Following commands (being tested in SandBox) produce output looking as runtime error: fricas (1) -> integrate(x^a*(x^b+1)^p,
Type: Union(Expression(Integer),
fricas differentiate(%,
Type: Expression(Integer)
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)
with the derivative: differentiate(%, x)
no patch available http://axiom.svn.sourceforge.net/viewvc/axiom/branches/wh-sandbox/src/algebra/intef.spad.pamphlet?r1=263&r2=388&view=patch Status: fixed somewhere => fix proposed Status: fix proposed => closed |
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last edited 6 years ago by test1 |
![{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}](images/1946845112997260189-16.0px.png "{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}")
![{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} +](images/8097002855006675929-16.0px.png "{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}](images/8364997091458089766-16.0px.png "{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}")