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)
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