Fyi;
The following are the integrals from the MIT integration
problems which are not solved broken per CAS.
The syntax used for the integrand below is that
from the Maple file which might need small modification
(if any) to make it run on each specific CAS.
The Hall of fame problem that no CAS could solve is this one:
(2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1)
Its anti-derivative is arctan(x^2017+x^2018) which is shown below:
integrand := (2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1);
anti := arctan(x^2017+x^2018);
simplify(diff(anti,x)-integrand)
0
Mathematica:
-------------
(2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1)
(-x^4+4*x^3-7*x^2+6*x+1)^11
(x+exp(1)+1)*x^exp(x)*exp(x)
ln(x/Pi)/(ln(x)^ln(exp(1)*Pi))
Fricas:
-------
ln(x+1)/(x^2+1)
sin(101*x)*sin(x)^99
x*(1-x)^2014 Exception raised: RecursionError >> maximum recursion
depth exceeded
(2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1) Timed out
cos(3*x)+sin(2*x)*(-sin(2019*x)+cos(3*x)) Timed out
x*(1-x)^2020 Exception raised: RecursionError >> maximum recursion depth
exceeded
(1-x)^3+(-x^2+x)^3+(x^2-1)^3-3*(1-x)*(-x^2+x)*(x^2-1)
(x+exp(1)+1)*x^exp(x)*exp(x)
(3*x^3+2*x^2+1)/(x^2+1)^(1/3)
(1/x*ln(1/x))^(1/2)
2^(1/2)*ln(x)^(1/2)+1/2*2^(1/2)/ln(x)^(1/2)
Maple:
----------
3*x^2*(x^3+1)^2*exp(-x^6-2*x^3)
cos(x)^(cos(x)+1)*tan(x)*(1+ln(cos(x)))
(2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1)
1/(x^(41/25)+x^(9/25))
x^(1/ln(x))
(x+exp(1)+1)*x^exp(x)*exp(x)
(2*x^2022+1)/(x^2023+x)
ln(x/Pi)/(ln(x)^ln(exp(1)*Pi))
(1-(-1/2*Pi+arcsin(sin(x)))^2)^(1/2)
(1/x*ln(1/x))^(1/2)
arcsin(x)*arccos(x)
2^(1/2)*ln(x)^(1/2)+1/2*2^(1/2)/ln(x)^(1/2)
x^(-ln(x))
((x+1)^(1/2)-x^(1/2))^Pi
sin(4*arctan(x))
tan(x)^(1/3)/(cos(x)+sin(x))^2
(1+x^2+(x^4+x^2+1)^(1/2))^(1/2)
Rubi:
-----
1/(sin(x)+sec(x))
(cos(x)*ln(x)-sin(x)/x)/ln(x)^2
exp(exp(x)+exp(-x)+x)-exp(exp(x)+exp(-x)-x)
(1+2*x*exp(x^2))*cos(x)-(x+exp(x^2))*sin(x)
cos(x)*cosh(x)+sin(x)*sinh(x)
(2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1)
x^(x^2+1)*(1+2*ln(x))
sin(x+sin(x))-sin(x-sin(x))
(1+ln(x))*ln(ln(x))
(x+exp(1)+1)*x^exp(x)*exp(x)
sin(x)/(2*exp(x)+cos(x)+sin(x))
(1-(-1/2*Pi+arcsin(sin(x)))^2)^(1/2)
(cos(x)-sin(x))/(2+sin(2*x))
arcsin(x)*arccos(x)
ln(3^(1/2)+tan(x))
exp(-2*x)*sin(3*x)/x
exp(x+1/x)*(x^6+x^4-x^2-1)/x^4
x^(-ln(x))
exp(cos(x))*cos(2*x+sin(x))
sin(4*arctan(x))
(1+x^2+(x^4+x^2+1)^(1/2))^(1/2)
Maxima:
-------
1/(sin(x)+sec(x))
(x/(-x^3+1))^(1/2)
sin(101*x)*sin(x)^99
1/(1+x^(1/2))/(-x^2+x)^(1/2)
x^(1/2)/((2012-x)^(1/2)+x^(1/2))
(-1+x)/(x+1)/(x^3+x^2+x)^(1/2)
(x+(x^2+1)^(1/2))^(1/2)
(1+sin(x))^(1/2)
