Try FriCAS calculations here. For example, here is a simple FriCAS command:
\begin{axiom}
integrate(1/(a+z^3), z=0..1,"noPole")
\end{axiom}
fricas
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.
fricas
integrate(1/sqrt(1+x^2), x)
Type: Union(Expression(Integer),...)
fricas
)set output algebra on
fricas
)set output tex off
F1:=integrate(cos(t)*sqrt(cos(2*t)),t)
(3)
+-+ 4 +-+ 2 +-+
+-+ 32 \|2 cos(t) - 48 \|2 cos(t) + 17 \|2
- \|2 atan(-----------------------------------------)
+-------------+
2 | 2
(32 cos(t) - 24)sin(t)\|2 cos(t) - 1
+
+-------------+
| 2
8 sin(t)\|2 cos(t) - 1
/
16
Type: Union(Expression(Integer),...)
fricas
draw(F1,t=-%pi/4..%pi/4)
fricas
Compiling function %BD 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
?
fricas
integrate(cos(t)*sqrt(cos(2*t)),t=-%pi/4..%pi/4)
(5) "potentialPole"
Type: Union(pole: potentialPole,...)
fricas
integrate(abs(x),x=0..1)
(6) "potentialPole"
Type: Union(pole: potentialPole,...)
fricas
integrate(abs(x),x=0..1,"noPole")
(7) "failed"
Type: Union(fail: failed,...)
fricas
integrate(abs(x),x=-1..1)
(8) "potentialPole"
Type: Union(pole: potentialPole,...)
fricas
integrate(abs(x),x=-1..1,"noPole")
(9) "failed"
Type: Union(fail: failed,...)
fricas
integrate(sqrt(x^2),x=0..1)
1
(10) -
2
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
fricas
integrate(sqrt(x^2),x=0..1,"noPole")
1
(11) -
2
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
fricas
integrate(sqrt(x^2),x=-1..1)
(12) "potentialPole"
Type: Union(pole: potentialPole,...)
fricas
integrate(sqrt(x^2),x=-1..1,"noPole")
(13) 0
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
fricas
)version
Value = "FriCAS 1.3.7 compiled at Wed Jun 30 16:44:06 UTC 2021"
fricas
solve(x*b -3*a*b + a*x - 9*b*b-4*b*x = a*a - 9*a*b ,x)
(14) [x = - 3 b + a]
Type: List(Equation(Fraction(Polynomial(Integer))))
fricas
solve(-1*(a+3*b)^2 - 3*b*x -a*x = 0,x)
(15) [x = - 3 b - a]
Type: List(Equation(Fraction(Polynomial(Integer))))
fricas
solve(-1*(a+3*b)^2 - 3*b*x +a*x = 0,x)
2 2
- 9 b - 6 a b - a
(16) [x = -------------------]
3 b - a
Type: List(Equation(Fraction(Polynomial(Integer))))
fricas
solve(-1*(a-3*b)^2 - 3*b*x +a*x = 0,x)
(17) [x = - 3 b + a]
Type: List(Equation(Fraction(Polynomial(Integer))))
fricas
solve((a-3*b)*(x-a+3*b) = 0,x)
(18) [x = - 3 b + a]
Type: List(Equation(Fraction(Polynomial(Integer))))
fricas
a : (INT,INT) := (2,3)
The constructor Tuple takes 1 argument and you have given 2 .
fricas
(1,2)
(19) [1, 2]
Type: Tuple(PositiveInteger
?)
fricas
('Mon,'Tue)
(20) [Mon, Tue]
fricas
a := 'x :: OutputForm
(21) x
fricas
b := 'y :: OutputForm
(22) y
fricas
a and b
Argument number 1 to "and" must be a Boolean.
fricas
)clear all
All user variables and function definitions have been cleared.
fricas
y := operator 'y
(1) y
fricas
deq := D(y(x), x, 2) + D(y(x), x) + y(x) + cos(y(x)) = 0
,, ,
(2) y (x) + y (x) + cos(y(x)) + y(x) = 0
Type: Equation(Expression(Integer))
fricas
solve(deq, y, x)
>> Error detected within library code:
parseLODE: not a linear ordinary differential equation
fricas
y := operator 'y;
fricas
deq := D(y(x), x, 2) + D(y(x), x) + y(x) + 1 = 0;
Type: Equation(Expression(Integer))
fricas
solve(deq, y, x);
Type: Union(Record(particular: Expression(Integer),basis: List(Expression(Integer))),...)
