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= (-x)*ArcSin[Sqrt[x] - Sqrt[1 + x]] + > Subst[Int[Sqrt[1 - x^2 + x*Sqrt[-1 + x^2]], x], x, Sqrt[1 + x]]/Sqrt
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
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.
Thanks for your comments and suggestions for Rubi 4.5.