3 ms·
This is fantastic. I’ve tried several times to understand this idea over the years, with no success. This clearly expressed the idea in only a few minutes. One
by dynm 5y ago
This is fantastic. I’ve tried several times to understand this idea over the years, with no success. This clearly expressed the idea in only a few minutes.
One question: It mentions that Wolfram alpha will fail on integrals that this trick can work for. Is that just because it will time out (we need more compute) or is the trick difficult to automate?
- nimish 5y agoA little bit of both. I don't think WA uses the full Risch algo, but even then, enough pattern matching rules https://rulebasedintegration.org/ https://rulebasedintegration.org/ beats it in perf. Differentiation under the integral sign only works for certain well behaved functions and isn't easy to automate since you now need to figure out where to parametrize and you don't have good structure theorems to help you. IMO contour integration is a more powerful and easier to intuit technique.
- kzrdude 5y agoAmazing website. I love that I could just click ahead and find the .pdf transcripts of the tests ran.
- Kranar 5y agoUnlike differentiation, indefinite integration is undecidable even for elementary functions so there will always be some limit to what an algorithm can compute.