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Topic: Charlwood Fifty test results
Replies: 16   Last Post: Sep 19, 2013 10:09 PM

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Albert D. Rich

Posts: 219
From: Hawaii Island
Registered: 5/30/09
Re: Charlwood Fifty test results
Posted: Jul 5, 2013 7:46 PM
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On Friday, July 5, 2013 11:15:41 AM UTC-10, clicl...@freenet.de wrote:

> Nice. Only for Charlwood's problem 44 does Rubi 4.1 (complex domain)
> fall behind Derive 6.10 (real domain). I am not surprised that problems
> 3 and 45 are not handled by Rubi. But why is problem 41 untractable?
>
> Martin.


Thanks for your compliment of the Charlwood Fifty test results I posted. Problem #41 is

integrate(log(sin(x)) sqrt(1+sin(x)), x)

Rubi starts correctly (I think) using integration by parts that gives the log free integral

integrate(cos(x) cot(x)/sqrt(1+sin(x)), x)

Unfortunately Rubi and the other systems tested cannot determine that its antiderivative is

2 cos(x)/sqrt(1+sin(x)) ? 2 arctanh(cos(x)/sqrt(1+sin(x)))

Obviously since its antiderivative is a function of cos(x)/sqrt(1+sin(x)), the log free integral above can be integrated by making the substitution u=cos(x)/sqrt(1+sin(x)) yielding the trivial integral

integrate(2-2/(1-u^2), x)

Any ideas how a rule-based system like Rubi should ?know? to make that substitution?

Albert



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