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fricas
f := x/(x^3-x+1)
 (1)
Type: Fraction(Polynomial(Integer))
fricas
)set output tex off

fricas
)set output algebra on
i := integrate(f, x)
(2)
+-----------+
|      2
4\|69%%F0  + 4
*
atan
+-----------+
+--+        +--+  |      2
(9\|23 %%F0 + \|23 )\|69%%F0  + 4
/
+---------------------------------------------------+
|                 2                       2
10\|(- 207x + 46)%%F0  + (23x - 69)%%F0 + 25x  - 6x - 7
+
2
- 207%%F0  + 23%%F0 + 50x - 6
+
+--+                2
2\|23 %%F0 log(207%%F0  - 23%%F0 + 25x + 6)
+
+--+                          2                       2
- \|23 %%F0 log((- 207x + 46)%%F0  + (23x - 69)%%F0 + 25x  - 6x - 7)
/
+--+
2\|23
Type: Union(Expression(Integer),...)
fricas
)set output tex on

fricas
)set output algebra off
D(i, x)
 (2)
Type: Expression(Integer)
fricas
ks := kernels i
 (3)
Type: List(Kernel(Expression(Integer)))
fricas
[definingPolynomial(k::Expression(Integer)) for k in ks | name operator k = 'rootOf]
 (4)
Type: List(Expression(Integer))
fricas
definingPolynomial(%%F0)
 (5)
Type: Expression(Integer)
fricas
s:=radicalSolve(%::Fraction Polynomial Integer)
 (6)
Type: List(Equation(Expression(Integer)))

fricas
i0 := integrate(f, x=1..2)
 (7)
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)
fricas
eval(i0,%%F0=rhs s(1));
Type: Expression(Integer)
fricas
complexNumeric %
 (8)
Type: Complex(Float)
fricas
eval(i0,%%F0=rhs s(2));
Type: Expression(Integer)
fricas
complexNumeric %
 (9)
Type: Complex(Float)
fricas
eval(i0,%%F0 = rhs s(3));
Type: Expression(Integer)
fricas
complexNumeric %
 (10)
Type: Complex(Float)

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