Is there any software which solves integrals STEP BY STEP?
All computer algebra systems solve integrals step-by-step, but they just use different steps to most humans. For integrals yielding only compositions of elementary functions, most use a version of the http://en.wikipedia.org/wiki/Risch_Algorithm" [Broken].
http://www.wolframalpha.com/" [Broken] has a "Show Steps" button for most elementary math problems which I think is just a very clever set of replacement rules (pattern recognition). Note that Mathematica (which underlies WA) does not actually use these steps in the calculation - they are an extra added on top.
If I'm not mistaken, http://en.wikipedia.org/wiki/TK_Solver" [Broken] allows you to view iterations, if you so desired.
It's not cheap, though.
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