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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 [145] had the largest ratio of [26]

# 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 2 1.00 8 0.250
2 A 3 2 1.00 8 0.250
3 A 3 2 1.00 8 0.250
4 A 2 2 1.00 8 0.250
5 A 2 2 1.00 8 0.250
6 A 1 1 1.00 6 0.167
7 A 1 1 1.00 6 0.167
8 A 2 2 1.00 8 0.250
9 A 2 2 1.00 8 0.250
10 A 3 2 1.00 8 0.250
11 A 3 2 1.00 8 0.250
12 A 4 2 1.00 8 0.250
13 A 7 6 1.00 12 0.500
14 A 6 6 1.00 12 0.500
15 A 6 6 1.00 12 0.500
16 A 5 5 1.00 12 0.417
17 A 5 5 1.00 12 0.417
18 A 6 6 1.00 12 0.500
19 A 6 6 1.00 12 0.500
20 A 7 6 1.00 12 0.500
21 A 9 9 1.00 8 1.125
22 A 2 2 1.00 8 0.250
23 A 2 2 1.00 10 0.200
24 A 3 3 1.00 10 0.300
25 A 2 2 1.00 10 0.200
26 A 2 2 1.00 10 0.200
27 A 4 3 1.00 14 0.214
28 A 3 3 1.00 14 0.214
29 A 2 2 1.00 14 0.143
30 A 2 2 1.00 14 0.143
31 A 3 3 1.00 14 0.214
32 A 4 3 1.00 14 0.214
33 A 7 7 1.00 8 0.875
34 A 8 7 1.00 10 0.700
35 A 7 7 1.00 10 0.700
36 A 7 7 1.00 10 0.700
37 A 5 3 1.00 10 0.300
38 A 3 3 1.00 10 0.300
39 A 3 3 1.00 10 0.300
40 A 3 3 1.00 12 0.250
41 A 5 3 1.00 12 0.250
42 A 4 3 1.00 12 0.250
43 A 3 3 1.00 12 0.250
44 A 2 2 1.00 12 0.167
45 A 2 2 1.00 12 0.167
46 A 3 2 1.00 12 0.167
47 A 4 2 1.00 12 0.167
48 A 5 2 1.00 12 0.167
49 A 6 2 1.00 12 0.167
50 A 5 3 1.00 8 0.375
51 A 4 3 1.00 8 0.375
52 A 3 3 1.00 8 0.375
53 A 2 2 1.00 8 0.250
54 A 3 3 1.00 8 0.375
55 A 4 3 1.00 8 0.375
56 A 5 3 1.00 8 0.375
57 A 5 4 1.00 12 0.333
58 A 4 4 1.00 12 0.333
59 A 3 3 1.00 12 0.250
60 A 2 2 1.00 12 0.167
61 A 2 2 1.00 12 0.167
62 A 3 3 1.00 12 0.250
63 A 4 4 1.00 12 0.333
64 A 5 4 1.00 12 0.333
65 A 2 2 1.00 12 0.167
66 A 2 2 1.00 12 0.167
67 A 5 4 1.00 14 0.286
68 A 5 4 1.00 14 0.286
69 A 5 4 1.00 11 0.364
70 A 9 7 1.00 11 0.636
71 A 5 4 1.00 11 0.364
72 A 8 6 1.00 9 0.667
73 A 8 7 1.00 9 0.778
74 A 3 2 1.00 11 0.182
75 A 8 7 1.00 11 0.636
76 A 4 3 1.00 11 0.273
77 A 9 8 1.00 11 0.727
78 A 4 3 1.00 11 0.273
79 A 10 8 1.00 11 0.727
80 A 5 3 1.00 13 0.231
81 A 10 9 1.00 13 0.692
82 A 4 3 1.00 13 0.231
83 A 6 6 1.00 11 0.546
84 A 6 5 1.00 11 0.454
85 A 3 2 1.00 13 0.154
86 A 15 11 1.00 13 0.846
87 A 3 2 1.00 13 0.154
88 A 29 13 1.00 13 1.000
89 A 3 2 1.00 13 0.154
90 A 6 5 1.00 11 0.454
91 A 4 3 1.00 11 0.273
92 A 3 2 1.00 11 0.182
93 A 4 3 1.00 11 0.273
94 A 2 2 1.00 9 0.222
95 A 1 1 1.00 9 0.111
96 A 2 2 1.00 11 0.182
97 A 2 2 1.00 11 0.182
98 A 2 1 1.00 11 0.091
99 A 3 3 1.00 11 0.273
100 A 3 2 1.00 11 0.182
101 A 4 3 1.00 11 0.273
102 A 3 2 1.00 13 0.154
103 A 3 2 1.00 13 0.154
104 A 3 2 1.00 13 0.154
105 A 2 2 1.00 13 0.154
106 A 2 2 1.00 8 0.250
107 A 4 3 1.00 13 0.231
108 A 5 4 1.00 13 0.308
109 A 14 6 1.19 13 0.462
110 A 9 6 1.07 13 0.462
111 A 5 5 1.00 13 0.385
112 A 2 2 1.00 11 0.182
113 A 5 5 1.00 11 0.454
114 A 9 6 1.00 13 0.462
115 A 5 4 1.00 11 0.364
116 A 4 4 1.00 11 0.364
117 A 3 3 1.00 11 0.273
118 A 3 2 1.00 11 0.182
119 A 2 2 1.00 9 0.222
120 A 2 2 1.00 6 0.333
121 A 4 4 1.00 9 0.444
122 A 4 4 1.00 11 0.364
123 A 5 4 1.00 11 0.364
