Try Axiom calculations here. For example, here is a simple Axiom command:
\begin{axiom}
integrate(1/(a+z^3), z=0..1,"noPole")
\end{axiom}
axiom
integrate(1/(a+z^3), z=0..1,"noPole")
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
Remember to type \begin{axiom} before each group of commands
and \end{axiom} after the commands.
axiom
integrate(1/sqrt(1 + x^2))
There are 4 exposed and 2 unexposed library operations named
integrate having 1 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op integrate
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
integrate with argument type(s)
Expression(Integer)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
integrate(1/sqrt(1+x^2), x)
Type: Union(Expression(Integer),...)
axiom
)set output algebra on
axiom
)set output tex off
F1:=integrate(cos(t)*sqrt(cos(2*t)),t)
(3)
+---------------------+
| 2
4 3 2 | 8cos(t) - 4
(16cos(t) + 16cos(t) - 4cos(t) - 4cos(t)) |---------------------
| 2
\|cos(t) + 2cos(t) + 1
+
+-+ 4 +-+ 2 +-+
- 32\|2 cos(t) + 16\|2 cos(t) - \|2
*
atan
+-+ 3 +-+ 2 +-+ +-+
(32\|2 cos(t) + 32\|2 cos(t) - 12\|2 cos(t) - 12\|2 )sin(t)
*
+---------------------+
| 2
| 8cos(t) - 4
|---------------------
| 2
\|cos(t) + 2cos(t) + 1
+
3
(- 128cos(t) + 80cos(t))sin(t)
/
ROOT
+---------------------+
| 2
+-+ 2 +-+ | 8cos(t) - 4
(- 128\|2 cos(t) - 128\|2 cos(t)) |---------------------
| 2
\|cos(t) + 2cos(t) + 1
+
2
512cos(t) - 128
+
+-+ 4 +-+ 3 +-+ 2
- 32\|2 cos(t) - 32\|2 cos(t) + 28\|2 cos(t)
+
+-+
28\|2 cos(t)
*
+---------------------+
| 2
| 8cos(t) - 4
|---------------------
| 2
\|cos(t) + 2cos(t) + 1
+
4 2
128cos(t) - 144cos(t) + 32
+
+---------------------+
| 2
4 3 2 | 8cos(t) - 4
(16cos(t) + 16cos(t) - 4cos(t) - 4cos(t)) |---------------------
| 2
\|cos(t) + 2cos(t) + 1
+
+-+ 4 +-+ 2 +-+
- 32\|2 cos(t) + 16\|2 cos(t) - \|2
*
atan
+---------------------+
| 2
| 8cos(t) - 4 +-+
(2cos(t) + 2)sin(t) |--------------------- - 4\|2 cos(t)sin(t)
| 2
\|cos(t) + 2cos(t) + 1
/
ROOT
+---------------------+
| 2
+-+ 2 +-+ | 8cos(t) - 4
(- 16\|2 cos(t) - 16\|2 cos(t)) |---------------------
| 2
\|cos(t) + 2cos(t) + 1
+
2
64cos(t) - 16
+
+---------------------+
| 2
2 | 8cos(t) - 4 +-+ 2
(2cos(t) + 2cos(t)) |--------------------- - 4\|2 cos(t)
| 2
\|cos(t) + 2cos(t) + 1
+
5 4 3 2
(- 32cos(t) - 32cos(t) + 16cos(t) + 16cos(t) - cos(t) - 1)sin(t)
*
+---------------------+
| 2
| 8cos(t) - 4
|---------------------
| 2
\|cos(t) + 2cos(t) + 1
+
+-+ 5 +-+ 3 +-+
(64\|2 cos(t) - 48\|2 cos(t) + 8\|2 cos(t))sin(t)
/
+-+ 4 +-+ 3 +-+ 2 +-+
(32\|2 cos(t) + 32\|2 cos(t) - 8\|2 cos(t) - 8\|2 cos(t))
*
+---------------------+
| 2
| 8cos(t) - 4
|---------------------
| 2
\|cos(t) + 2cos(t) + 1
+
4 2
- 128cos(t) + 64cos(t) - 4
Type: Union(Expression(Integer),...)
axiom
draw(F1,t=-%pi/4..%pi/4)
axiom
Compiling function %BA with type DoubleFloat -> DoubleFloat
Graph data being transmitted to the viewport manager...
