Ok, I just added TimeConstraints to bypass this. I do not think it is worth reporting. How many people will want to TeXForm such a large expression? :) Not many.

@Nasser It is entirely possible that the set of extensions to Risch in Fricas, and the extensions in Mathematica, have only a small intersection.

I'm not too familiar with the Risch algorithm, but from reading some notes on internal implementation of MMA, I think it was mentioned that a huge percent of the code is to translate some internal representation of the solved integral back to something interepretable by people.

Good luck getting any LaTeX renderer able to show any TeXForm with a leaf count of 1,819,057 :P

@CoryWalker I think you had the Mellin-type internal algorithm in mind.

Yes, a good amount of definite integrals are mechanically reducible to an appropriate Mellin convolution.

But, that's for the definite case. Risch is what you still use in the indefinite case.

Mathematica of course has made proprietary extensions.

(Anybody interested in the guts of basic Risch should read Geddes/Czapor/Labahn.)

@J.M. I think whole computer algebra field is stagnated now. The one killer app I see for CAS is this: Make a CAS which also show step by step solutions, as we would solve by hand. And I do not mean just for simple problems like Wolfram alpha does now, but for the really hard problems outside calc 100. ps. I have that book you linked to. Too advanced for me. I need someone to write "Risch algorithms for dummies" book :)

@Nasser The difficulty circles back to "what's easy for the computer is hard for humans and vice versa".

Yeah, I figure a "Risch for dummies" book would be nice. Unfortunately nobody's bothered yet.

@J.M. Sure, I know it is difficult, that is why I said this is the killer app for CAS. Imagine a CAS which will show step by step solution, as we would do, for solving a heat PDE on even 1-D using eigenfunction expansion method. Or CAS which will show finding Fourier series, step by step, using the standard formulas in books. and so on. This will be great for students.

There are 1,000 of uses for such a CAS. This will replace all the problem solver books and schuam books which are designed to show step-by-step solutions.

Something to wonder about:

=========================
In[24]:= $Version
Out[24]= 11.2.0 for Microsoft Windows (64-bit) (September 11, 2017)

In[25]:= ClearAll[x]
          result=Integrate[Sqrt[a+b*x^2+c*x^4]/(x^3*(d+e*x^2)),x];
          LeafCount[result]
Out[27]= 10848


In[28]:= result=Integrate[1/(x^1*(d+e*x^2)*Sqrt[a+b*x^2+c*x^4]),x];
          LeafCount[result]
Out[29]= 3622
=================================

Compare to

======================================
In[1]:= $Version
Out[1]= 9.0 for Microsoft Windows (64-bit) (January 25, 2013)