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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 [177] had the largest ratio of [.5294]

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 2 1 1.00 17 0.059
2 A 2 1 1.00 17 0.059
3 A 2 1 1.00 17 0.059
4 A 2 1 1.00 15 0.067
5 A 7 7 1.00 17 0.412
6 A 7 7 1.00 17 0.412
7 A 8 8 1.00 17 0.471
8 A 2 1 1.00 19 0.053
9 A 2 1 1.00 19 0.053
10 A 2 1 1.00 17 0.059
11 A 8 7 1.00 19 0.368
12 A 9 8 1.00 19 0.421
13 A 8 8 1.00 19 0.421
14 A 8 7 1.00 19 0.368
15 A 8 7 1.00 19 0.368
16 A 8 7 1.00 19 0.368
17 A 7 7 1.00 17 0.412
18 A 13 7 1.00 19 0.368
19 A 14 8 1.00 19 0.421
20 A 9 8 1.00 19 0.421
21 A 9 8 1.00 19 0.421
22 A 9 8 1.00 19 0.421
23 A 9 8 1.00 19 0.421
24 A 7 7 1.00 17 0.412
25 A 14 8 1.00 19 0.421
26 A 15 9 1.00 19 0.474
27 A 3 3 1.00 20 0.150
28 A 2 2 1.00 20 0.100
29 A 2 2 1.00 20 0.100
30 A 2 2 1.00 20 0.100
31 A 3 3 1.00 20 0.150
32 A 4 3 1.00 20 0.150
33 A 5 3 1.00 20 0.150
34 C 2 2 0.15 22 0.091
35 A 4 4 1.00 22 0.182
36 A 3 3 1.00 22 0.136
37 A 3 3 1.00 22 0.136
38 A 3 3 1.00 22 0.136
39 A 3 2 1.00 22 0.091
40 A 4 3 1.00 22 0.136
41 A 5 4 1.00 22 0.182
42 A 6 4 1.00 22 0.182
43 A 4 3 1.00 19 0.158
44 A 3 3 1.00 19 0.158
45 A 2 2 1.00 19 0.105
46 A 2 2 1.00 19 0.105
47 A 2 2 1.00 19 0.105
48 A 3 3 1.00 19 0.158
49 A 4 3 1.00 19 0.158
50 A 5 3 1.00 19 0.158
51 A 5 4 1.00 21 0.190
52 A 4 4 1.00 21 0.190
53 A 3 3 1.00 21 0.143
54 A 3 3 1.00 21 0.143
55 A 3 3 1.00 21 0.143
56 A 3 2 1.00 21 0.095
57 A 4 3 1.00 21 0.143
58 A 5 4 1.00 21 0.190
59 A 6 4 1.00 21 0.190
60 A 4 2 1.00 21 0.095
61 C 2 2 0.19 21 0.095
62 C 2 2 0.22 21 0.095
63 C 2 2 0.25 21 0.095
64 A 7 7 1.40 21 0.333
65 A 8 8 1.33 21 0.381
66 C 2 2 2.75 21 0.095
67 C 2 2 4.19 21 0.095
68 C 2 2 0.18 21 0.095
69 C 2 2 0.20 21 0.095
70 A 8 8 1.32 21 0.381
71 A 8 8 1.27 21 0.381
72 C 2 2 2.39 21 0.095
73 C 2 2 3.75 21 0.095
74 C 2 2 0.11 21 0.095
75 C 2 2 0.14 21 0.095
76 C 2 2 0.16 21 0.095
77 A 9 8 1.27 21 0.381
78 A 9 9 1.22 21 0.429
79 C 2 2 0.54 21 0.095
80 C 2 2 1.14 21 0.095
81 C 2 2 4.30 21 0.095
82 A 1 1 1.00 50 0.020
83 A 2 1 1.00 17 0.059
84 A 2 1 1.00 17 0.059
85 A 2 1 1.00 17 0.059
86 A 2 1 1.00 15 0.067
87 A 10 7 1.00 17 0.412
88 A 10 7 1.00 17 0.412
89 A 11 8 1.00 17 0.471
90 A 2 1 1.00 19 0.053
91 A 2 1 1.00 19 0.053
92 A 2 1 1.00 19 0.053
93 A 2 1 1.00 17 0.059
94 A 11 7 1.00 19 0.368
95 A 12 8 1.00 19 0.421
96 A 11 8 1.00 19 0.421
97 A 11 7 1.00 19 0.368
98 A 11 7 1.00 19 0.368
99 A 11 7 1.00 19 0.368
100 A 10 7 1.00 17 0.412
101 A 19 7 1.00 19 0.368
102 A 20 8 1.00 19 0.421
103 A 12 8 1.00 19 0.421
104 A 12 8 1.00 19 0.421
105 A 12 8 1.00 19 0.421
106 A 12 8 1.00 19 0.421
107 A 10 7 1.00 17 0.412
108 A 20 8 1.00 19 0.421
109 A 21 9 1.00 19 0.474
110 A 4 4 1.00 25 0.160
111 A 1 1 1.00 25 0.040
112 A 10 9 1.00 21 0.429
113 A 9 8 1.00 21 0.381
114 A 4 4 1.00 21 0.190
115 A 5 5 1.00 21 0.238
116 A 7 7 1.00 21 0.333
117 A 8 7 1.00 21 0.333
118 A 11 10 1.00 21 0.476
