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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 [128] had the largest ratio of [.7778]

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 9 6 1.00 17 0.353
2 A 9 6 1.00 18 0.333
3 A 3 3 1.00 18 0.167
4 A 3 3 1.00 19 0.158
5 A 5 3 1.00 17 0.176
6 A 3 2 1.00 17 0.118
7 A 2 2 1.00 17 0.118
8 A 2 2 1.00 17 0.118
9 A 5 3 1.00 27 0.111
10 A 3 2 1.00 28 0.071
11 A 5 3 1.00 21 0.143
12 A 3 2 1.00 22 0.091
13 A 3 3 1.00 15 0.200
14 A 5 3 1.00 26 0.115
15 A 5 3 1.00 26 0.115
16 A 5 3 1.00 27 0.111
17 A 5 3 1.00 27 0.111
18 A 3 2 1.00 27 0.074
19 A 3 2 1.00 27 0.074
20 A 3 2 1.00 28 0.071
21 A 3 2 1.00 28 0.071
22 A 3 2 1.00 30 0.067
23 A 5 3 1.00 29 0.103
24 A 6 4 1.00 29 0.138
25 A 3 2 1.00 32 0.062
26 A 5 3 1.00 31 0.097
27 A 5 3 1.00 22 0.136
28 A 5 3 1.00 23 0.130
29 A 3 2 1.00 22 0.091
30 A 3 2 1.00 22 0.091
31 A 3 3 1.00 22 0.136
32 A 5 3 1.00 22 0.136
33 A 5 3 1.00 22 0.136
34 A 5 3 1.00 20 0.150
35 A 5 3 1.00 17 0.176
36 A 5 3 1.00 22 0.136
37 A 5 3 1.00 22 0.136
38 A 5 3 1.00 22 0.136
39 A 2 2 1.00 22 0.091
40 A 7 3 1.00 22 0.136
41 A 5 3 1.00 22 0.136
42 A 3 2 1.00 22 0.091
43 A 3 2 1.00 22 0.091
44 A 3 2 1.00 22 0.091
45 A 2 2 1.00 22 0.091
46 A 3 2 1.00 22 0.091
47 A 3 2 1.00 22 0.091
48 A 3 2 1.00 20 0.100
49 A 3 2 1.00 17 0.118
50 A 3 2 1.00 22 0.091
51 A 3 2 1.00 22 0.091
52 A 3 2 1.00 22 0.091
53 A 3 3 1.00 22 0.136
54 A 7 3 1.00 22 0.136
55 A 5 3 1.00 22 0.136
56 A 5 3 1.00 18 0.167
57 A 3 2 1.00 18 0.111
58 A 3 2 1.00 18 0.111
59 A 3 2 1.00 18 0.111
60 A 2 2 1.00 18 0.111
61 A 5 3 1.00 16 0.188
62 A 5 3 1.00 13 0.231
63 A 5 3 1.00 18 0.167
64 A 2 2 1.00 18 0.111
65 A 7 3 1.00 18 0.167
66 A 5 3 1.00 18 0.167
67 A 5 3 1.00 18 0.167
68 A 3 2 1.00 20 0.100
69 A 3 2 1.00 20 0.100
70 A 3 2 1.00 20 0.100
71 A 3 2 1.00 20 0.100
72 A 2 2 1.00 20 0.100
73 A 3 2 1.00 18 0.111
74 A 3 2 1.00 15 0.133
75 A 3 2 1.00 20 0.100
76 A 3 3 1.00 20 0.150
77 A 5 3 1.00 20 0.150
78 A 5 3 1.00 20 0.150
79 A 5 3 1.00 20 0.150
80 A 5 3 1.00 23 0.130
81 A 5 3 1.00 22 0.136
82 A 3 3 1.00 20 0.150
83 A 3 2 1.00 22 0.091
84 A 3 2 1.00 22 0.091
85 A 3 2 1.00 18 0.111
86 A 9 5 1.00 18 0.278
87 A 10 6 1.00 18 0.333
88 A 9 5 1.00 18 0.278
89 A 10 6 1.00 18 0.333
90 A 9 5 1.00 29 0.172
91 A 9 5 1.00 26 0.192
92 A 9 5 1.00 24 0.208
93 A 9 5 1.00 22 0.227
94 A 9 5 1.00 25 0.200
95 A 9 5 1.00 31 0.161
96 A 9 5 1.00 32 0.156
97 A 9 5 1.00 23 0.217
98 A 9 5 1.00 25 0.200
99 A 9 5 1.00 29 0.172
100 A 9 5 1.00 32 0.156
101 A 2 1 1.00 17 0.059
102 A 2 1 1.00 17 0.059
103 A 2 1 1.00 17 0.059
104 A 2 1 1.00 15 0.067
105 A 3 2 1.00 17 0.118
