I wonder how we can support a user to interpret the result of this
integration. I bet that many people will fail to figure out that %%E0
and %%E1 are rootOf expressions.
Maybe I'm too blind, but I couldn't find something in the FriCAS Book.
Ralf
(1) -> res := integrate(1/(1+x^5),x)
(1)
+----------------------------------------------------------+
| 2 2
\|- 75 %%E1 + (- 50 %%E0 - 10)%%E1 - 75 %%E0 - 10 %%E0 - 3
+
- 5 %%E1 - 5 %%E0 - 1
*
log
+----------------------------------------------------------+
| 2 2
\|- 75 %%E1 + (- 50 %%E0 - 10)%%E1 - 75 %%E0 - 10 %%E0 - 3
+
- 5 %%E1 - 5 %%E0 + 2 x - 1
+
+----------------------------------------------------------+
| 2 2
- \|- 75 %%E1 + (- 50 %%E0 - 10)%%E1 - 75 %%E0 - 10 %%E0 - 3
+
- 5 %%E1 - 5 %%E0 - 1
*
log
+----------------------------------------------------------+
| 2 2
- \|- 75 %%E1 + (- 50 %%E0 - 10)%%E1 - 75 %%E0 - 10
%%E0 - 3
+
- 5 %%E1 - 5 %%E0 + 2 x - 1
+
10 %%E1 log(5 %%E1 + x) + 10 %%E0 log(5 %%E0 + x) + 2 log(x + 1)
/
10
Type:
Union(Expression(Integer),...)
(2) -> tower res
(2)
[x, log(x + 1), %%E0, log(5 %%E0 + x), %%E1, log(5 %%E1 + x),
+----------------------------------------------------------+
| 2 2
\|- 75 %%E1 + (- 50 %%E0 - 10)%%E1 - 75 %%E0 - 10 %%E0 - 3 ,
log
+----------------------------------------------------------+
| 2 2
- \|- 75 %%E1 + (- 50 %%E0 - 10)%%E1 - 75 %%E0 - 10 %%E0 - 3
+
- 5 %%E1 - 5 %%E0 + 2 x - 1
,
log
+----------------------------------------------------------+
| 2 2
\|- 75 %%E1 + (- 50 %%E0 - 10)%%E1 - 75 %%E0 - 10 %%E0 - 3
- 5 %%E1
+
- 5 %%E0 + 2 x - 1
]
Type:
List(Kernel(Expression(Integer)))
(3) -> definingPolynomial(%%E0)
4 3 2
625 %%E0 + 125 %%E0 + 25 %%E0 + 5 %%E0 + 1
(3) ---------------------------------------------
625
Type:
Expression(Integer)
(4) ->
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