Doug Stewart wrote:
> I think there is a problem with an Integral in Maxima:
>
> (%i3) integrate(1/(x*sqrt(x^n-a^n)),x);
> Is a positive or negative?p;
> (%o3) (2*atan(sqrt(x^n-a^n)/a^(n/2)))/(a^(n/2)*n)
> (%i4) integrate(1/(x*sqrt(x^n-a^n)),x);
> Is a positive or negative?n;
> (%o4)
> 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)
>
>
>
>
>
>
>
> 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))
>
> Would someone here in Maxima please check this out.
>
> From my beginners view point it looks wrong.
>
What is the issue? If you differentiate them, you get the integrand back.
Also recall that there is a relationship between atan and acos.
Ray