An integral

[jebem]

(09-06-2014 07:57 PM)patrice Wrote:  

(09-06-2014 06:31 PM)lrdheat Wrote:  I wonder if there is a way in CAS to get the (8*pi*sqrt 3)/3 answer?

Since sqrt(3) / 3 is the same as 1 / sqrt(3)

jebem Wrote:(8*pi)/sqrt(3)

is your answer, only presented differently.

Hi Patrice,
I believe you misread me in Post#2.
What the OP is asking is why is the Prime not giving an exact result (like 8*pi*sqrt 3)/3 or (8*pi)/sqrt(3))?
What the Prime is doing is to answer with another integral. I also tested with XCAS (see post #4) and the behavior is similar to the Prime.
The only choice found so far is to use the approx to get a real number.