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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 [100] had the largest ratio of [.708332999999999990]

# 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 7 6 0.81 22 0.273
2 A 5 4 0.70 20 0.200
3 A 5 4 0.79 19 0.211
4 A 5 4 0.88 22 0.182
5 A 5 4 1.10 22 0.182
6 A 7 6 1.01 22 0.273
7 A 2 2 1.00 22 0.091
8 A 3 3 0.99 22 0.136
9 A 4 4 0.97 22 0.182
10 A 9 8 0.74 24 0.333
11 A 7 6 0.74 22 0.273
12 A 7 6 0.79 21 0.286
13 A 7 6 0.89 24 0.250
14 A 7 6 0.92 24 0.250
15 A 9 8 1.16 24 0.333
16 A 1 1 0.01 24 0.042
17 A 5 5 1.34 24 0.208
18 A 6 6 1.04 24 0.250
19 A 7 7 1.03 24 0.292
20 A 9 8 0.77 22 0.364
21 A 7 6 0.71 21 0.286
22 A 9 8 0.92 24 0.333
23 A 9 8 0.92 24 0.333
24 A 11 10 1.14 24 0.417
25 A 4 4 1.31 24 0.167
26 A 1 1 0.01 24 0.042
27 A 8 8 1.58 24 0.333
28 A 9 9 1.18 24 0.375
29 A 10 10 1.02 24 0.417
30 A 13 12 1.25 24 0.500
31 A 8 7 1.07 22 0.318
32 A 7 6 1.22 21 0.286
33 A 2 2 1.68 24 0.083
34 A 5 4 1.35 24 0.167
35 A 6 5 1.18 24 0.208
36 A 10 9 1.21 24 0.375
37 A 12 11 1.20 24 0.458
38 A 14 13 1.24 24 0.542
39 A 7 6 1.09 22 0.273
40 A 7 6 1.21 21 0.286
41 A 5 4 1.38 24 0.167
42 A 6 5 1.39 24 0.208
43 A 10 9 1.30 24 0.375
44 A 12 11 1.25 24 0.458
45 A 15 14 1.13 24 0.583
46 A 14 13 1.22 24 0.542
47 A 8 7 1.15 22 0.318
48 A 4 3 0.95 21 0.143
49 A 6 5 1.25 24 0.208
50 A 10 9 1.09 24 0.375
51 A 12 11 1.08 24 0.458
52 A 2 2 1.68 24 0.083
53 A 3 3 1.68 22 0.136
54 F 0 0 N/A 0.000 N/A
55 A 4 4 1.68 23 0.174
56 A 8 7 0.75 22 0.318
57 A 6 5 0.66 20 0.250
58 A 6 5 0.71 19 0.263
59 A 6 5 0.78 22 0.227
60 A 6 5 0.97 22 0.227
61 A 6 5 0.98 22 0.227
62 A 8 7 1.07 22 0.318
63 A 8 7 0.99 22 0.318
64 A 2 2 1.00 22 0.091
65 A 3 3 0.99 22 0.136
66 A 4 4 0.97 22 0.182
67 A 10 9 0.65 24 0.375
68 A 8 7 0.63 22 0.318
69 A 8 7 0.65 21 0.333
70 A 8 7 0.72 24 0.292
71 A 8 7 0.84 24 0.292
72 A 8 7 0.85 24 0.292
73 A 10 9 0.88 24 0.375
74 A 10 9 1.07 24 0.375
75 A 1 1 0.01 24 0.042
76 A 5 5 1.34 24 0.208
77 A 6 6 1.02 24 0.250
78 A 7 7 1.03 24 0.292
79 A 12 11 0.60 24 0.458
80 A 10 9 0.64 22 0.409
81 A 8 7 0.59 21 0.333
82 A 10 9 0.71 24 0.375
83 A 10 9 0.81 24 0.375
84 A 10 9 0.82 24 0.375
85 A 12 11 0.87 24 0.458
86 A 12 11 1.10 24 0.458
87 A 4 4 1.26 24 0.167
88 A 1 1 0.01 24 0.042
89 A 8 8 1.58 24 0.333
