Talk:Primitive of Reciprocal of x cubed by a x + b squared

Incorrect result

Mathematica confirms your result and denies Spiegel's --Ybab321 (talk) 09:33, 19 May 2014 (UTC)

I take that completely back, they're both correct --Ybab321 (talk) 09:37, 19 May 2014 (UTC)

I had a feeling that was probably what it was, I just lacked the patience to flog through all the algebra. Thank you big-time for your work here.

In the plan is to use the various general formulas that I am by-and-by approaching, and use those rather than this piecemeal (and tedious) partial fraction approach. --prime mover (talk) 19:39, 19 May 2014 (UTC)

I must ask whether you believe the written formula for the primitive to be superior to the intermediate result calculated directly from the partial fraction decomposition? The extra steps read like a corollary at the moment, but I personally see no advantage of one expression over the other. --Ybab321 (talk) 10:44, 20 May 2014 (UTC)

Depends on how you approach it. I am posting up some general reduction formulas which are to be used (in due course) to provide further proofs of these results, which may (I'll find out when I get there) directly provide the form as provided by Spiegel. If that is the case, then it will be appropriate to quote the results in both forms, and then implement (as a separate result) the conversion you provided so as to demonstrate their equivalence. While manual calculation of integrals in this form is a dead art (equation solvers are everywhere nowadays), it is still an instructive enough exercise to be important enough to document on this website. --prime mover (talk) 11:01, 20 May 2014 (UTC)

Sounds good to me. But it's obvious that there are going to be many other equivalent expressions for each primitive, how do we decide which ones are worth documenting? --Ybab321 (talk) 11:06, 20 May 2014 (UTC)

The ones you can find in the literature, is the way I work. If someone somewhere has seen fit to consider it worth documenting, then it's probably worth mentioning. This site errs on the side of inclusivity. --prime mover (talk) 11:14, 20 May 2014 (UTC)