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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 [63] had the largest ratio of [.5556]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 5 4 1.00 25 0.160
2 A 5 4 1.00 27 0.148
3 A 5 4 1.00 27 0.148
4 A 8 8 1.00 27 0.296
5 A 9 9 1.00 27 0.333
6 A 9 6 1.00 30 0.200
7 A 5 3 1.00 30 0.100
8 A 6 4 1.00 30 0.133
9 A 7 5 1.00 30 0.167
10 A 5 4 1.00 23 0.174
11 A 5 4 1.00 23 0.174
12 A 5 4 1.00 30 0.133
13 A 6 5 0.99 28 0.179
14 A 6 5 1.00 30 0.167
15 A 9 5 0.98 30 0.167
16 A 10 6 0.99 30 0.200
17 A 5 5 1.00 34 0.147
18 A 5 5 1.00 34 0.147
19 A 9 6 1.00 32 0.188
20 A 10 7 1.00 32 0.219
21 A 5 3 1.00 32 0.094
22 A 5 3 1.00 29 0.103
23 A 5 3 1.00 29 0.103
24 A 6 6 1.00 26 0.231
25 A 5 4 1.00 30 0.133
26 A 7 6 1.00 30 0.200
27 A 7 6 1.00 30 0.200
28 A 5 3 1.00 30 0.100
29 A 6 4 1.00 30 0.133
30 A 7 5 1.00 30 0.167
31 A 2 2 1.00 26 0.077
32 A 5 5 1.00 26 0.192
33 A 2 2 1.00 24 0.083
34 A 5 5 1.00 20 0.250
35 A 6 5 1.00 36 0.139
36 A 2 2 1.00 36 0.056
37 A 2 2 1.00 32 0.062
38 A 13 9 1.00 32 0.281
39 A 5 5 1.00 38 0.132
40 A 6 6 1.00 35 0.171
41 A 5 5 1.00 33 0.152
42 A 5 5 1.00 32 0.156
43 A 8 8 1.00 35 0.229
44 A 8 8 1.00 35 0.229
45 A 8 8 1.00 35 0.229
46 A 6 6 1.00 38 0.158
47 A 5 5 1.00 36 0.139
48 A 5 5 1.00 35 0.143
49 A 7 6 1.00 38 0.158
50 A 7 6 1.00 38 0.158
51 A 7 6 1.00 38 0.158
52 A 9 6 1.00 27 0.222
53 A 9 6 1.00 25 0.240
54 A 8 5 1.00 24 0.208
55 A 12 9 1.00 27 0.333
56 A 18 12 1.00 27 0.444
57 A 22 13 1.00 27 0.482
58 A 10 7 1.00 27 0.259
59 A 10 7 1.00 25 0.280
60 A 9 6 1.00 24 0.250
61 A 17 11 1.00 27 0.407
62 A 21 14 1.00 27 0.518
63 A 26 15 1.00 27 0.556
64 A 10 6 1.00 27 0.222
65 A 8 5 1.00 27 0.185
66 A 5 3 1.00 25 0.120
67 A 5 3 1.00 24 0.125
68 A 10 7 1.00 27 0.259
69 A 11 8 1.00 27 0.296
70 A 15 9 1.00 27 0.333
71 A 10 7 1.00 27 0.259
72 A 6 4 1.00 27 0.148
73 A 6 4 1.00 25 0.160
74 A 6 4 1.00 24 0.167
75 A 12 9 1.00 27 0.333
76 A 14 11 1.00 27 0.407
77 A 15 9 1.00 28 0.321
78 A 9 6 1.00 28 0.214
79 A 9 6 1.00 26 0.231
80 A 8 5 1.00 25 0.200
81 A 17 9 1.00 28 0.321
82 A 16 8 1.00 28 0.286
83 A 20 10 1.00 28 0.357
84 A 17 10 1.00 28 0.357
85 A 10 7 1.00 28 0.250
86 A 10 7 1.00 26 0.269
87 A 9 6 1.00 25 0.240
88 A 19 11 1.00 28 0.393
89 A 18 10 1.00 28 0.357
90 A 26 13 1.00 28 0.464
91 A 9 6 1.00 24 0.250
92 A 8 6 1.00 22 0.273
93 A 10 9 1.00 17 0.529
94 A 13 7 1.00 28 0.250
95 A 10 6 1.00 28 0.214
96 A 8 5 1.00 28 0.179
97 A 5 3 1.00 26 0.115
98 A 5 3 1.00 25 0.120
99 A 9 4 1.00 28 0.143
100 A 10 5 1.00 28 0.179
101 A 13 6 1.00 28 0.214
102 A 13 9 1.00 28 0.321
103 A 9 6 1.00 28 0.214
104 A 6 4 1.00 28 0.143
105 A 6 4 1.00 26 0.154
106 A 6 4 1.00 25 0.160
107 A 12 7 1.00 28 0.250
108 A 12 7 1.00 28 0.250
109 A 9 6 1.00 30 0.200
110 A 9 6 1.00 28 0.214
111 A 8 5 1.00 27 0.185
112 A 17 9 1.00 30 0.300
113 A 23 10 1.00 30 0.333
114 A 12 6 1.00 30 0.200
115 A 8 5 1.00 30 0.167
116 A 5 3 1.00 28 0.107
117 A 5 3 1.00 27 0.111
118 A 9 4 1.00 30 0.133
119 A 12 5 1.00 30 0.167
120 A 16 7 1.00 30 0.233
121 A 10 7 1.00 30 0.233
122 A 6 4 1.00 30 0.133
123 A 6 4 1.00 28 0.143
124 A 6 4 1.00 27 0.148
125 A 12 7 1.00 30 0.233
126 A 24 14 1.00 30 0.467
127 A 20 13 1.00 30 0.433
128 A 16 12 1.00 30 0.400
129 A 6 4 1.01 28 0.143
130 A 10 8 1.00 27 0.296
131 A 17 11 1.00 30 0.367
132 A 20 12 1.00 30 0.400
133 A 8 6 1.00 34 0.176
134 A 6 5 1.00 30 0.167
135 A 3 3 1.00 34 0.088
136 A 5 5 1.00 34 0.147
137 A 7 7 1.00 34 0.206
138 A 1 1 1.00 17 0.059
139 A 1 1 1.00 15 0.067
140 A 2 2 1.00 23 0.087
141 A 3 3 1.00 21 0.143
142 A 2 2 1.00 40 0.050
143 A 2 2 1.00 104 0.019

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