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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 [49] had the largest ratio of [.736841999999999997]

# 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 4 4 1.00 19 0.211
2 A 1 1 1.00 18 0.056
3 A 4 3 1.00 23 0.130
4 A 4 3 1.00 23 0.130
5 A 4 3 1.00 29 0.103
6 A 1 1 1.00 18 0.056
7 A 5 4 1.13 20 0.200
8 A 5 4 1.13 20 0.200
9 A 5 4 1.13 22 0.182
10 A 1 1 1.00 18 0.056
11 A 4 3 1.00 23 0.130
12 A 4 3 1.00 23 0.130
13 A 4 3 1.00 29 0.103
14 A 1 1 1.00 18 0.056
15 A 1 1 1.00 25 0.040
16 C 1 1 4.30 38 0.026
17 A 1 1 1.00 27 0.037
18 A 1 1 1.00 31 0.032
19 A 1 1 1.00 56 0.018
20 A 1 1 1.00 51 0.020
21 A 1 1 1.00 49 0.020
22 A 1 1 1.00 46 0.022
23 A 2 2 1.00 48 0.042
24 A 1 1 1.00 49 0.020
25 A 1 1 1.00 48 0.021
26 A 1 1 1.00 48 0.021
27 A 2 2 1.00 18 0.111
28 A 2 2 1.00 16 0.125
29 A 2 2 1.00 15 0.133
30 A 2 2 1.00 18 0.111
31 A 2 2 1.00 20 0.100
32 A 2 2 1.00 18 0.111
33 A 2 2 1.00 17 0.118
34 A 2 2 1.00 20 0.100
35 A 2 2 1.00 20 0.100
36 A 2 2 1.00 18 0.111
37 A 2 2 1.00 17 0.118
38 A 2 2 1.00 20 0.100
39 A 2 2 1.00 20 0.100
40 A 2 2 1.00 20 0.100
41 A 2 2 1.00 20 0.100
42 A 2 2 1.00 20 0.100
43 A 2 2 1.00 18 0.111
44 A 2 2 1.00 17 0.118
45 A 2 2 1.00 20 0.100
46 A 2 2 1.00 20 0.100
47 A 2 2 1.00 22 0.091
48 A 2 2 1.00 20 0.100
49 A 15 14 0.92 19 0.737
50 F 0 0 N/A 0.000 N/A
51 A 2 2 1.00 22 0.091
52 A 2 2 1.00 22 0.091
53 C 2 2 3.15 22 0.091
54 A 2 2 1.00 22 0.091
55 A 2 2 1.00 20 0.100
56 C 2 2 4.19 19 0.105
57 A 2 2 1.00 22 0.091
58 A 2 2 1.00 22 0.091
59 A 2 2 1.00 22 0.091
60 A 2 2 1.00 22 0.091
61 A 2 2 1.00 22 0.091
62 A 1 1 1.00 56 0.018
63 A 1 1 1.00 51 0.020
64 A 1 1 1.00 49 0.020
65 A 1 1 1.00 46 0.022
66 A 2 2 1.00 48 0.042
67 A 1 1 1.00 49 0.020
68 A 1 1 1.00 48 0.021
69 A 1 1 1.00 48 0.021
70 A 2 2 1.00 20 0.100
71 A 2 2 1.00 22 0.091
72 A 9 8 0.70 38 0.211
73 A 9 8 0.67 37 0.216
74 A 12 11 0.73 40 0.275
75 A 13 12 0.72 40 0.300
76 A 11 10 0.69 40 0.250
77 A 12 11 0.75 40 0.275
78 A 9 8 0.68 40 0.200
79 A 11 10 0.68 40 0.250
80 A 3 2 1.00 40 0.050
81 A 2 2 1.00 18 0.111
82 A 2 2 1.00 20 0.100
83 A 2 2 1.00 20 0.100
84 A 2 2 1.25 20 0.100
85 B 3 3 2.15 38 0.079
86 A 5 4 1.84 41 0.098
87 A 3 3 0.64 52 0.058
88 F 0 0 N/A 0.000 N/A
89 A 3 2 1.00 28 0.071
90 A 3 2 1.00 32 0.062
91 A 3 2 1.00 30 0.067
92 A 3 2 1.00 30 0.067
93 A 3 2 1.00 53 0.038
94 A 3 2 1.00 55 0.036
95 A 3 2 1.00 56 0.036
96 A 3 2 1.00 56 0.036
97 A 3 2 1.00 30 0.067
98 A 5 4 1.03 24 0.167
99 A 6 5 1.02 28 0.179
100 A 6 5 1.02 26 0.192
101 A 5 4 1.03 26 0.154
102 A 5 4 1.04 24 0.167
103 A 6 5 1.04 28 0.179
104 A 6 5 1.04 26 0.192
105 A 5 4 1.04 26 0.154
106 A 5 4 1.00 38 0.105
107 A 6 5 1.00 40 0.125
108 A 6 5 1.00 41 0.122
109 A 5 4 1.00 41 0.098
110 A 5 4 1.00 29 0.138
111 A 5 4 1.00 20 0.200
112 A 6 5 1.00 24 0.208
113 A 6 5 1.00 22 0.227
114 A 5 4 1.00 22 0.182
115 A 5 4 1.00 34 0.118
116 A 6 5 1.00 36 0.139
117 A 6 5 1.00 37 0.135
118 A 5 4 1.00 37 0.108
119 A 5 4 1.00 25 0.160