124 A 6 4 1.00 11 0.364
125 A 4 4 1.00 11 0.364
126 A 3 3 1.00 11 0.273
127 A 3 3 1.00 11 0.273
128 A 4 4 1.00 11 0.364
129 A 4 4 1.00 13 0.308
130 A 3 3 1.00 13 0.231
131 A 4 4 1.00 13 0.308
132 A 4 4 1.00 13 0.308
133 A 7 7 1.00 13 0.538
134 A 6 6 1.00 13 0.462
135 A 5 5 1.00 13 0.385
136 A 4 4 1.00 13 0.308
137 A 2 2 1.00 11 0.182
138 A 2 2 1.00 8 0.250
139 A 3 3 1.00 11 0.273
140 A 4 4 1.00 13 0.308
141 A 5 5 1.00 13 0.385
142 A 6 6 1.00 13 0.462
143 A 3 3 1.00 14 0.214
144 A 9 6 1.00 24 0.250
145 A 11 7 1.00 26 0.269
146 A 4 3 1.00 11 0.273
147 A 11 8 1.00 11 0.727
148 A 4 4 1.00 9 0.444
149 A 11 8 1.00 7 1.143
150 A 2 1 1.00 11 0.091
151 A 11 8 1.00 11 0.727
152 A 4 4 1.00 11 0.364
153 A 4 3 1.00 13 0.231
154 A 12 9 1.00 13 0.692
155 A 5 5 1.00 11 0.454
156 A 13 9 1.00 9 1.000
157 A 3 2 1.00 13 0.154
158 A 12 9 1.00 13 0.692
159 A 5 5 1.00 13 0.385
160 A 3 3 1.00 13 0.231
161 A 4 4 1.00 15 0.267
162 A 5 5 1.00 15 0.333
163 A 3 3 1.00 9 0.333
164 A 3 3 1.00 15 0.200
165 A 2 2 1.00 11 0.182
166 A 4 4 1.00 11 0.364
167 A 5 5 1.00 11 0.454
168 A 5 5 1.00 11 0.454
169 A 3 3 1.00 7 0.429
170 A 3 3 1.00 9 0.333
171 A 3 3 1.00 9 0.333
172 A 4 4 1.00 17 0.235
173 A 4 4 1.00 17 0.235
174 A 4 4 1.00 15 0.267
175 A 4 4 1.00 13 0.308
176 A 2 1 1.00 17 0.059
177 A 4 4 1.00 17 0.235
178 A 4 4 1.00 17 0.235
179 A 5 5 1.00 19 0.263
180 A 5 5 1.00 19 0.263
181 A 5 5 1.00 17 0.294
182 A 5 5 1.00 15 0.333
183 A 3 2 1.00 19 0.105
184 A 5 5 1.00 19 0.263
185 A 5 5 1.00 19 0.263
186 A 3 2 1.00 17 0.118
187 A 4 2 1.00 17 0.118
188 A 4 2 1.00 17 0.118
189 A 4 4 1.00 19 0.210
190 A 5 5 1.00 21 0.238
191 A 6 6 1.00 21 0.286
192 A 4 4 1.00 15 0.267
193 A 4 4 1.00 21 0.190
194 A 7 6 1.00 19 0.316
195 A 7 6 1.00 19 0.316
196 A 6 5 1.00 19 0.263
197 A 6 5 1.00 19 0.263
198 A 7 6 1.00 19 0.316
199 A 7 6 1.00 19 0.316
200 A 8 7 1.00 23 0.304
201 A 7 6 1.00 23 0.261
202 A 4 4 1.00 21 0.190
203 A 8 5 1.00 21 0.238
204 A 11 6 1.00 23 0.261
205 A 8 7 1.00 21 0.333
206 A 7 6 1.00 16 0.375
207 A 7 6 1.00 16 0.375
208 A 5 4 1.00 16 0.250
209 A 3 3 1.00 14 0.214
210 A 3 3 1.00 14 0.214
211 A 5 4 1.00 16 0.250
212 A 7 6 1.00 16 0.375
213 A 7 6 1.00 16 0.375
214 A 13 9 1.00 10 0.900
215 A 11 8 1.00 8 1.000
216 A 5 5 1.00 8 0.625
217 A 7 6 1.00 10 0.600
218 A 14 9 1.00 10 0.900
219 A 12 8 1.00 8 1.000
220 A 12 8 1.00 8 1.000
221 A 14 9 1.00 10 0.900
222 A 23 9 1.00 10 0.900
223 A 21 8 1.00 8 1.000
224 A 15 12 1.00 8 1.500
225 A 17 13 1.00 10 1.300
226 A 5 5 1.00 14 0.357
227 A 7 6 1.00 14 0.429
228 A 6 3 1.00 18 0.167
229 A 5 3 1.00 18 0.167
230 A 4 3 1.00 16 0.188
231 A 4 3 1.00 16 0.188
232 A 5 3 1.00 18 0.167
233 A 6 3 1.00 18 0.167
234 A 9 7 1.00 25 0.280
235 A 8 7 1.00 25 0.280
236 A 4 4 1.00 25 0.160
237 A 4 4 1.00 25 0.160
238 A 8 7 1.00 25 0.280
239 A 9 7 1.00 25 0.280
240 A 19 5 1.00 9 0.556
241 A 13 5 1.00 9 0.556
242 A 9 4 1.00 7 0.571
243 A 0 0 0.00 0 0.000
244 A 19 5 1.00 9 0.556
245 A 13 5 1.00 9 0.556
246 A 9 4 1.00 7 0.571
247 A 0 0 0.00 0 0.000

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