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Topic: Rubi 4.5 released
Replies: 21   Last Post: Jun 29, 2014 4:29 AM

 Messages: [ Previous | Next ]
 Nasser Abbasi Posts: 6,677 Registered: 2/7/05
Re: Rubi 4.5 released
Posted: Jun 22, 2014 1:06 AM

On 6/21/2014 10:06 AM, clicliclic@freenet.de wrote:
>

> Integration Example #75 from Chapter 5 of the Timofeev Test Suite ran
> into a 25-second timeout on Version 4.4. Does Rubi 4.5 resurface
> eventually, and what is the final result, or error message?
>

Taking the problem from

http://www.apmaths.uwo.ca/~arich/IndependentTestResults/TimofeevIntegrationProblems.pdf
page 55:

Rubi 4.5 solves this on my PC in about 5 seconds.

num = (Cos[2 x] - 3 Tan[x]) Cos[x]^3;
den = (Sin[x]^2 - Sin[2 x]) Sin[2 x]^(5/2);
Int[num/den, x]

(*The result is too large to post here as is, but after
simplify, here it is:)

Simplify[%]

-((1/(240*Sqrt[Sin[2*x]]))*((495*Cos[x]*EllipticF[ArcSin[Sqrt[Tan[x/2]]], -1])/
(Sqrt[Cot[x/2]]*Sqrt[Cos[x]*Sec[x/2]^2]) +
(1/2)*Sin[x/2]^2*(990*I*Cot[x/2]^(3/2)*
EllipticPi[-(2/(-1 + Sqrt[5])), I*ArcSinh[Sqrt[Tan[x/2]]], -1]*
Sqrt[Cos[x]*Sec[x/2]^2] + 990*I*Cot[x/2]^(3/2)*
EllipticPi[2/(1 + Sqrt[5]), I*ArcSinh[Sqrt[Tan[x/2]]], -1]*
Sqrt[Cos[x]*Sec[x/2]^2] + (1/8)*Csc[x/2]^4*Sec[x/2]^2*
(99*Cos[x] - 147*Cos[3*x] + 200*Cos[x]^2*Sin[x]))))

> I am curious how far Rubi 4.5 allows one to go with Martin's integrals:
>
> <http://mathforum.org/kb/message.jspa?messageID=6477150&tstart=0>
> <http://mathforum.org/kb/message.jspa?messageID=6872137&tstart=0>
>

I looked at these links. The integrals you have there are definite ones, but
Rubi only does indefinite. How should one apply these to Rubi?

---------- from one of the above links--------

int(int((jxx(r*cos(p)-a/2, r*SIN(p), z) * jxx(r*COS(p)+a/2, r*SIN(p),
z) + jxy(r*cos(p)-a/2, r*SIN(p), z) * jxy(r*COS(p)+a/2, r*SIN(p),
z))*r, r, 0, inf), p, 0, 2*pi)
------------------------------

--Nasser