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 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)