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, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142 }

B grade: { 34 }

C grade: { }

F grade: { 28, 32 }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 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, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 131, 134, 135, 136, 137, 138, 139, 140, 141, 142 }

B grade: { 7, 21, 22, 63, 99, 101, 102, 124, 130, 132, 133 }

C grade: { }

F grade: { }

2.1.3 Maple

A grade: { 2, 3, 4, 9, 11, 12, 13, 18, 29, 30, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 139, 140 }

B grade: { 34, 35, 51, 67 }

C grade: { 31, 32, 33 }

F grade: { 1, 5, 6, 7, 8, 10, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 53, 54, 55, 56, 137, 138, 141, 142 }

2.1.4 Maxima

A grade: { 9, 18, 29, 30, 31, 32, 33, 38, 47, 48, 49, 50, 51, 52, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 79, 80, 81, 82, 84, 104, 105, 106, 107, 110, 111, 112, 113, 115 }

B grade: { 2, 3, 4, 11, 12, 13, 34, 35, 39, 40, 41, 42, 43, 44, 45, 46, 63, 77, 78, 83, 88, 90, 91, 93, 97, 99, 100, 102, 103, 108, 109, 114, 119, 121, 122, 124, 128, 130, 131, 133, 134, 135, 136, 139, 140 }

C grade: { 36, 37, 85, 86, 87, 89, 92, 94, 95, 96, 98, 101, 116, 117, 118, 120, 123, 125, 126, 127, 129, 132 }

F grade: { 1, 5, 6, 7, 8, 10, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 53, 54, 55, 56, 137, 138, 141, 142 }

2.1.5 FriCAS

A grade: { 2, 3, 4, 9, 11, 12, 13, 18, 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, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 76, 77, 78, 85, 86, 87, 88, 89, 94, 95, 96, 104, 107, 108, 109, 116, 117, 118, 119, 120, 125, 126, 127, 135, 136, 139, 140 }

B grade: { 63, 70, 74, 75, 79, 80, 81, 82, 83, 84, 90, 91, 92, 93, 97, 98, 99, 100, 101, 102, 103, 105, 106, 110, 111, 112, 113, 114, 115, 121, 122, 123, 124, 128, 129, 130, 131, 132, 133, 134 }

C grade: { }

F grade: { 1, 5, 6, 7, 8, 10, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 53, 54, 55, 56, 137, 138, 141, 142 }

2.1.6 Sympy

A grade: { 3, 4, 9, 12, 13, 18, 29, 30, 34, 35, 38, 39, 40, 41, 42, 44, 47, 48, 49, 50, 51, 52, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 73, 104, 135, 136, 139, 140 }

B grade: { }

C grade: { }

F grade: { 1, 2, 5, 6, 7, 8, 10, 11, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 31, 32, 33, 36, 37, 43, 45, 46, 53, 54, 55, 56, 57, 58, 59, 60, 63, 68, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 141, 142 }

2.1.7 Giac

A grade: { 9, 18, 29, 30, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 104, 105, 106 }

B grade: { 31, 32, 63, 70, 79, 80, 81, 82, 83, 84, 110, 111, 112, 113, 114, 115 }

C grade: { 2, 3, 4, 11, 12, 13, 34, 35, 135, 136, 139, 140 }

F grade: { 1, 5, 6, 7, 8, 10, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 33, 36, 37, 53, 54, 55, 56, 57, 58, 59, 60, 76, 77, 78, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 107, 108, 109, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 141, 142 }

2.1.8 Mupad

A grade: { 29, 30 }

B grade: { 2, 3, 4, 9, 11, 12, 13, 18, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 104, 135, 136, 139, 140 }

C grade: { }

F grade: { 1, 5, 6, 7, 8, 10, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 53, 54, 55, 56, 57, 58, 59, 60, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 138, 141, 142 }

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 \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)