(2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1)
1/(x^(41/25)+x^(9/25))
1/(x^(3/2)-x^2)^(1/2)
x/((-1+x)^(1/2)+(x+1)^(1/2))
exp(exp(x))-exp(-x+exp(x))
(x+exp(1)+1)*x^exp(x)*exp(x)
ln(x/Pi)/(ln(x)^ln(exp(1)*Pi))
(3*x^3+2*x^2+1)/(x^2+1)^(1/3)
(cos(x)-sin(x))/(2+sin(2*x))
(1/x*ln(1/x))^(1/2)
1/((x+1)^3*(-1+x))^(1/2)
sin(23*x)/sin(x)
x^(-ln(x))
exp(cos(x))*cos(2*x+sin(x))
((x+1)^(1/2)-x^(1/2))^Pi
(1+x^2+(x^4+x^2+1)^(1/2))^(1/2)
Giac
-----
ln(x+1)/(x^2+1)
(csc(x)-sin(x))^(1/2)
1/x^2/(x^4+1)^(3/4)
x^(1/2)/((2012-x)^(1/2)+x^(1/2))
(-1+x)/(x+1)/(x^3+x^2+x)^(1/2)
(csc(x)-sin(x))^(1/2)
(x+(x^2+1)^(1/2))^(1/2)
(csc(x)-sin(x))^(1/2)
sin(x+1/4*Pi)^2/exp(x^2)
cos(x)^(cos(x)+1)*tan(x)*(1+ln(cos(x)))
(2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1)
exp(-2019/4/x^2)/x^2
x^(x^2+1)*(1+2*ln(x))
exp(exp(x))-exp(-x+exp(x))
(x+exp(1)+1)*x^exp(x)*exp(x)
ln(x/Pi)/(ln(x)^ln(exp(1)*Pi))
(1-(-1/2*Pi+arcsin(sin(x)))^2)^(1/2)
(3*x^3+2*x^2+1)/(x^2+1)^(1/3)
(1/x*ln(1/x))^(1/2)
sin(1/x^11)
x*(exp(-x)+1)/(exp(x)-1)
ln(3^(1/2)+tan(x))
x^(1/3)*(1-x)^(2/3)
x*cot(x)
((x+1)^(1/2)-x^(1/2))^Pi
(1+x^2+(x^4+x^2+1)^(1/2))^(1/2)
Mupad
------
ln(x+1)/(x^2+1)
(x/(-x^3+1))^(1/2)
1/(1+x^(1/2))/(-x^2+x)^(1/2)
x*arcsin(x)/(-x^2+1)^(1/2)
sin(x)*(1+tan(x)^2)^(1/2)
sin(x)*ln(sin(x))
1/(1-ln(1-x))
(x+(x^2+1)^(1/2))^(1/2)
sin(x+1/4*Pi)^2/exp(x^2)
(2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1)
1/(x^(3/2)-x^2)^(1/2)
exp(-x^40)
arcsin(x)/x^3
(arctan(x)+arccot(x))/x
(x+exp(1)+1)*x^exp(x)*exp(x)
(2*x^2022+1)/(x^2023+x)
ln(x/Pi)/(ln(x)^ln(exp(1)*Pi))
(1-(-1/2*Pi+arcsin(sin(x)))^2)^(1/2)
(3*x^3+2*x^2+1)/(x^2+1)^(1/3)
(sec(1+ln(x))^2-tan(1+ln(x)))/x^2
(1/x*ln(1/x))^(1/2)
(4-(x+1)^2)^(1/2)-3^(1/2)-(-x^2+4)^(1/2)
arcsin(x)*arccos(x)
sin(1/x^11)
x*(exp(-x)+1)/(exp(x)-1)
ln(3^(1/2)+tan(x))
x^(1/3)*(1-x)^(2/3)
x*cot(x)
x^(-ln(x))
cos(1/2*Pi*x^2*2^(1/2))^2
((x+1)^(1/2)-x^(1/2))^Pi
tan(x)^(1/3)/(cos(x)+sin(x))^2
(1+x^2+(x^4+x^2+1)^(1/2))^(1/2)
Sympy
------
sqrt(tan(x))
ln(x+1)/(x^2+1)
x^(1/2)/(x^(1/2)-x^(1/3))
1/(sin(x)+sec(x))
1/(1+exp(x)+exp(2*x))^(1/2)
(csc(x)-sin(x))^(1/2)
1/(9*cos(x)^2+4*sin(x)^2)
(x/(-x^3+1))^(1/2)
sin(101*x)*sin(x)^99
((1-x)/(x+1))^(1/2)
1/(1+x^(1/2))/(-x^2+x)^(1/2)
x^(1/2)/((2012-x)^(1/2)+x^(1/2))
(-1+x)/(x+1)/(x^3+x^2+x)^(1/2)
(csc(x)-sin(x))^(1/2)
sin(x)*(1+tan(x)^2)^(1/2)
x*sec(4*x)^2
1/(1-ln(1-x))
exp(sin(x))/tan(x)/csc(x)
(csc(x)-sin(x))^(1/2)
1/(sin(x)^4+cos(x)^4)
(1+2*x*exp(x^2))*cos(x)-(x+exp(x^2))*sin(x)
arccosh(x)
tanh(x)/exp(x)
(1+sin(x))^(1/2)
sin(x+1/4*Pi)^2/exp(x^2)
cos(x)/(1-cos(2*x))
(2018*x^2017+2017*x^2016)/(x^4036+2*x^4035+x^4034+1)
1/(x^(41/25)+x^(9/25))
1/(x^(3/2)-x^2)^(1/2)
