Can Mathematica (or its extensions) do integration following Risch algorithm?

I wonder whether there are option for indefinite integration in Mathematica that alow to choose the algorithm?

Is there an option to use this algorithm in Mathematica?

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You should post the code for your Integrate/NIntegrate and explain why you think the result is disappointing – Dr. belisarius Nov 28 '13 at 5:20
Mathematica uses the Risch algorithm for many indefinite integrals. But it is not something that can be altered by option settings. – Daniel Lichtblau Nov 28 '13 at 20:46

This is what I get. Open reduce. It does not evaluate the integral? Or are you using different version?

   int( x/sqrt(x^4+10*x^2-96*x-71),x);


Mathematica does evaluate it, yes, the result is large, but it does it:

   Integrate[x/Sqrt[x^4 + 10 x^2 - 96 x - 71], x]


But integration is tricky business. Here is a report of the first 10 Charlwood's integrals, comparing 11 different CAS systems (Reduce among them) and you can see the final result there.

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Thanks for pointing out Rubi. Seems like a nice package for when Integrate chokes or spits out an unwieldy expression. – Oleksandr R. Nov 28 '13 at 23:42

This notebook provides an alternative integration engine for Mathematica, claimed to outperform the standard one.

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apmaths.uwo.ca/~arich – ssch Nov 29 '13 at 0:08
Really the results of Rubi 4.3 outperforms MMA 9. But loading the integrator could have been streamlined. – PlatoManiac Nov 29 '13 at 11:07
@PlatoManiac by "outperforms" I mean better results rather than "works faster" – Anixx Nov 29 '13 at 14:56