If you are interested in listing to me ramble for an hour about integration algorithms, it looks like the recording of the Webinar I gave in early September has been posted to the academic webinar archive: Theory and Practice of Symbolic Integration in Maple. I tried to make it a broad introduction for someone with a mathematical background so there probably isn't anything too too exciting for computer algebra experts.  But, give it a listen/watch if you are interested in how we do symbolic integration.

Edit: I got a request to put a copy of slides up.  So here they are: jmay-integration201.pdf


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