
integrate(a*x,x)
 (11)
Type: Polynomial(Fraction(Integer))