Re: [Axiom-developer] problems with integrate

[Raymond Rogers]

On 11/22/2014 09:47 AM, Waldek Hebisch wrote:

Tim Daly wrote:

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))

AFAICS logarithmic terms got lost.  FriCAS on the same input
produces ugly, long answer containing several logarithmic
terms.  The above agrees with rational part of FriCAS answer.
Old code contained a bug which sometimes caused such effect.

A clue for someone competent?  In any case a work around for
Thomas Baruchel

54) -> cc
(54) ->
             16       12        8       4
   (54)  256x   + 480x   + 1025x  + 750x  + 625
                                                    Type: Polynomial(Integer)
(55) -> D(complexIntegrate(x^2*(1)/(cc),x),x)
(55) ->
                            2
                           x
   (55)  --------------------------------------
             16       12        8       4
         256x   + 480x   + 1025x  + 750x  + 625
                                                    Type: _expression_(Integer)
(56) -> D(integrate(x^2*(1)/(cc),x),x)      
(56) ->
                          14         10         6        2
                      768x   - 11360x   - 10125x  + 8625x
   (56)  -------------------------------------------------------------
                 16            12            8            4
         7040000x   + 13200000x   + 28187500x  + 20625000x  + 17187500
                                                    Type: _expression_(Integer)
-----------------------------------------
This particular case:
                                                
(57) -> bb
(57) ->
            14       10       6       2
   (57)  16x   - 125x   + 150x  + 375x
                                                    Type: Polynomial(Integer)
(58) -> cc
(58) ->
             16       12        8       4
   (58)  256x   + 480x   + 1025x  + 750x  + 625
                                                    Type: Polynomial(Integer)
(59) -> D(integrate(bb/(cc),x),x)    
(59) ->
                   14        10       6        2
              - 80x   - 2575x   + 350x  + 2625x
   (59)  -------------------------------------------
              16        12         8        4
         2816x   + 5280x   + 11275x  + 8250x  + 6875
                                                    Type: _expression_(Integer)
(60) -> D(complexIntegrate(bb/(cc),x),x)
(60) ->
                14       10       6       2
             16x   - 125x   + 150x  + 375x
   (60)  --------------------------------------
             16       12        8       4
         256x   + 480x   + 1025x  + 750x  + 625
                                                    Type: _expression_(Integer)