106 A 3 3 1.00 17 0.176
107 A 3 3 1.00 17 0.176
108 A 4 4 1.00 17 0.235
109 A 2 1 1.00 19 0.053
110 A 2 1 1.00 19 0.053
111 A 2 1 1.00 17 0.059
112 A 2 1 1.00 9 0.111
113 A 3 2 1.00 19 0.105
114 A 4 3 1.00 19 0.158
115 A 5 4 1.00 19 0.210
116 A 5 5 1.00 19 0.263
117 A 5 5 1.00 19 0.263
118 A 11 7 1.00 19 0.368
119 A 11 7 1.00 19 0.368
120 A 11 7 1.00 19 0.368
121 A 9 6 1.00 17 0.353
122 A 9 6 1.00 9 0.667
123 A 12 8 1.00 19 0.421
124 A 14 9 1.00 19 0.474
125 A 11 8 1.00 19 0.421
126 A 11 8 1.00 19 0.421
127 A 10 7 1.00 17 0.412
128 A 10 7 1.00 9 0.778
129 A 22 9 1.00 19 0.474
130 A 24 10 1.00 19 0.526
131 A 4 3 1.00 24 0.125
132 A 4 3 1.00 24 0.125
133 A 3 3 1.00 24 0.125
134 A 2 2 1.00 22 0.091
135 A 5 5 1.00 24 0.208
136 A 6 6 1.00 24 0.250
137 A 6 6 1.00 26 0.231
138 A 3 3 1.00 26 0.115
139 A 4 4 1.00 26 0.154
140 A 6 6 1.00 26 0.231
141 A 5 5 1.00 28 0.179
142 A 4 4 1.00 28 0.143
143 A 3 3 1.00 28 0.107
144 A 3 3 1.00 28 0.107
145 A 4 4 1.00 28 0.143
146 A 6 6 1.00 28 0.214
147 A 5 5 1.00 29 0.172
148 A 4 4 1.00 29 0.138
149 A 3 3 1.00 29 0.103
150 A 3 3 1.00 29 0.103
151 A 4 4 1.00 29 0.138
152 A 6 6 1.00 29 0.207
153 A 2 2 1.00 19 0.105
154 A 3 3 1.67 19 0.158
155 A 7 5 0.99 31 0.161
156 A 4 3 1.00 39 0.077
157 A 4 3 1.00 39 0.077
158 A 3 3 1.00 39 0.077
159 A 2 2 1.00 37 0.054
160 A 5 5 1.00 39 0.128
161 A 6 6 1.00 39 0.154
162 A 7 7 1.00 41 0.171
163 A 6 6 1.00 41 0.146
164 A 3 3 1.00 41 0.073
165 A 4 4 1.00 41 0.098
166 A 6 6 1.00 41 0.146
167 A 2 1 1.00 22 0.045
168 A 2 1 1.00 22 0.045
169 A 2 1 1.00 22 0.045
170 A 2 1 1.00 20 0.050
171 A 3 2 1.00 22 0.091
172 A 3 3 1.00 22 0.136
173 A 3 3 1.00 22 0.136
174 A 4 4 1.00 22 0.182
175 A 2 1 1.00 24 0.042
176 A 2 1 1.00 24 0.042
177 A 2 1 1.00 22 0.045
178 A 2 1 1.00 14 0.071
179 A 3 2 1.00 24 0.083
180 A 4 3 1.00 24 0.125
181 A 5 4 1.00 24 0.167
182 A 5 4 1.00 24 0.167
183 A 5 4 1.00 24 0.167
184 A 3 3 1.00 22 0.136
185 A 3 3 1.00 23 0.130
186 A 5 3 1.00 24 0.125
187 A 5 3 1.00 24 0.125
188 A 5 3 1.00 24 0.125
189 A 3 2 1.00 22 0.091
190 A 3 2 1.00 14 0.143
191 A 6 3 1.00 24 0.125
192 A 8 4 1.00 24 0.167
193 A 4 3 1.00 24 0.125
194 A 4 3 1.00 24 0.125
195 A 4 3 1.00 22 0.136
196 A 4 3 1.00 14 0.214
197 A 10 4 1.00 24 0.167
198 A 12 5 1.00 24 0.208
199 A 7 5 1.00 24 0.208
200 A 6 5 1.00 24 0.208
201 A 5 5 1.00 24 0.208
202 A 4 4 1.00 24 0.167
203 A 4 4 1.00 24 0.167
204 A 4 4 1.00 24 0.167
205 A 4 4 1.00 24 0.167
206 A 5 5 1.00 24 0.208
207 A 6 5 0.99 24 0.208
208 A 7 5 1.00 24 0.208
209 A 2 2 1.00 40 0.050
210 A 2 2 1.00 40 0.050
211 A 2 2 1.00 46 0.043
212 A 2 2 1.00 46 0.043

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