[Axiom-developer] problems with integrate

[daly]

Question from Thomas Baruchel

integrate((16*x^14-125*x^10+150*x^6+375*x^2)/(256*x^16+480*x^12+1025*x^8+750*x^4
 +625),x=0..1)

          5
    (1)  --
         77
                   Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
(2) -> 
integrate((16*x^14-125*x^10+150*x^6+375*x^2)/(256*x^16+480*x^12+1025*x^8+750*x^4
 +625),x)

                7      3
              5x  + 35x
    (2)  -------------------
             8       4
         176x  + 165x  + 275
                                          Type: Union(Expression(Integer),...)
(3) -> D( (5*x^7+35*x^3)/(176*x^8+165*x^4+275) ,x)

                   14        10       6        2
              - 80x   - 2575x   + 350x  + 2625x
    (3)  -------------------------------------------
              16        12         8        4
         2816x   + 5280x   + 11275x  + 8250x  + 6875
                                           Type: Fraction(Polynomial(Integer))