FriCAS2D data being transmitted to the viewport manager...
(4) TwoDimensionalViewport: "FriCAS2D"
Type: TwoDimensionalViewport
?
axiom
integrate(cos(t)*sqrt(cos(2*t)),t=-%pi/4..%pi/4)
(5) potentialPole
Type: Union(pole: potentialPole,...)
axiom
integrate(abs(x),x=0..1)
(6) potentialPole
Type: Union(pole: potentialPole,...)
axiom
integrate(abs(x),x=0..1,"noPole")
(7) "failed"
Type: Union(fail: failed,...)
axiom
integrate(abs(x),x=-1..1)
(8) potentialPole
Type: Union(pole: potentialPole,...)
axiom
integrate(abs(x),x=-1..1,"noPole")
(9) "failed"
Type: Union(fail: failed,...)
axiom
integrate(sqrt(x^2),x=0..1)
(10) potentialPole
Type: Union(pole: potentialPole,...)
axiom
integrate(sqrt(x^2),x=0..1,"noPole")
1
(11) -
2
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
axiom
integrate(sqrt(x^2),x=-1..1)
(12) potentialPole
Type: Union(pole: potentialPole,...)
axiom
integrate(sqrt(x^2),x=-1..1,"noPole")
(13) 0
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
axiom
)version
Value = "FriCAS 2010-12-08 compiled at Thursday March 10, 2011 at 19:56:28 "
axiom
solve(x*b -3*a*b + a*x - 9*b*b-4*b*x = +a*a - 9*a*b ,x)
There are no library operations named + having 1 argument(s) though
there are 11 exposed operation(s) and 7 unexposed operation(s)
having a different number of arguments. Use HyperDoc Browse, or
issue
)what op +
to learn what operations contain " + " in their names, or issue
)display op +
to learn more about the available operations.
Cannot find a definition or applicable library operation named +
with argument type(s)
Polynomial(Integer)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
solve(x*b -3*a*b + a*x - 9*b*b-4*b*x = a*a - 9*a*b ,x)
(14) [x= - 3b + a]
Type: List(Equation(Fraction(Polynomial(Integer))))
axiom
solve(-1*(a+3*b)**2 - 3*b*x -a*x = 0,x)
(15) [x= - 3b - a]
Type: List(Equation(Fraction(Polynomial(Integer))))
axiom
solve(-1*(a+3*b)**2 - 3*b*x +a*x = 0,x)
2 2
- 9b - 6a b - a
(16) [x= -----------------]
3b - a
Type: List(Equation(Fraction(Polynomial(Integer))))
axiom
solve(-1*(a-3*b)**2 - 3*b*x +a*x = 0,x)
(17) [x= - 3b + a]
Type: List(Equation(Fraction(Polynomial(Integer))))
axiom
solve((a-3*b)(x-a+3*b) = 0= 0,x)
There are 1 exposed and 1 unexposed library operations named elt
having 1 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op elt
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find application of object of type Polynomial(Integer) to
argument(s) of type(s)
Polynomial(Integer)
axiom
solve((a-3*b)(x-a+3*b) = 0,x)
There are 1 exposed and 1 unexposed library operations named elt
having 1 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op elt
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find application of object of type Polynomial(Integer) to
argument(s) of type(s)
Polynomial(Integer)
axiom
solve((a-3*b)*(x-a+3*b) = 0= 0,x)
There are 18 exposed and 3 unexposed library operations named solve
having 2 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op solve
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named solve
with argument type(s)
Equation(Equation(Polynomial(Integer)))
Variable(x)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
solve((a-3*b)*(x-a+3*b) = 0,x)
(18) [x= - 3b + a]
Type: List(Equation(Fraction(Polynomial(Integer))))
axiom
integrate(1/(a+z^3), z=0..1,"noPole")
(19)
+--+2 +--+
+-+ 2 3| 2 3 2 3| 2 4 3
- \|3 log(3a \|a + (- 2a + a )\|a + a - 2a )
+
+--+
+--+2 +--+ +-+3| 2 +-+
+-+ 3| 2 3| 2 2 2\|3 \|a - a\|3
2\|3 log(\|a + 2a\|a + a ) + 12atan(------------------) + 2%pi
3a
/
+--+
+-+3| 2
12\|3 \|a
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
x*y
axiom
a : (INT,INT) := (2,3)
The constructor Tuple takes 1 argument and you have given 2 .