SandBoxMaybe
fricas
factor(1-x^900)
(6)
-
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))
fricas
simplify((a+b+2*sqrt(a)*sqrt(b))/(sqrt(a)+sqrt(b)))
+-+ +-+
2 \|a \|b + b + a
(7) ------------------
+-+ +-+
\|b + \|a
Type: Expression(Integer)
fricas
simplify ( sin(a)^2+sin(%pi/2-a)^2 )
%pi - 2 a 2 2
(8) - cos(---------) - cos(a) + 2
2
Type: Expression(Integer)
fricas
d:=sin(series(asin(x)))-x
21
(9) O(x )
Type: UnivariatePuiseuxSeries
?(Expression(Integer),
x,
0)
fricas
1.2*d
21
(10) O(x )
Type: UnivariatePuiseuxSeries
?(Expression(Float),
x,
0.0)
fricas
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)
3 n n
4 n log(n) - 3 n log(---) - n log(-)
4 4
------------------------------------
15 n + 32
(11) [m = %e ]
Type: List(Equation(Expression(Integer)))
fricas
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)
3 n n
4 log(n) - 3 log(---) - log(-)
4 4
------------------------------
15 n + 32
(12) [m = %e ]
Type: List(Equation(Expression(Integer)))
fricas
solve( log(n)/log(m) = log(n/4)/log(m) + log(3/4*n)/log(m) + 15/4*n + 8, m)
3 n n
4 log(n) - 4 log(---) - 4 log(-)
4 4
--------------------------------
15 n + 32
(13) [m = %e ]
Type: List(Equation(Expression(Integer)))
fricas
integrate((P*cos(x))/(2*e)*cos(x)*sin(x), x=0..%pi,"noPole")
P
(14) ---
3 e
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
Bessel Integral
fricas
integrate(exp(z*cos(t)),t=0..2*%pi)
(15) "failed"
Type: Union(fail: failed,...)
fricas
integrate(x/sqrt(x^4+10*x^2-96*x-71),x)
(16)
log
+----------------------+
6 4 3 2 | 4 2
(x + 15 x - 80 x + 27 x - 528 x + 781)\|x + 10 x - 96 x - 71
+
8 6 5 4 3 2
x + 20 x - 128 x + 54 x - 1408 x + 3124 x + 10001
/
8
Type: Union(Expression(Integer),...)
fricas
integrate(1/x, x=1..2)
(17) log(2)
Type: Union(f1: OrderedCompletion
?(Expression(Integer)),
...)
fricas
integrate(a/x^3, x)
a
(18) - ----
2
2 x
Type: Union(Expression(Integer),...)
fricas
solve(a^2+b^2=c^2,c)
2 2 2
(19) [c - b - a = 0]
Type: List(Equation(Fraction(Polynomial(Integer))))
fricas
integrate(1/sqrt(tan(x)), x)
(20)
-
+-+
4 \|2
*
atan
1
/
+---------------------------------------------+
| +------+
| +-+ |sin(x)
|- 2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|---------------------------------------------
\| cos(x)
+
+------+
+-+ |sin(x)
\|2 |------ - 1
\|cos(x)
+
-
+-+
4 \|2
*
atan
1
/
+-------------------------------------------+
| +------+
| +-+ |sin(x)
|2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|-------------------------------------------
\| cos(x)
+
+------+
+-+ |sin(x)
\|2 |------ + 1
\|cos(x)
+
+------+
+-+ |sin(x)
2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
+-+ \|cos(x)
\|2 log(-------------------------------------------)
cos(x)
+
+------+
+-+ |sin(x)
- 2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
+-+ \|cos(x)
- \|2 log(---------------------------------------------)
cos(x)
/
4
Type: Union(Expression(Integer),...)
