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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