In terms of integration, I usually utilize Mathematica 9 to compute scattering amplitudes in quantum field theory. Recently, I employed it to compute a particularly difficult integral, and it outputted a lengthy combination of hypergeometric Appell functions. Is there any way I can determine how Mathematica actually 'evaluated' the integral, or more appropriately, 'manipulated' the integral into the form required to equate it to a bunch of Appell functions. What I'm looking for is essentially what Wolfram Alpha does when you click 'step by step solution,' but for Mathematica.

  • $\begingroup$ 1) You can use WolframAlpha directly from within Mathematica. Wolfram Alpha uses Mathematica for computations. 2) To find out which Method a certain mathematica routine used, take a look at this thread: mathematica.stackexchange.com/questions/145/… $\endgroup$
    – Wizard
    Apr 2 '14 at 10:03
  • $\begingroup$ @Wizard Loop integrals are quite complicated, and often WolframAlpha will not compute it, or say it ran out of allowed computation time. $\endgroup$ Apr 2 '14 at 10:34