Raymond Toy wrote:
> 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
>
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. Please
thanks
doug