axiom
(1,2)
(20) [1,2]
axiom
('Mon,'Tue)
(21) [Mon,Tue]
axiom
a := 'x :: OutputForm
(22) x
axiom
b := 'y :: OutputForm
(23) y
axiom
a and b
Argument number 1 to "and" must be a Boolean.
axiom
y := operator y
deq := D(y(x), x, 2) + D(y(x), x) + y(x) + cos(y(x)) = 0
solve(deq, y, x)
There are no library operations named y
Use HyperDoc Browse or issue
)what op y
to learn if there is any operation containing " y " in its name.
Cannot find a definition or applicable library operation named y
with argument type(s)
Variable(x)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
y := operator y;
axiom
deq := D(y(x), x, 2) + D(y(x), x) + y(x) + cos(y(x)) = 0;
Type: Equation(Expression(Integer))
axiom
solve(deq, y, x)
>> Error detected within library code:
parseLODE: not a linear ordinary differential equation
axiom
y := operator y;
There are 2 exposed and 9 unexposed library operations named
operator having 1 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op operator
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
operator with argument type(s)
BasicOperator
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
deq := D(y(x), x, 2) + D(y(x), x) + y(x) + 1 = 0;
Type: Equation(Expression(Integer))
axiom
solve(deq, y, x);
Type: Union(Record(particular: Expression(Integer),basis: List(Expression(Integer))),...)
SandBoxMaybe
axiom
factor(1-x^900)
(28)
-
2 2 2 4 3 2
(x - 1)(x + 1)(x - x + 1)(x + 1)(x + x + 1)(x - x + x - x + 1)
*
4 2 4 3 2 6 3 6 3
(x - x + 1)(x + x + x + x + 1)(x - x + 1)(x + x + 1)
*
8 7 5 4 3 8 6 4 2
(x - x + x - x + x - x + 1)(x - x + x - x + 1)
*
8 7 5 4 3 12 6
(x + x - x - x - x + x + 1)(x - x + 1)
*
16 14 10 8 6 2 20 15 10 5
(x + x - x - x - x + x + 1)(x - x + x - x + 1)
*
20 15 10 5 24 21 15 12 9 3
(x + x + x + x + 1)(x - x + x - x + x - x + 1)
*
24 21 15 12 9 3
(x + x - x - x - x + x + 1)
*
40 35 25 20 15 5 40 30 20 10
(x - x + x - x + x - x + 1)(x - x + x - x + 1)
*
40 35 25 20 15 5
(x + x - x - x - x + x + 1)
*
48 42 30 24 18 6
(x + x - x - x - x + x + 1)
*
80 70 50 40 30 10
(x + x - x - x - x + x + 1)
*
120 105 75 60 45 15
(x - x + x - x + x - x + 1)
*
120 105 75 60 45 15
(x + x - x - x - x + x + 1)
*
240 210 150 120 90 30
(x + x - x - x - x + x + 1)
Type: Factored(Polynomial(Integer))
axiom
simplify ( (a+b+2*sqrt(a)*sqrt(b))/(sqrt(a)+sqrt(b)) )
There are 4 exposed and 1 unexposed library operations named sqrt
having 1 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op sqrt
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named sqrt
with argument type(s)
OutputForm
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
simplify ( sin(a)^2+sin(%pi/2-a)^2 )
There are 1 exposed and 7 unexposed library operations named sin
having 1 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op sin
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named sin
with argument type(s)
OutputForm
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
I was mistaken with
factor example: I didn't see the ``-'' sign :)
axiom
d:=sin(series(asin(x)))-x
21
(29) O(x )
Type: UnivariatePuiseuxSeries
?(Expression(Integer),
x,
0)
axiom
1.2*d
21
(30) O(x )
Type: UnivariatePuiseuxSeries
?(Expression(Float),
x,
0.0)
This seems to be a bug.
