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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi only. 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 also given. The larger this ratio is, the harder the integral is to solve. In this test file, problem number [77] had the largest ratio of [.540541000000000049]

# 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 2 2 1.00 21 0.095
2 A 2 2 1.00 23 0.087
3 A 2 2 1.00 25 0.080
4 A 2 2 1.00 27 0.074
5 A 2 2 1.00 29 0.069
6 A 2 2 1.00 17 0.118
7 A 3 3 1.00 22 0.136
8 A 9 8 1.07 25 0.320
9 A 7 6 1.03 25 0.240
10 A 5 4 1.00 23 0.174
11 A 5 4 1.02 18 0.222
12 A 6 5 1.06 25 0.200
13 A 6 5 1.10 25 0.200
14 A 8 7 1.14 25 0.280
15 A 9 8 1.07 25 0.320
16 A 7 6 1.03 25 0.240
17 A 5 4 1.00 23 0.174
18 A 5 4 1.02 18 0.222
19 A 7 6 1.06 25 0.240
20 A 7 6 1.09 25 0.240
21 A 9 8 1.15 25 0.320
22 A 9 8 1.21 26 0.308
23 A 8 7 1.21 26 0.269
24 A 7 6 1.21 24 0.250
25 A 5 4 1.16 23 0.174
26 A 6 5 1.48 26 0.192
27 A 3 3 1.18 26 0.115
28 A 4 4 1.12 26 0.154
29 A 5 5 1.14 26 0.192
30 A 6 6 1.16 26 0.231
31 A 5 4 1.00 24 0.167
32 A 6 5 1.00 36 0.139
33 A 3 3 0.96 45 0.067
34 A 5 5 1.00 39 0.128
35 A 16 16 1.09 35 0.457
36 A 14 14 1.08 35 0.400
37 A 12 12 1.08 33 0.364
38 A 10 10 1.06 28 0.357
39 A 15 14 1.09 35 0.400
40 A 15 14 1.07 35 0.400
41 A 16 15 1.08 35 0.429
42 A 18 17 1.10 35 0.486
43 A 13 12 1.05 35 0.343
44 A 14 14 1.08 35 0.400
45 A 12 12 1.07 35 0.343
46 A 10 10 1.06 33 0.303
47 A 8 8 1.03 28 0.286
48 A 13 12 1.07 35 0.343
49 A 15 14 1.07 35 0.400
50 A 17 16 1.09 35 0.457
51 A 12 12 1.07 35 0.343
52 A 10 10 1.07 35 0.286
53 A 8 8 1.03 33 0.242
54 A 3 3 1.00 28 0.107
55 A 10 9 1.08 35 0.257
56 A 15 14 1.06 35 0.400
57 A 17 16 1.09 35 0.457
58 A 9 8 1.11 35 0.229
59 A 2 2 1.00 35 0.057
60 A 11 11 1.07 35 0.314
61 A 10 10 1.07 35 0.286
62 A 9 9 1.05 35 0.257
63 A 6 6 1.03 33 0.182
64 A 3 3 1.00 28 0.107
65 A 6 5 1.16 35 0.143
66 A 14 13 1.05 35 0.371
67 A 16 15 1.08 35 0.429
68 A 3 3 1.00 36 0.083
69 A 6 6 1.00 33 0.182
70 A 5 4 1.19 35 0.114
71 A 2 2 1.00 35 0.057
72 A 2 2 1.00 35 0.057
73 A 4 3 1.24 36 0.083
74 A 5 4 1.24 31 0.129
75 A 4 3 1.23 40 0.075
76 A 5 4 1.23 31 0.129
77 A 21 20 1.25 37 0.541
78 A 19 18 1.27 37 0.486
79 A 16 15 1.27 37 0.405
80 A 15 14 1.30 37 0.378
81 A 15 14 1.30 37 0.378
82 A 17 16 1.27 37 0.432
83 A 14 13 1.31 37 0.351
84 A 17 16 1.29 37 0.432
85 A 19 18 1.27 37 0.486
86 A 17 16 1.27 37 0.432
87 A 14 13 1.30 37 0.351
88 A 13 12 1.67 37 0.324
89 A 11 10 1.01 37 0.270
90 A 13 12 1.33 37 0.324
91 A 14 13 1.31 37 0.351
92 A 17 16 1.29 37 0.432
93 A 17 16 1.27 37 0.432
94 A 15 14 1.30 37 0.378
95 A 13 12 1.67 37 0.324
96 A 4 3 1.00 37 0.081
97 B 7 6 6.03 37 0.162
98 A 13 12 1.33 37 0.324
99 A 8 7 1.00 37 0.189
100 A 3 2 1.29 37 0.054
101 A 14 13 1.29 37 0.351
102 A 17 16 1.52 37 0.432
103 A 4 3 1.00 37 0.081
104 B 4 3 2.32 37 0.081
105 B 11 10 2.72 37 0.270
106 A 12 11 1.33 37 0.297
107 A 10 9 0.99 37 0.243
108 A 3 2 1.00 37 0.054
109 A 3 2 1.23 37 0.054
110 A 6 5 1.00 37 0.135
111 F 0 0 N/A 0.000 N/A
112 A 2 2 1.00 25 0.080
113 A 2 2 1.00 25 0.080
114 A 2 2 1.00 25 0.080
115 A 2 2 1.00 23 0.087
116 A 2 2 1.00 22 0.091
117 A 2 2 1.00 25 0.080
118 A 2 2 1.00 25 0.080
119 A 2 2 1.00 23 0.087
120 A 2 2 1.01 25 0.080
121 A 2 2 1.00 27 0.074
122 A 2 2 1.00 29 0.069
123 A 2 2 1.00 25 0.080
124 A 3 3 1.00 25 0.120
125 A 3 3 1.00 29 0.103
126 A 3 3 1.00 27 0.111
127 A 3 3 1.00 29 0.103
128 A 3 3 1.01 29 0.103
129 A 3 3 1.00 29 0.103
130 A 3 3 0.78 29 0.103
131 A 4 4 0.68 29 0.138
132 A 13 13 0.73 31 0.419
133 A 11 11 0.89 31 0.355
134 A 3 3 0.78 29 0.103
135 A 3 3 0.90 24 0.125
136 A 5 5 1.07 27 0.185
137 A 6 6 0.99 29 0.207
138 A 4 4 1.00 29 0.138
139 B 6 6 2.03 29 0.207
140 A 5 5 1.35 29 0.172
141 A 4 4 1.00 27 0.148
142 A 3 3 1.00 22 0.136
143 N/A 1 0 1.00 29 0.000
144 A 4 4 1.00 33 0.121
145 A 4 4 1.00 34 0.118
146 A 5 5 1.00 34 0.147
147 A 3 3 0.99 34 0.088
148 A 4 4 1.03 34 0.118
149 A 7 7 1.20 31 0.226
150 A 5 5 1.03 30 0.167
151 A 10 9 1.00 33 0.273
152 A 9 8 1.00 33 0.242
153 A 8 7 1.04 33 0.212
154 A 9 8 1.57 30 0.267
155 A 4 4 1.35 29 0.138
156 A 10 9 1.62 32 0.281
157 A 9 8 1.62 32 0.250
158 A 7 6 1.23 32 0.188
159 A 8 7 1.15 32 0.219

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