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

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 Albert D. Rich Posts: 311 From: Hawaii Island Registered: 5/30/09
Re: Rubi 4.5 released
Posted: Jun 21, 2014 4:24 AM

On Friday, June 20, 2014 4:56:06 PM UTC-10, Nasser M. Abbasi wrote:

> I tried it on the 3rd Charlwood which in previous Version
> Rubi did not integrate,
>
> http://12000.org/my_notes/ten_hard_integrals/inse3.htm#x4-30003
>
> and was hoping it will now, so it can get 10/10, but
> still difficulties show:
>
> Int[ArcSin[Sqrt[x + 1] - Sqrt[x]], x]
>
> Out[68]= (-x)*ArcSin[Sqrt[x] - Sqrt[1 + x]] +
> Subst[Int[Sqrt[1 - x^2 + x*Sqrt[-1 + x^2]], x], x, Sqrt[1 + x]]/Sqrt[2]

As the above output shows, using integration by parts Rubi is able to find one term of the antiderivative (ie (-x)*ArcSin[Sqrt[x]). However it is unable to integrate the resulting algebraic integrand

Sqrt[-x + Sqrt[x]*Sqrt[1 + x]]/Sqrt[1 + x]

to get the antiderivative

1/2*(Sqrt[x] + 3*Sqrt[1 + x])*Sqrt[-x + Sqrt[x]*Sqrt[1 + x]] -
3*ArcSin[Sqrt[x] - Sqrt[1 + x]]/(2*Sqrt[2])

Mathematica is able to integrate it but gets an antiderivative 3 times the above size. I do not know how to integrate this algebraic integrand. Tell me the integration steps you would use to integrate it, and I will be happy to teach Rubi how to do it.

> ps. is it possible to make the default to be ShowSteps=False
> instead of True? Most of the time one does not want to see the steps,
> at least at first. Just as a suggestion.

To make Rubi start in non-showstep mode, just change the assignment in Rubi4.5.nb to ShowSteps=False and then save the file.