Re: [Axiom-developer] Schaums help

[Doug Stewart]

Doug Stewart wrote:
> root wrote:
> > > > My copy of Schaums (1968, printing 4) shows
> > > >
> > > > 14:334:
> > > >
> > > > int(1/(x*sqrt(x^n-a^n)),x) == 2/(n*sqrt(a^n))*acos(sqrt(a^n/x^n))
> > > >
> > > > It seems this cannot be the answers.
> > > > Can someone with a later version please check for a typo?
> > > >
> > > > Tim
> > > >
> > > >
> > > > _______________________________________________
> > > > Axiom-developer mailing list
> > > > address@hidden
> > > > http://lists.nongnu.org/mailman/listinfo/axiom-developer
> > > >
> > > >         
> > > My schaums shows that answer.
> > > also usind Maxima to do the derivative  I get the LHS.
> > > (%i5) diff(2/(n*sqrt(a^n))*acos(sqrt(a^n/x^n)),x);
> > > (%o5) (a^n*x^(-n-1))/(sqrt(a^n)*sqrt(a^n/x^n)*sqrt(1-a^n/x^n))
> > > (%i6) radcan(%);
> > > (%o6) 1/(x*sqrt(x^n-a^n))
> > >     
> >
> > If you compute
> > aa:=integrate(1/(x*sqrt(x^n-a^n)),x)
> > bb:=2/(n*sqrt(a^n))*acos(sqrt(a^n/x^n))
> > cc1:=aa.1-bb
> > cc2:=aa.2-bb
> >
> > Can you find a simplification path (in Axiom) such that either cc1 or 
> > cc2 simplify to a constant?
> >
> > Alternatively, can you use Maxima to find the constant?
> >
> > I'm failing to do either, although I'm still trying.
> >
> > Tim
> >
> >   
>
> Maxima seems to give a wrong answer for this integration.
>
>
> (%i1) aa:integrate(1/(x*sqrt(x^n-a^n)),x);
> Is  a  positive or negative?p;
>
> (%o1) (2*atan(sqrt(x^n-a^n)/a^(n/2)))/(a^(n/2)*n)
>
> and
> (%i2) aa:integrate(1/(x*sqrt(x^n-a^n)),x);
> Is  a  positive or negative?n;
> (%o2) 
> log((2*sqrt(x^n-a^n)-2*sqrt(-a^n))/(2*sqrt(x^n-a^n)+2*sqrt(-a^n)))/(sqrt(-a^n)*n) 
>
>
>
> I'm not good enough at simplifying to help you.
> Doug
>
>
> _______________________________________________
with help from Maxima
> >Can you show me how to start with
> >
> >(2*atan(sqrt(x^n-a^n)/a^(n/2)))/(a^(n/2)*n)
> >
> >and differentiate it to get
> >
> >1/(x*sqrt(x^n-a^n)
> >
> >using Maxima.
>   

(%i4) (2*atan(sqrt(x^n-a^n)/a^(n/2)))/(a^(n/2)*n)$
(%i5) ratsimp(diff(%,x));
(%o5) 1/(x*sqrt(x^n-a^n))

Barton



so Maxima is not wrong.

Doug