Chapter 2
detailed summary tables of results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 20, 22, 23, 24, 25, 26, 28, 29, 31, 32, 34, 36, 38, 47, 48, 49, 50, 51, 52, 53 }

B grade: { 10, 17, 19, 27, 30, 33, 35, 39 }

C grade: { 21, 37, 40, 41, 42, 43, 44, 45, 46 }

F grade: { }

2.1.3 Maple

A grade: { 5, 9, 10, 11, 12, 13, 14, 15, 50, 51, 52 }

B grade: { 1, 2, 3, 4, 6, 7, 8, 16, 17, 18, 19, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 43, 44, 45, 48, 49 }

C grade: { 53 }

F grade: { 20, 21, 26, 27, 36, 37, 41, 42, 46, 47 }

2.1.4 Maxima

A grade: { 11, 13, 15

B grade: { 1, 2, 3, 4, 9, 50 }

C grade: { 10, 12, 14 }

F grade: { 5, 6, 7, 8, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53 }

2.1.5 FriCAS

A grade: { 10, 11, 12, 14, 15 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 9, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 50, 51, 52, 53 }

C grade: { 29, 31, 49 }

F grade: { 8, 23, 46 }

2.1.6 Sympy

A grade: { 3, 4, 5, 9 }

B grade: { 50 }

C grade: { }

F grade: { 1, 2, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53 }

2.1.7 Giac

A grade: { 5, 11, 15, 50 }

B grade: { 1, 2, 3, 4, 6, 7, 8, 9, 13, 28, 30, 48 }

C grade: { 10, 12, 14, 29, 31, 49 }

F grade: { 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 51, 52, 53 }

2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [50] had the largest ratio of [ 0.625 ]