90 A 9 9 1.18 24 0.375
91 A 10 10 1.02 24 0.417
92 A 10 9 1.01 22 0.409
93 A 9 8 1.10 21 0.381
94 A 11 10 1.23 24 0.417
95 A 9 8 1.32 24 0.333
96 B 2 2 3.92 24 0.083
97 A 6 5 1.28 24 0.208
98 A 7 6 1.04 24 0.250
99 A 12 11 1.18 24 0.458
100 A 18 17 1.18 24 0.708
101 A 9 8 1.02 22 0.364
102 A 10 9 1.07 21 0.429
103 A 11 10 1.28 24 0.417
104 B 2 2 4.24 24 0.083
105 A 6 5 1.42 24 0.208
106 A 7 6 1.21 24 0.250
107 A 12 11 1.28 24 0.458
108 A 18 17 1.29 24 0.708
109 A 9 8 0.92 22 0.364
110 A 8 7 0.99 21 0.333
111 B 2 2 3.80 24 0.083
112 A 6 5 1.23 24 0.208
113 A 7 6 1.15 24 0.250
114 A 12 11 1.29 24 0.458
115 A 12 11 0.99 22 0.500
116 A 11 10 1.02 21 0.476
117 A 15 14 1.22 24 0.583
118 A 13 12 1.20 24 0.500
119 A 11 10 1.23 24 0.417
120 A 11 10 1.26 24 0.417
121 B 2 2 6.37 24 0.083
122 A 7 6 1.22 24 0.250
123 A 8 7 0.90 24 0.292
124 A 9 8 1.09 24 0.333
125 A 7 6 0.93 22 0.273
126 A 6 5 0.93 22 0.227
127 A 4 3 0.82 20 0.150
128 A 4 3 1.00 19 0.158
129 A 4 3 1.00 22 0.136
130 A 2 2 1.00 22 0.091
131 A 3 3 0.99 22 0.136
132 A 4 4 0.97 22 0.182
133 A 5 5 0.96 22 0.227
134 A 9 8 0.83 24 0.333
135 A 8 7 0.87 24 0.292
136 A 6 5 0.95 22 0.227
137 A 6 5 1.05 21 0.238
138 A 6 5 1.12 24 0.208
139 A 1 1 0.01 24 0.042
140 A 5 5 1.34 24 0.208
141 A 6 6 1.04 24 0.250
142 A 7 7 1.03 24 0.292
143 A 11 10 1.29 24 0.417
144 A 9 8 1.36 24 0.333
145 A 6 5 1.20 22 0.227
146 A 3 2 1.31 21 0.095
147 A 5 4 1.33 24 0.167
148 A 8 7 1.29 24 0.292
149 A 10 9 1.23 24 0.375
150 A 11 10 1.32 24 0.417
151 A 9 8 1.42 24 0.333
152 A 4 3 1.22 22 0.136
153 A 4 3 1.21 21 0.143
154 A 8 7 1.22 24 0.292
155 A 10 9 1.12 24 0.375
156 A 12 11 1.09 24 0.458
157 A 10 9 1.12 24 0.375
158 A 11 10 1.12 22 0.455
159 A 13 12 1.12 38 0.316
160 A 13 12 1.12 36 0.333
161 A 8 7 1.01 22 0.318
162 A 5 4 1.02 22 0.182
163 A 5 4 1.00 20 0.200
164 A 1 1 0.69 19 0.053
165 A 2 2 0.70 22 0.091
166 A 3 3 0.75 22 0.136
167 A 4 4 0.79 22 0.182
168 A 11 10 1.01 24 0.417
169 A 10 9 0.96 24 0.375
170 A 7 6 0.86 24 0.250
171 A 6 5 1.00 22 0.227
172 A 7 6 1.13 21 0.286
173 A 4 4 1.07 24 0.167
174 A 5 5 0.88 24 0.208
175 A 6 6 0.89 24 0.250
176 A 7 7 0.89 24 0.292
177 F 0 0 N/A 0.000 N/A
178 C 2 2 0.27 24 0.083
179 F 0 0 N/A 0.000 N/A
180 A 2 2 1.00 22 0.091
181 A 2 2 0.46 21 0.095
182 A 5 5 0.76 24 0.208
183 A 6 6 0.75 24 0.250
