Changes 
http://wiki.axiom-developer.org/290AxiomFailedToIntegrateElementaryFunction/diff
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??changed:
-integrate(simplify(D((x-x/(x+exp(x)/(x*log(x+x))))*exp(2), x)), x)
+\begin{axiom}
+ex1:=(x-x/(x+exp(x)/(x*log(x+x))))*exp(2)
+ex2:=D(ex1, x)
+ex3:=simplify(ex2)
+integrate(ex3, x)
+\end{axiom}
 then Axiom 3.9 returns unevaluated integral. 

 compute the integral.
++added:
+\begin{axiom}
+ex4:=(x-x/(x+exp(x)/(x*log(x+x))))
+ex5:=D(ex1, x)
+ex6:=simplify(ex2)
+integrate(ex3, x)
+\end{axiom}

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