Many thanks to all who tried or suggested alternatives for this problem. I
agree that obtaining a closed-form solution to this problem is not likely.
Even if we did get a closed-form solution, it could be so complicated as to
be unusable from a programming point of view.
I'll proceed with the magnetic vector potential approach. A closed-form
solution is not be likely to succeed there either, but it is easy to try,
thanks to Maxima.
Joe Koski
on 5/4/04 1:30 PM, Richard Fateman at fateman@cs.berkeley.edu wrote:
> It shouldn't take forever, but it would be surprising
> if it could be done in closed form. Mathematica doesn't
> find any integral, and it does so fairly immediately.
> Same for Macsyma 2.4.
> RJF
>
>
>
> Stavros Macrakis wrote:
>
>> Joe Koski asks about an integral which is taking forever.
>>
>> I was curious to see what Maxima could do with a simple case of this
>> integral, so I set all the parameters to small numbers to simplify the
>> expression:
>>
>> subst([a=1,b=0,c=0,d=1,x1=0,xp=0,yp=0,zp=1],bx);
>> => 3*x^2/(sqrt(9*x^4+1)*((-x^3-1)^2+x^2+1)^(3/2))
>> == 3*x^2/(sqrt(9*x^4+1)*(x^6+2*x^3+x^2+2)^(3/2))
>>
>> Maxima can't integrate this, so it seems unlikely that it can integrate
>> the integral with 8 arbitrary values of the parameters.
>>
>> ...though there are actually cases where Maxima can integrate a more
>> general case but not a special case, cf. bug report 917505:
>>
>> assume(b>1)$
>> integrate(1/(cos(b*x)+b),x); Works
>> integrate(1/(cos( x )+1),x); Works
>> integrate(1/(cos(2*x)+2),x); Doesn't work
>>
>>
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>>
>
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