119 A 10 9 1.00 21 0.429
120 A 5 5 1.00 21 0.238
121 A 5 5 1.00 21 0.238
122 A 7 7 1.00 21 0.333
123 A 8 7 1.00 21 0.333
124 A 4 4 1.00 17 0.235
125 A 4 4 1.00 26 0.154
126 A 7 7 1.00 21 0.333
127 A 6 6 1.00 21 0.286
128 A 6 6 1.00 21 0.286
129 A 5 5 1.00 19 0.263
130 A 4 4 1.00 11 0.364
131 A 7 6 1.00 21 0.286
132 A 8 7 1.00 21 0.333
133 A 9 7 1.00 21 0.333
134 A 7 7 1.00 21 0.333
135 A 7 6 1.00 21 0.286
136 A 6 5 1.00 19 0.263
137 A 5 5 1.00 11 0.454
138 A 7 6 1.00 21 0.286
139 A 8 7 1.00 21 0.333
140 A 9 7 1.00 21 0.333
141 A 8 7 1.00 21 0.333
142 A 8 6 1.00 21 0.286
143 A 7 5 1.00 19 0.263
144 A 6 5 1.00 11 0.454
145 A 8 7 1.00 21 0.333
146 A 8 7 1.00 21 0.333
147 A 9 8 1.00 21 0.381
148 A 5 5 1.00 21 0.238
149 A 5 5 1.00 21 0.238
150 A 4 4 1.00 19 0.210
151 A 4 4 1.00 11 0.364
152 A 7 6 1.00 21 0.286
153 A 8 7 1.00 21 0.333
154 A 9 7 1.00 21 0.333
155 A 5 5 1.00 21 0.238
156 A 5 5 0.96 21 0.238
157 A 5 5 1.00 19 0.263
158 A 5 4 1.02 11 0.364
159 A 8 7 1.00 21 0.333
160 A 9 8 1.00 21 0.381
161 A 10 8 1.00 21 0.381
162 A 5 5 1.00 21 0.238
163 A 6 6 0.97 21 0.286
164 A 6 5 1.00 19 0.263
165 A 6 4 1.04 11 0.364
166 A 9 7 1.00 21 0.333
167 A 10 8 1.00 21 0.381
168 A 11 8 1.00 21 0.381
169 A 8 8 1.00 23 0.348
170 A 4 4 1.00 23 0.174
171 A 5 5 1.00 23 0.217
172 A 3 3 1.00 17 0.176
173 A 8 8 1.00 17 0.471
174 A 3 2 1.00 21 0.095
175 A 3 2 1.00 17 0.118
176 A 4 4 1.00 17 0.235
177 A 9 9 1.00 17 0.529
178 A 4 3 1.00 17 0.176
179 A 2 1 1.00 17 0.059
180 A 2 1 1.00 17 0.059
181 A 2 1 1.00 17 0.059
182 A 2 1 1.00 15 0.067
183 A 2 1 1.00 19 0.053
184 A 2 1 1.00 19 0.053
185 A 2 1 1.00 17 0.059
186 A 4 2 1.00 25 0.080
187 A 3 2 1.00 25 0.080
188 A 2 2 1.00 23 0.087
189 A 1 1 1.00 15 0.067
190 A 1 1 1.00 69 0.014
191 A 5 3 1.00 25 0.120
192 A 3 3 1.00 23 0.130
193 A 2 2 1.00 15 0.133
194 A 6 4 1.08 31 0.129
195 A 4 4 1.08 31 0.129
196 A 2 2 1.07 29 0.069
197 A 5 5 1.00 31 0.161
198 A 5 5 1.19 31 0.161
199 A 5 4 1.36 31 0.129
200 A 9 8 1.00 31 0.258
201 A 7 7 1.00 31 0.226
202 A 5 5 1.00 28 0.179
203 A 5 5 1.00 31 0.161
204 A 6 6 1.00 31 0.194
205 A 5 5 1.00 29 0.172
206 A 4 4 1.00 29 0.138
207 A 3 3 1.00 29 0.103
208 A 2 2 1.00 27 0.074
209 A 2 2 1.00 26 0.077
210 A 3 3 1.00 29 0.103
211 A 2 2 1.00 29 0.069
212 A 3 3 1.00 29 0.103
213 A 2 2 1.00 29 0.069
214 A 5 5 1.00 29 0.172
215 A 8 7 1.00 31 0.226
216 A 4 4 1.00 31 0.129
217 A 6 6 1.00 31 0.194
218 A 2 2 1.00 29 0.069
219 A 4 4 1.00 28 0.143
220 A 3 3 1.00 31 0.097
221 A 4 4 1.00 31 0.129
222 A 3 3 1.00 31 0.097
223 A 2 2 1.00 31 0.065
224 A 5 5 1.00 31 0.161
225 A 8 8 1.00 31 0.258
226 A 4 4 1.00 31 0.129
227 A 7 7 1.00 31 0.226
228 A 2 2 1.00 29 0.069
229 A 4 4 1.00 28 0.143
230 A 3 3 1.00 31 0.097
231 A 2 2 1.00 31 0.065
232 A 5 5 1.00 31 0.161
233 A 4 4 1.00 31 0.129
234 A 7 7 1.00 31 0.226
235 A 3 3 1.00 31 0.097
236 A 1 1 1.00 57 0.018
237 A 3 3 1.00 32 0.094
238 A 4 4 1.00 41 0.098
239 A 2 2 1.08 76 0.026

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