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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 %%E0  + 4
*
atan
+------------+
+--+        +--+  |       2
(9 \|23 %%E0 + \|23 )\|69 %%E0  + 4
/
+-------------------------------------------------------+
|                  2                         2
10 \|(- 207 x + 46)%%E0  + (23 x - 69)%%E0 + 25 x  - 6 x - 7
+
2
- 207 %%E0  + 23 %%E0 + 50 x - 6
+
+--+                 2
2 \|23 %%E0 log(207 %%E0  - 23 %%E0 + 25 x + 6)
+
+--+                           2                         2
- \|23 %%E0 log((- 207 x + 46)%%E0  + (23 x - 69)%%E0 + 25 x  - 6 x - 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(%%E0)
 (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,%%E0=rhs s(1));
Type: Expression(Integer)
fricas
complexNumeric %
 (8)
Type: Complex(Float)
fricas
eval(i0,%%E0=rhs s(2));
Type: Expression(Integer)
fricas
complexNumeric %
 (9)
Type: Complex(Float)
fricas
eval(i0,%%E0 = rhs s(3));
Type: Expression(Integer)
fricas
complexNumeric %
 (10)
Type: Complex(Float)

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