I am practicing computing Fourier transform integrals, and am wondering if Wolfram Alpha or Mathematica has any ability to show the steps it takes to get to a solution. Once I struggle enough, I'd just like to see how Mathematica computed it -- to learn and perhaps even see a better way.
Can Mathematica or Wolfram Alpha do this? Do I have to pay extra for this functionality? I only use the online Wolfram Alpha and the Mathematica software provided by my university.
I believe that Mathematica concentrates on being able to find integrals of, sometimes very difficult, problems and the methods and algorithms it uses to do this do not lend themselves to showing the steps that you might take to do this by hand. Thus I don't think you will get the steps that you are looking for with either WolframAlpha or Mathematica.
There is one possibility that you might explore. There is a free package at https://rulebasedintegration.org/ that you might be able to download and use within your Mathematica session. That has an option to show the steps that it used to perform the integration. I don't know if the results will be what you are looking for, but you could try it and see. One limitation is that I believe it only does indefinite integration and you are probably looking at definite integrals for your fourier transform. But you might still be able to get some insight into the process and be able to apply that.
As with any other application of Mathematica, I would suggest starting with relatively simple problems, see if the results are understandable, and gradually work up to more complicated problems.
Thanks Bill -- I will see if I can get Rubi working for Mathematica. Sometimes I get stuck, and perhaps I can use that package to help me see the next step -- that is what I want to use something like this for. Eventually, I hope to ditch it all together once I have more practice.
Thanks for sharing.