Integration Error



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