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#307 repeatedly asks me to set preference before editing ←	↑	→ #309 partial fraction with unknown constants

#308 Runtime error on integration

Edit detail for #308 Runtime error on integration revision 1 of 9

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Editor: Time: 2007/11/17 22:24:25 GMT-8
Note: Maple result

changed:
-
Following commands (being tested in SandBox) produce output looking as runtime error::

  !\begin{axiom}
  integrate(x^a*(x^b+1)^p, x)
  differentiate(%, x)
  \end{axiom}

if you replace p with, say, 2, it works. AFAIK, this binomial differential can be integrated in closed form only if a, b, and p satisfy certain constraints (aka "Chebyshev theorem"), so the failure itself is not surprising, but IMHO the produced output probably signals about some internal Axiom error or server misconfiguration. Version of the software reported: "Axiom (April 2006), Wednesday June 21, 2006 at 03:45:56".

The error returned by Axiom on linux is::

  Segmentation fault

and Axiom crashes. A similar abort occurs on the Windows
version of Axiom.

From BillPage Thu Aug 3 08:59:30 -0500 2006
From: Bill Page
Date: Thu, 03 Aug 2006 08:59:30 -0500
Subject: Maple result
Message-ID: <20060803085930-0500@wiki.axiom-developer.org>

In response to::

  integrate(x^a*(x^b+1)^p, x)

Maple 10 gives the result
$$
{x}^{a+1}{\it hypergeom} \left( [-p,{\frac {a}{b}}+{b}^{-1}],[1+{
\frac {a}{b}}+{b}^{-1}],-{x}^{b} \right) {b}^{-1} \left( {\frac {a}{b}
}+{b}^{-1} \right) ^{-1}
$$

with the derivative::

  differentiate(%, x)

$$
{x}^{a+1} \left( a+1 \right) {\it hypergeom} \left( [-p,{\frac {a}{b}}
+{b}^{-1}],[1+{\frac {a}{b}}+{b}^{-1}],-{x}^{b} \right) {b}^{-1}
 \left( {\frac {a}{b}}+{b}^{-1} \right) ^{-1}{x}^{-1} +
$$
$$
{x}^{a+1}p{\it hypergeom} \left( [-p+1,1+{\frac {a}{b}}+{b}^{-1}],[2+{
\frac {a}{b}}+{b}^{-1}],-{x}^{b} \right) {x}^{b} \left( 1+{\frac {a}{b
}}+{b}^{-1} \right) ^{-1}{x}^{-1}
$$

Following commands (being tested in SandBox?) produce output looking as runtime error:

  \begin{axiom}
  integrate(x^a*(x^b+1)^p, x)
  differentiate(%, x)
  \end{axiom}

if you replace p with, say, 2, it works. AFAIK, this binomial differential can be integrated in closed form only if a, b, and p satisfy certain constraints (aka "Chebyshev theorem"), so the failure itself is not surprising, but IMHO the produced output probably signals about some internal Axiom error or server misconfiguration. Version of the software reported: "Axiom (April 2006), Wednesday June 21, 2006 at 03:45:56".

The error returned by Axiom on linux is:

  Segmentation fault

and Axiom crashes. A similar abort occurs on the Windows version of Axiom.

Maple result --Bill Page, Thu, 03 Aug 2006 08:59:30 -0500 reply

In response to:

  integrate(x^a*(x^b+1)^p, x)

Maple 10 gives the result

with the derivative:

  differentiate(%, x)