Hi, 
In the ticket of Laplace transform (see trac ticket #22422) I have the same 
dilemma. One could:
1- do nothing (keeping the same behaviour as, say, `symbolic_sum`), 
expecting that the user asks for inline help, figures out there is an 
'algorithm' argument that can be changed, and tries that.
2- print a message when the returned transform is unevaluated, saying 
something like "Hey, there are ... available algorithms!"
3- add a new algorithm='any' (that ships by default in Sage), which works 
by trial and error with the available ones.

El domingo, 26 de febrero de 2017, 7:52:26 (UTC+1), Ralf Stephan escribió:
>
> Users of integrate() usually don't care which "algorithm" is used,
> just that the thing is solved. At the moment the default behaviour
> is calling Maxima only, and you have to know/read that you can
> try other algorithms too. Many beginners don't know about this.
>
> I propose to make the default "try all algorithms in a specific order".
> It will return as soon as one library returns a result. An additional
> advantage could be that the fast methods can be used first.
>
> Any objections?
>

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