If the answer, as the OP describes it, uses an external tool to solve a problem, that seems ok (even if it costs money, with appropriate disclosure). It may not help everybody, but it will help some. It may not get many votes if the solution is not easy to check.
If the answer were merely a solution in MATLAB, or Python, or C, or whatever, then in almost all cases, I would vote to delete, since this is a site for questions about how to do things with Mathematica. There are sites (e.g. StackOverflow) for asking for solutions for other languages/systems or general programming problems, but presumably a question here is about Mathematica specifically.
A common exception is the use of something like Maple to compare with the performance of Integrate/DSolve. For the purpose of comparison, this seems acceptable. Sometimes the answer simply presents the answer so the OP might use it in their work/research. Strictly viewed, I think this falls into my first case. But I tolerate such an answer, and no one else AFAIR objects to them either. In its defense I can offer two points.
- Integration is hard, and getting an answer in any way is such a kindness to the OP that it seems mean-spirited to deny it. A programming problem that cannot be solved in Mathematica alone would deserve a similar consideration.
- The fact that the integration can be performed computationally in another system is evidence that it might be possible to do it in Mathematica. Sometimes you have to tweak things to get
Integrate/DSolve to work out the answer, and the evidence will encourage others to try.