axiom
solve( n*log(n)/log(m) = 1/4*n*log(n/4)/log(m) + 3/4*n*log(3/4*n)/log(m) + 15/4*n + 8, m)
3n n
4n log(n) - 3n log(--) - n log(-)
4 4
---------------------------------
15n + 32
(31) [m= %e ]
Type: List(Equation(Expression(Integer)))
axiom
solve( log(n)/log(m) = 1/4*log(n/4)/log(m) + 3/4*log(3/4*n)/log(m) + 15/4*n + 8, m)
3n n
4log(n) - 3log(--) - log(-)
4 4
---------------------------
15n + 32
(32) [m= %e ]
Type: List(Equation(Expression(Integer)))
axiom
solve( log(n)/log(m) = log(n/4)/log(m) + log(3/4*n)/log(m) + 15/4*n + 8, m)
3n n
4log(n) - 4log(--) - 4log(-)
4 4
----------------------------
15n + 32
(33) [m= %e ]
Type: List(Equation(Expression(Integer)))
axiom
integrate((P*cos(x))/(2*e)*cos(x)*sin(x), x=0..%pi,"noPole")
P
(34) --
3e
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
Bessel Integral
axiom
integrate(exp(z*cos(t)),t=0..2*%pi)
(35) "failed"
Type: Union(fail: failed,...)
axiom
integrate(x^2,x)
1 3
(36) - x
3
Type: Polynomial(Fraction(Integer))
integrate(x/sqrt(x^4+10
x^2-96x-71,x)
axiom
integrate(x/sqrt(x^4+10*x^2-96*x-71,x)
Line 1: integrate(x/sqrt(x^4+10*x^2-96*x-71,x)
.........A...........................B
Error A: Missing mate.
Error B: syntax error at top level
Error B: Possibly missing a )
3 error(s) parsing
axiom
integrate(x/sqrt(x^4+10*x^2-96*x-71),x)
(37)
-
log
+--------------------+
6 4 3 2 | 4 2 8
(x + 15x - 80x + 27x - 528x + 781)\|x + 10x - 96x - 71 - x
+
6 5 4 3 2
- 20x + 128x - 54x + 1408x - 3124x - 10001
/
8
Type: Union(Expression(Integer),...)
axiom
integrate(1/x, x=1..2)
(38) log(2)
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
axiom
integrate(1/x, x=1..2)
(39) log(2)
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
axiom
integrate(a/x^3, x)
There are 11 exposed and 8 unexposed library operations named
integrate having 2 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op integrate
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
integrate with argument type(s)
OutputForm
Variable(x)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
9*9
axiom
integrate(1/(a+z^3), z=0..1,"noPole")
There are 4 exposed and 1 unexposed library operations named
integrate having 3 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op integrate
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
integrate with argument type(s)
OutputForm
SegmentBinding(NonNegativeInteger)
String
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
integrate(x/(sqrt((x^4)+(10*(x^2))+(96*x)-71)), x)
(40)
-
log
+--------------------+
6 4 3 2 | 4 2 8
(x + 15x + 80x + 27x + 528x + 781)\|x + 10x + 96x - 71 - x
+
6 5 4 3 2
- 20x - 128x - 54x - 1408x - 3124x - 10001
/
8
Type: Union(Expression(Integer),...)
axiom
integrate(x/(sqrt((x^4)+(10*(x^2))+(96*x)-71)), x )
(41)
-
log
+--------------------+
6 4 3 2 | 4 2 8
(x + 15x + 80x + 27x + 528x + 781)\|x + 10x + 96x - 71 - x
+
6 5 4 3 2
- 20x - 128x - 54x - 1408x - 3124x - 10001
/
8
Type: Union(Expression(Integer),...)
