Changes http://wiki.axiom-developer.org/308RuntimeErrorOnIntegration/diff
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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)
$$
{x}^{a+1} \left( a+1 \right) {\it hypergeom} \left( [-p,{\frac {a}{b}}
+{b}^{-1}],[1+{\frac {a}{b}}+{b}^{-1}],-{x}^{b} \right) {b}^{-1}
\left( {\frac {a}{b}}+{b}^{-1} \right) ^{-1}{x}^{-1} +
$$
$$
{x}^{a+1}p{\it hypergeom} \left( [-p+1,1+{\frac {a}{b}}+{b}^{-1}],[2+{
\frac {a}{b}}+{b}^{-1}],-{x}^{b} \right) {x}^{b} \left( 1+{\frac {a}{b
}}+{b}^{-1} \right) ^{-1}{x}^{-1}
$$
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