I've been thinking about doing something like this myself, just for 
shits and giggles, and I was just wondering if it would be good to use 
infinite series expressions to integrate. It seems like it would be a 
more standardized way of integration (unless an ln shows up somewhere). 
Perhaps once you can write something that will integrate polynomial 
expressions, it would be reasonable to use infinite series like this. 
However, I haven't really taken the time to mess with it.  I don't know 
how much calculus you know, either, so I don't know if you really want 
to teach yourself Taylor and Maclauren series just to do this.  If 
you're really into it, though, that way seems possible.

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