solve(a^2+b^2=c^2,c)
axiom
solve(a^2+b^2=c^2,c)
There are 18 exposed and 3 unexposed library operations named solve
having 2 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op solve
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named solve
with argument type(s)
Equation(OutputForm)
Variable(c)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
integrate(1/sqrt(tan(x)),x)
(42)
+-+
2\|2
*
atan
+------+
|sin(x) +-+ +-+ 2 +-+
2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) - \|2
\|cos(x)
/
ROOT
+------+
+-+ +-+ 2 |sin(x)
(- 4\|2 cos(x)sin(x) - 4\|2 cos(x) ) |------
\|cos(x)
+
8cos(x)sin(x) + 2
+
+------+
2 |sin(x) +-+ +-+ 2
2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x)
\|cos(x)
+
-
+-+
2\|2
*
atan
+------+
|sin(x) +-+ +-+ 2
4cos(x)sin(x) |------ - 2\|2 cos(x)sin(x) + 2\|2 cos(x)
\|cos(x)
+
+-+
- \|2
/
2
*
ROOT
+------+
+-+ +-+ 2 |sin(x)
(- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------
\|cos(x)
+
4cos(x)sin(x) + 1
+
+------+
2 |sin(x) +-+ +-+ 2 +-+
4cos(x) |------ - 2\|2 cos(x)sin(x) - 2\|2 cos(x) + \|2
\|cos(x)
+
-
+-+
\|2
*
+------+
+-+ +-+ 2 |sin(x)
log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------ + 4cos(x)sin(x) + 1)
\|cos(x)
+
+------+
|sin(x) +-+ +-+ 2
2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x)
+-+ \|cos(x)
- 2\|2 atan(----------------------------------------------------------)
+------+
2 |sin(x) +-+ +-+ 2 +-+
2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) + 2\|2
\|cos(x)
/
4
Type: Union(Expression(Integer),...)
axiom
a:=simplify(integrate(1/sqrt(tan(x))))
b:=simplify(differentiate(a),x)
The form on the left hand side of an assignment must be a single
variable, a Tuple of variables or a reference to an entry in an
object supporting the setelt operation.
axiom
a:=simplify(integrate(1/sqrt(tan(x))),x);
There are 4 exposed and 2 unexposed library operations named
integrate having 1 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op integrate
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
integrate with argument type(s)
Expression(Integer)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
b:=simplify(differentiate(a),x);
There are 3 exposed and 0 unexposed library operations named
differentiate having 1 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op differentiate
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
differentiate with argument type(s)
OutputForm
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
a:=simplify(integrate(1/sqrt(tan(x)),x)
Line 1: a:=simplify(integrate(1/sqrt(tan(x)),x)
...........A..........................B
Error A: Missing mate.
Error B: syntax error at top level
Error B: Possibly missing a )
3 error(s) parsing
b:=simplify(differentiate(a),x)
There are 3 exposed and 0 unexposed library operations named
differentiate having 1 argument(s) but none was determined to be
applicable. Use HyperDoc Browse, or issue
)display op differentiate
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named
differentiate with argument type(s)
OutputForm
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
axiom
b:=simplify(differentiate(a),x))
Line 1: b:=simplify(differentiate(a),x))
...............................A
Error A: Improper syntax.
1 error(s) parsing
![\label{eq1}{\left(
\begin{array}{@{}l}
\displaystyle
-{{\sqrt{3}}\ {\log{\left({{3 \ {a^2}\ {{\root{3}\of{a^2}}^2}}+{{\left(-{2 \ {a^3}}+{a^2}\right)}\ {\root{3}\of{a^2}}}+{a^4}-{2 \ {a^3}}}\right)}}}+{2 \ {\sqrt{3}}\ {\log \left({{{\root{3}\of{a^2}}^2}+{2 \ a \ {\root{3}\of{a^2}}}+{a^2}}\right)}}+
\
\
\displaystyle
{{12}\ {\arctan \left({{{2 \ {\sqrt{3}}\ {\root{3}\of{a^2}}}-{a \ {\sqrt{3}}}}\over{3 \ a}}\right)}}+{2 \ \pi}](images/3852001129321091490-16.0px.png "\label{eq1}{\left(
\begin{array}{@{}l}
\displaystyle
-{{\sqrt{3}}\ {\log{\left({{3 \ {a^2}\ {{\root{3}\of{a^2}}^2}}+{{\left(-{2 \ {a^3}}+{a^2}\right)}\ {\root{3}\of{a^2}}}+{a^4}-{2 \ {a^3}}}\right)}}}+{2 \ {\sqrt{3}}\ {\log \left({{{\root{3}\of{a^2}}^2}+{2 \ a \ {\root{3}\of{a^2}}}+{a^2}}\right)}}+
\
\
\displaystyle
{{12}\ {\arctan \left({{{2 \ {\sqrt{3}}\ {\root{3}\of{a^2}}}-{a \ {\sqrt{3}}}}\over{3 \ a}}\right)}}+{2 \ \pi}")