exp(x+exp(x))+exp(x-exp(x))
(sin(20*x)+sin(19*x))/(cos(20*x)+cos(19*x))
(arctan(x)+arccot(x))/x
x/((-1+x)^(1/2)+(x+1)^(1/2))
sin(x+sin(x))-sin(x-sin(x))
1/(1+sin(x))+1/(1+cos(x))+1/(tan(x)+1)+1/(1+cot(x))+1/(1+sec(x))+1/(1+csc(x))
(x+exp(1)+1)*x^exp(x)*exp(x)
x^2/(-x^2+2)+2^(1/2)*(x/(x+1))^(1/2)
(2*x^2022+1)/(x^2023+x)
(1-(-1/2*pi+arcsin(sin(x)))^2)^(1/2)
(cos(x)-sin(x))/(2+sin(2*x))
(sec(1+ln(x))^2-tan(1+ln(x)))/x^2
(1/x*ln(1/x))^(1/2)
x*(exp(-x)+1)/(exp(x)-1)
ln(3^(1/2)+tan(x))
((sin(20*x)+3*sin(21*x)+sin(22*x))^2+(cos(20*x)+3*cos(21*x)+cos(22*x))^2)^(1/2)
exp(-2*x)*sin(3*x)/x
x*cot(x)
1/((x+1)^3*(-1+x))^(1/2)
x^(-ln(x))
exp(cos(x))*cos(2*x+sin(x))
sin(4*arctan(x))
tan(x)^(1/3)/(cos(x)+sin(x))^2
sin(2*x)^2*sin(3*x)^2*sin(5*x)^2*sin(30*x)^2/sin(x)^2/sin(6*x)^2/sin(10*x)^2/sin(15*x)^2
(1+x^2+(x^4+x^2+1)^(1/2))^(1/2)
On Friday, March 3, 2023 at 12:58:37 PM UTC-6 Nasser M. Abbasi wrote:
> fyi;
>
> MIT Integration Bee problems are now included in the CAS integration tests.
>
> These problems came from https://math.mit.edu/~yyao1/integrationbee.html
>
> Updated the summer 2022 edition of the CAS integration tests pages to
> include these problems showing the result for all CAS systems currently
> supported. They can be found under the link called
>
> "links to individual test reports"
>
> Starting at file #211 in the list
>
> <
> https://12000.org/my_notes/CAS_integration_tests/reports/summer_2022/index.htm/
> >
>
> At the very bottom of the page.
> (one file per year starting from 2010, and per each competition held) so
> they match the order shown in the MIT page above.
>
> A number (may be half) of the MIT integration problems are definite,
> so those were solved as indefinite integration only as that is the only
> mode supported.
>
> 316 new integrals were added. The total number of integrals now is 85,795.
>
> This is the result of percentage solved per each CAS just
> for the MIT problems section (i.e. 316 problems).
>
> =============
>
> 1. Mathematica 13.2.1 98.73 %
> 2. Fricas 1.3.8/sage 9.8 96.52 %
> 3. Maple 2022.2 94.3 %
> 4. Rubi 4.16.1 93.35 %
> 5. Maxima 5.46/sage 9.8 92.41 %
> 6. Giac 1.9.0-37/sage 9.8 91.77 %
> 7. Mupad Matlab 2021a 89.56 %
> 8. Sympy 1.11.1 82.28 %
>
> Any problems, issues, please let me know so I can fix it.
>
> --Nasser
>
> On Wednesday, March 1, 2023 at 12:45:36 AM UTC-6 [email protected] wrote:
>
>> https://math.mit.edu/~yyao1/integrationbee.html
>>
>> See the Test and Answers at the bottom of the page.
>> It would be interesting to see how many can be integrated.
>>
>> Tim
>>
>>
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