120 A 3 2 1.00 20 0.100
121 A 3 2 1.00 22 0.091
122 A 3 2 1.00 20 0.100
123 A 3 2 1.00 22 0.091
124 A 3 2 1.00 43 0.047
125 A 3 2 1.00 44 0.045
126 A 3 2 1.00 45 0.044
127 A 3 2 1.00 46 0.043
128 A 3 2 1.00 30 0.067
129 A 6 5 1.00 22 0.227
130 A 6 5 1.00 22 0.227
131 A 6 5 1.00 20 0.250
132 A 6 5 1.00 24 0.208
133 A 6 5 0.98 35 0.143
134 A 6 5 0.98 35 0.143
135 A 6 5 0.98 36 0.139
136 A 6 5 0.98 38 0.132
137 A 5 4 1.00 29 0.138
138 A 6 5 1.00 18 0.278
139 A 6 5 1.00 18 0.278
140 A 6 5 1.00 16 0.312
141 A 6 5 1.00 20 0.250
142 A 6 5 1.00 31 0.161
143 A 6 5 1.00 31 0.161
144 A 6 5 1.00 32 0.156
145 A 6 5 1.00 34 0.147
146 A 5 4 1.00 25 0.160
147 A 3 2 1.00 30 0.067
148 A 3 2 1.00 36 0.056
149 A 3 2 1.00 34 0.059
150 A 3 2 1.00 32 0.062
151 A 3 2 1.00 58 0.034
152 A 3 2 1.00 61 0.033
153 A 3 2 1.00 62 0.032
154 A 3 2 1.00 61 0.033
155 A 3 2 1.00 52 0.038
156 A 3 2 1.00 55 0.036
157 A 3 2 1.00 56 0.036
158 A 3 2 1.00 55 0.036
159 A 3 2 1.00 30 0.067
160 A 3 2 1.00 36 0.056
161 A 3 2 1.00 34 0.059
162 A 3 2 1.00 32 0.062
163 A 3 2 1.00 58 0.034
164 A 3 2 1.00 61 0.033
165 A 3 2 1.00 62 0.032
166 A 3 2 1.00 61 0.033
167 A 3 2 1.00 52 0.038
168 A 3 2 1.00 55 0.036
169 A 3 2 1.00 56 0.036
170 A 3 2 1.00 55 0.036
171 A 6 5 1.00 23 0.217
172 A 6 5 1.00 25 0.200
173 A 6 5 1.00 25 0.200
174 A 6 5 0.98 29 0.172
175 A 6 5 0.98 27 0.185
176 A 6 5 1.00 27 0.185
177 A 6 5 1.00 42 0.119
178 A 6 5 1.00 44 0.114
179 A 6 5 1.00 45 0.111
180 A 6 5 1.00 45 0.111
181 A 6 5 1.30 21 0.238
182 A 6 5 1.27 25 0.200
183 A 6 5 1.14 23 0.217
184 A 6 5 1.15 23 0.217
185 A 6 5 1.12 23 0.217
186 A 6 5 1.06 38 0.132
187 A 6 5 1.06 40 0.125
188 A 6 5 1.13 41 0.122
189 A 6 5 1.13 41 0.122
190 A 8 7 0.94 25 0.280
191 A 7 6 0.92 29 0.207
192 A 7 6 0.92 27 0.222
193 A 8 7 0.93 27 0.259
194 A 8 7 0.86 27 0.259
195 A 7 6 0.87 31 0.194
196 A 7 6 0.87 29 0.207
197 A 8 7 0.86 29 0.241
198 A 6 5 1.00 21 0.238
199 A 7 6 1.00 25 0.240
200 A 7 6 1.00 23 0.261
201 A 6 5 1.00 23 0.217
202 A 6 5 1.00 23 0.217
203 A 7 6 1.00 27 0.222
204 A 7 6 1.00 25 0.240
205 A 6 5 1.00 25 0.200
206 A 10 9 0.99 16 0.562
207 A 9 8 1.00 18 0.444
208 A 9 8 1.02 16 0.500
209 A 10 9 0.96 18 0.500
210 A 10 9 1.00 22 0.409
211 A 9 8 0.97 24 0.333
212 A 9 8 0.97 22 0.364
213 A 10 9 0.99 24 0.375
214 A 7 6 1.00 18 0.333
215 A 7 6 1.00 20 0.300
216 A 7 6 1.00 18 0.333
217 A 7 6 1.00 20 0.300
218 A 1 1 1.00 31 0.032
219 A 3 3 0.97 30 0.100
220 A 3 2 1.00 27 0.074
221 A 3 2 1.00 29 0.069
222 A 3 2 1.00 27 0.074
223 A 3 2 1.00 29 0.069
224 A 3 2 1.00 31 0.065
225 A 3 2 1.00 35 0.057
226 A 3 2 1.00 33 0.061
227 A 3 2 1.00 33 0.061
228 A 10 9 1.04 24 0.375
229 A 11 10 1.00 26 0.385
230 A 10 9 1.03 29 0.310
231 A 11 10 1.05 31 0.323
232 A 3 2 1.12 40 0.050
233 A 3 2 1.11 40 0.050
234 A 3 2 1.11 46 0.043
235 A 3 2 1.10 46 0.043
236 A 2 2 1.04 37 0.054
237 A 2 2 1.00 25 0.080
238 A 2 2 1.00 23 0.087
239 A 2 2 1.00 21 0.095
240 A 2 2 1.00 28 0.071

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