fricas
a :=simplify(integrate(1/sqrt(tan(x)), x))
(21)
-
+-+
4 \|2
*
atan
1
/
+---------------------------------------------+
| +------+
| +-+ |sin(x)
|- 2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|---------------------------------------------
\| cos(x)
+
+------+
+-+ |sin(x)
\|2 |------ - 1
\|cos(x)
+
-
+-+
4 \|2
*
atan
1
/
+-------------------------------------------+
| +------+
| +-+ |sin(x)
|2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|-------------------------------------------
\| cos(x)
+
+------+
+-+ |sin(x)
\|2 |------ + 1
\|cos(x)
+
+------+
+-+ |sin(x)
2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
+-+ \|cos(x)
\|2 log(-------------------------------------------)
cos(x)
+
+------+
+-+ |sin(x)
- 2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
+-+ \|cos(x)
- \|2 log(---------------------------------------------)
cos(x)
/
4
Type: Expression(Integer)
fricas
b:=simplify(differentiate(a, x))
(22)
+------+
3 4 2 |sin(x)
(48 cos(x) sin(x) + 39 cos(x) - 64 cos(x) ) |------
\|cos(x)
*
+---------------------------------------------+
| +------+
| +-+ |sin(x)
|- 2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|---------------------------------------------
\| cos(x)
+
+------+
3 4 2 |sin(x)
(- 64 cos(x) sin(x) - 29 cos(x) + 64 cos(x) ) |------
\|cos(x)
+
+-+ 3 +-+ +-+ 4
(45 \|2 cos(x) - 64 \|2 cos(x))sin(x) - 32 \|2 cos(x)
+
+-+ 2
32 \|2 cos(x)
*
+-------------------------------------------+
| +------+
| +-+ |sin(x)
|2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|-------------------------------------------
\| cos(x)
+
+------+
3 4 2 |sin(x)
(64 cos(x) sin(x) + 29 cos(x) - 64 cos(x) ) |------
\|cos(x)
+
+-+ 3 +-+ +-+ 4
(45 \|2 cos(x) - 64 \|2 cos(x))sin(x) - 32 \|2 cos(x)
+
+-+ 2
32 \|2 cos(x)
*
+---------------------------------------------+
| +------+
| +-+ |sin(x)
|- 2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|---------------------------------------------
\| cos(x)
+
+------+
3 4 2 |sin(x)
((14 cos(x) - 128 cos(x))sin(x) - 47 cos(x) + 96 cos(x) ) |------
\|cos(x)
/
3 4 2
((39 cos(x) - 64 cos(x))sin(x) - 48 cos(x) + 48 cos(x) )
*
+---------------------------------------------+
| +------+
| +-+ |sin(x)
|- 2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|---------------------------------------------
\| cos(x)
+
+-+ 3 +-+ +-+ 4
(45 \|2 cos(x) - 64 \|2 cos(x))sin(x) - 32 \|2 cos(x)
+
+-+ 2
32 \|2 cos(x)
*
+------+
|sin(x)
|------
\|cos(x)
+
3 4 2
(- 29 cos(x) + 64 cos(x))sin(x) + 64 cos(x) - 64 cos(x)
*
+-------------------------------------------+
| +------+
| +-+ |sin(x)
|2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|-------------------------------------------
\| cos(x)
+
+-+ 3 +-+ +-+ 4
(45 \|2 cos(x) - 64 \|2 cos(x))sin(x) - 32 \|2 cos(x)
+
+-+ 2
32 \|2 cos(x)
*
+------+
|sin(x)
|------
\|cos(x)
+
3 4 2
(29 cos(x) - 64 cos(x))sin(x) - 64 cos(x) + 64 cos(x)
*
+---------------------------------------------+
| +------+
| +-+ |sin(x)
|- 2 \|2 cos(x) |------ + 2 sin(x) + 2 cos(x)
| \|cos(x)
|---------------------------------------------
\| cos(x)
+
3 4 2
(- 47 cos(x) + 96 cos(x))sin(x) - 14 cos(x) + 142 cos(x) - 128
Type: Expression(Integer)
fricas
normalize(b - 1/sqrt(tan(x)))
(23) 0
Type: Expression(Integer)
![\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/4322038355343098202-16.0px.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}")
