People have been working on computer programs for integration since about 
1961.  There are 
at least 8 PhD theses on the topic.

If you think there is "low hanging fruit" like   writing a better 
simplification program, or
using binary search instead of pattern matching, or something else you just 
thought up,
like running the differentiation program backwards  ---
there is a high probability that you are mistaken.

Of course you might be right, and all that stuff over the last 55 years is 
irrelevant,
and all you have to do is write some neat python program.

Check out the definition of "irony"


On Monday, March 20, 2017 at 2:27:46 AM UTC-7, Ralf Stephan wrote:
>
> ...In principle there can be fast progress if the first version only 
>> implements general fallback rules like the mentioned 2F1 solutions. Many 
>> Rubi rules only specialize 2F1 solutions, a sort of 
>> simplify_hypergeometric() if you want. But then, with only the 
>> hypergeometric (H) rules the output is ugly as well. You'll get more 
>> integrals solved than usual algorithms, however, so this low-hanging fruit 
>> would have a place *after eg Maxima returns an unsolved integral.
>>
>
> https://trac.sagemath.org/ticket/22650
>

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