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

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 clicliclic@freenet.de Posts: 1,245 Registered: 4/26/08
Re: Charlwood Fifty test results
Posted: Jul 5, 2013 8:20 PM

Albert Rich schrieb:
>
> On Friday, July 5, 2013 11:15:41 AM UTC-10, clicl...@freenet.de wrote:
>

> > [...] But why is problem 41 untractable?
>
> [...] 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)))
>
> [...]

The integrand COT(x)*COS(x)/SQRT(1 + SIN(x)) equals (1 - SIN(x)^2)
/(SIN(x)*SQRT(1 + SIN(x))) which equals (1 - SIN(x))*SQRT(1 + SIN(x))
/SIN(x). That is, the integrand obtained after integration by parts is a
function of SIN(x) only, and of a type that Rubi should be able to
handle.

Martin.