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An FYI on hp prime integration...
07-11-2017, 12:07 PM
Post: #1
An FYI on hp prime integration...
I was confused recently with various problems I was encountering with integrating on the Prime, especially when limits of [0,infinity] were used.
I kept getting these cryptic messages about singularities were not checked for in the antiderivatives and this internal representation of intermediate steps were printed in the message.
I now realize that these are just informative messages. e.g. When using wolfram alpha you will often get intermediate steps described and problems encountered.
A few tips if I may. If you are using variables other than x in your equations, I found I got much better results by using the assume statement to say things like assume(r>0) assume(s,integer) etc... Put as much info like this in there as possible and you'll get better results.
Also, these cryptic messages are just informative and are not necessarily errors.

The prime's integration code is very good actually. Take this problem for wolfram alpha times out on my laptop with this problem....and thus, with the free version, is unable to solve it.

integrate 4*pi*x*sqrt(r^2-(x-s)^2) for x from s-r to s+r

On the prime, when I use assume(r>0); assume(s>0);
This problem gives me a cryptic message, but on hitting enter again, I get the result of

So, in this case, the prime beats out WolframAlpha.....pretty impressive!

So, remember to give your integral as much information about the variables that you have in advance using assume() and additionally(), and remember that these cryptic messages are just informative and are nothing to be worried about.

I put this in it's own post as I believe this is a good one to refer to when people start having these problems.
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