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## Re: [Axiom-developer] Schaums help

 From: root Subject: Re: [Axiom-developer] Schaums help Date: Sat, 3 May 2008 00:10:04 -0400

```>> 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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>>
>>
>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))
>(%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

```