## Does Mathematica implement Risch Algorithm? If it does, in which cases?

I am asking this questions because when trying to evaluate the Integrals:  (1)\ \int \frac{x}{\sqrt{x^4+10x^2-96×-71}}\ dx  (2)\ \int \frac{x^2+2x+1+(3x+1)\sqrt{x+\ln(x)}}{x(x+\sqrt{x+\ln(x)})\sqrt{x+\ln(x)}}\ dx
$\textbf{Mathematica 11}$ : For $(1)$ I obtain an evaluation involving non-elementary functions, while $(2)$ is not even evaluated.
 \ $\textbf{Maple 2016}$ : I get the same results as in Mathematica.
 \ $\textbf{Rubi 4.11}$ neither are evaluated.

 \ The two indefinite integrals can be expressed with elementary functions.   $\textbf{Code:}\ (Mathematica)$  \
$(1)$ Integrate[x/Sqrt[x^4 + 10 x^2 - 96 x - 71], x]

$(2)$ Integrate[(x^2 + 2 x + 1 + (3 x + 1) Sqrt[x + Log[x]])/(x (x + Sqrt[x + Log[x]]) Sqrt[ x + Log[x]]), x]

  ADDENDUM: The antiderivative of the integrand $(1)$ is correctly expressed with elementary functions using $\textbf{Axiom}$ . Why can’t the two powerful Computer Algebra Systems listed above, obtain the same result as Axiom?

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