184 A 7 7 0.73 24 0.292
185 A 9 8 1.14 28 0.286
186 A 3 3 0.93 28 0.107
187 A 3 3 0.89 28 0.107
188 A 5 4 0.98 28 0.143
189 A 5 4 0.97 28 0.143
190 A 8 7 1.01 28 0.250
191 A 10 9 1.02 28 0.321
192 A 12 11 0.99 28 0.393
193 A 14 13 0.98 28 0.464
194 A 7 6 1.80 26 0.231
195 A 12 12 0.99 26 0.462
196 A 10 10 0.99 26 0.385
197 A 8 8 1.11 26 0.308
198 B 8 8 2.57 24 0.333
199 A 8 8 1.15 23 0.348
200 A 12 12 1.17 26 0.462
201 A 14 14 1.19 26 0.538
202 A 12 12 1.09 26 0.462
203 A 10 10 1.11 26 0.385
204 A 8 8 1.14 26 0.308
205 A 5 5 0.79 26 0.192
206 A 5 5 0.74 24 0.208
207 A 8 8 1.20 23 0.348
208 A 12 12 1.30 26 0.462
209 A 14 14 1.28 26 0.538
210 B 8 7 2.48 20 0.350
211 A 9 8 1.81 22 0.364
212 A 4 4 1.00 22 0.182
213 B 4 3 2.68 20 0.150
214 A 3 2 1.36 19 0.105
215 A 4 4 1.00 22 0.182
216 A 4 4 1.00 22 0.182
217 C 4 4 0.34 23 0.174
218 C 4 4 0.37 23 0.174
219 A 5 4 1.20 21 0.190
220 A 4 3 1.21 20 0.150
221 C 4 4 0.44 23 0.174
222 C 4 4 0.37 23 0.174
223 A 4 3 1.00 20 0.150
224 A 4 4 0.96 24 0.167
225 A 3 3 0.98 24 0.125
226 A 2 2 1.00 22 0.091
227 A 2 2 0.97 21 0.095
228 A 4 3 0.97 24 0.125
229 A 5 4 0.92 24 0.167
230 A 6 5 0.92 24 0.208
231 A 7 6 0.92 24 0.250
232 A 3 3 0.90 26 0.115
233 A 3 3 0.93 26 0.115
234 A 3 3 0.99 24 0.125
235 A 2 2 1.16 23 0.087
236 A 7 6 1.13 26 0.231
237 A 7 6 1.07 26 0.231
238 A 8 7 0.91 26 0.269
239 A 9 8 0.83 26 0.308
240 A 3 3 0.94 26 0.115
241 A 3 3 0.99 26 0.115
242 A 5 4 1.10 26 0.154
243 A 4 3 1.29 24 0.125
244 A 6 5 1.08 23 0.217
245 A 8 7 1.12 26 0.269
246 A 10 9 1.09 26 0.346
247 A 12 11 1.06 26 0.423
248 A 7 6 1.16 26 0.231
249 A 5 4 1.08 26 0.154
250 A 5 4 1.09 24 0.167
251 A 8 7 1.17 23 0.304
252 A 10 9 1.14 26 0.346
253 A 12 11 1.10 26 0.423
254 A 14 13 1.07 26 0.500
255 A 7 6 0.82 36 0.167
256 A 7 6 0.82 36 0.167
257 A 5 4 0.80 34 0.118
258 A 2 2 1.00 27 0.074
259 A 5 4 0.84 36 0.111
260 A 7 6 0.95 36 0.167
261 A 7 6 0.83 36 0.167
262 A 3 3 1.01 36 0.083
263 A 3 3 1.00 37 0.081
264 A 3 3 1.00 37 0.081
265 A 3 3 1.00 38 0.079
266 C 2 2 1.10 36 0.056
267 A 2 2 1.00 36 0.056
268 A 2 2 1.00 36 0.056
269 A 2 2 1.00 36 0.056
270 A 4 4 1.00 28 0.143
271 A 4 4 1.00 26 0.154
272 A 4 4 1.00 24 0.167
273 A 4 4 1.00 23 0.174
274 A 4 4 1.00 26 0.154
275 A 4 4 1.00 26 0.154

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