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http://wiki.axiom-developer.org/346ReturnsFormatIntegrationSignFor1TanX13WhichIsElementary/diff
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I'm not so sure whether this integral really is elementary. Mathematica gives

\begin{verbatim}
In[1]:= Integrate[(1 + Tan[x])^(1/3),x]

                                                          1/3
                        3     6     Log[-#1 + (1 + Tan[x])   ] #1
        RootSum[2 - 2 #1  + #1  & , ----------------------------- & ]
                                                     3
                                              -1 + #1
Out[1]= -------------------------------------------------------------
                                      2

In[2]:= ?RootSum
RootSum[f, form] represents the sum of form[x] for all x that satisfy the
   polynomial equation f[x] == 0.
\end{verbatim}

Is the function "n-th root of some univariate polynomial" elementary?

Martin
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