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
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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
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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
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