@b3m2a1 Wavelets was the main topic in a course on image processing that I took once. The teacher was an astrophysicist. In machine learning I have also seen it as a means of compressing signals and making them faster to process. Just two examples, but it's definitely something that people who do signal processing use.
@C.E. I do a some stuff where some generalizations of the wavelet stuff might be useful so I was wondering what Mathematica itself was aiming for with them
Reading the docs it does look like the primary applications WRI sees is for image process and sound processing
Mathematica gives an answer to this: Integrate[1/(1/E^(s*13) + 1/E^(s*29) + 1/E^(s*37)), s] So in principle this: Integrate[1/(1/1^s + 1/2^s + 1/3^s), s] is solvable too. Algebra and Rootsums seem to be the obstacle though.