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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 [207] had the largest ratio of [57]

# 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 6 3 1.00 23 0.130
2 A 6 4 1.00 20 0.200
3 A 6 4 1.00 20 0.200
4 A 6 4 1.00 18 0.222
5 A 7 7 1.00 17 0.412
6 A 2 2 1.00 20 0.100
7 A 8 7 1.00 20 0.350
8 A 7 5 1.00 20 0.250
9 A 7 5 1.00 20 0.250
10 A 15 9 1.00 22 0.409
11 A 14 9 1.00 22 0.409
12 A 13 9 1.00 20 0.450
13 A 14 12 1.00 19 0.632
14 A 3 3 1.00 22 0.136
15 A 10 10 1.00 22 0.454
16 A 14 9 1.00 22 0.409
17 A 29 12 1.00 22 0.546
18 A 26 12 1.00 22 0.546
19 A 23 12 1.00 20 0.600
20 A 24 16 1.00 19 0.842
21 A 4 3 1.00 22 0.136
22 A 14 11 1.00 22 0.500
23 A 22 10 1.00 22 0.454
24 A 7 5 1.00 26 0.192
25 A 8 9 1.00 24 0.375
26 A 2 2 1.00 26 0.077
27 A 9 8 1.00 26 0.308
28 A 9 7 1.00 26 0.269
29 A 8 7 1.00 23 0.304
30 A 7 6 1.00 26 0.231
31 A 8 7 1.00 26 0.269
32 A 13 9 1.00 28 0.321
33 A 15 16 1.00 26 0.615
34 A 3 3 1.00 28 0.107
35 A 11 11 1.00 28 0.393
36 A 30 17 1.00 28 0.607
37 A 26 16 1.00 25 0.640
38 A 16 12 1.00 28 0.429
39 A 22 14 1.00 28 0.500
40 A 22 11 1.00 28 0.393
41 A 24 21 1.00 26 0.808
42 A 4 3 1.00 28 0.107
43 A 15 12 1.00 28 0.429
44 A 42 17 1.00 25 0.680
45 A 26 13 1.00 28 0.464
46 A 7 5 1.00 28 0.179
47 A 7 5 1.00 26 0.192
48 A 7 5 1.00 25 0.200
49 A 2 2 1.00 28 0.071
50 A 8 6 1.00 28 0.214
51 A 8 6 1.00 28 0.214
52 A 8 6 1.00 28 0.214
53 A 18 10 1.00 30 0.333
54 A 16 10 1.00 28 0.357
55 A 14 9 1.00 27 0.333
56 A 3 3 1.00 30 0.100
57 A 17 14 1.00 30 0.467
58 A 19 14 1.00 30 0.467
59 A 30 13 1.00 28 0.464
60 A 24 12 1.00 27 0.444
61 A 4 3 1.00 30 0.100
62 A 28 16 1.00 30 0.533
63 A 34 16 1.00 30 0.533
64 A 5 3 1.00 28 0.107
65 A 4 3 1.00 28 0.107
66 A 3 3 1.00 28 0.107
67 A 2 2 1.00 26 0.077
68 A 0 0 0.00 0 0.000
69 A 0 0 0.00 0 0.000
70 A 7 5 1.00 24 0.208
71 A 7 5 1.00 24 0.208
72 A 7 5 1.00 22 0.227
73 A 8 8 1.00 21 0.381
74 A 4 4 1.00 24 0.167
75 A 9 8 1.00 24 0.333
76 A 8 6 1.00 24 0.250
77 A 8 6 1.00 24 0.250
78 A 24 12 1.00 26 0.462
79 A 21 12 1.00 24 0.500
80 A 18 11 1.00 23 0.478
81 A 5 5 1.00 26 0.192
82 A 10 10 1.00 26 0.385
83 A 14 9 1.00 26 0.346
84 A 19 9 1.00 26 0.346
85 A 34 13 1.00 24 0.542
86 A 28 12 1.00 23 0.522
87 A 6 5 1.00 26 0.192
88 A 14 11 1.00 26 0.423
89 A 22 10 1.00 26 0.385
90 A 9 6 1.00 26 0.231
91 A 9 10 1.00 24 0.417
92 A 4 4 1.00 26 0.154
93 A 11 9 1.00 26 0.346
94 A 10 7 1.00 26 0.269
95 A 9 6 1.00 26 0.231
96 A 8 6 1.00 23 0.261
97 A 7 5 1.00 26 0.192
98 A 8 6 1.00 26 0.231
99 A 9 6 1.00 26 0.231
100 A 17 11 1.00 26 0.423
101 A 5 5 1.00 28 0.179
102 A 11 11 1.00 28 0.393
103 A 15 10 1.00 28 0.357
104 A 30 17 1.00 28 0.607
105 A 26 16 1.00 25 0.640
106 A 16 12 1.00 28 0.429
107 A 22 14 1.00 28 0.500
108 A 26 12 1.00 26 0.462
109 A 6 5 1.00 28 0.179
110 A 15 12 1.00 28 0.429
111 A 49 18 1.00 28 0.643
112 A 42 17 1.00 25 0.680
113 A 26 13 1.00 28 0.464
114 A 36 15 1.00 28 0.536
115 A 9 6 1.00 28 0.214
116 A 9 6 1.00 26 0.231
117 A 9 7 1.00 25 0.280
118 A 4 4 1.00 28 0.143
119 A 10 7 1.00 28 0.250
120 A 10 7 1.00 28 0.250
121 A 10 7 1.00 28 0.250
122 A 22 13 1.00 28 0.464
123 A 20 13 1.00 26 0.500
124 A 18 13 1.00 25 0.520
125 A 5 5 1.00 28 0.179
126 A 21 17 1.00 28 0.607
127 A 23 17 1.00 28 0.607
128 A 36 16 1.00 26 0.615
129 A 30 16 1.00 25 0.640
130 A 6 5 1.00 28 0.179
131 A 34 19 1.00 28 0.679
132 A 40 19 1.00 28 0.679
133 A 9 6 1.00 30 0.200
134 A 9 6 1.00 30 0.200
135 A 11 9 1.00 30 0.300
136 A 10 7 1.00 30 0.233
137 A 10 7 1.00 30 0.233
138 A 0 0 0.00 0 0.000
139 A 6 5 1.00 28 0.179
140 A 5 5 1.00 28 0.179
141 A 4 4 1.00 26 0.154
142 A 0 0 0.00 0 0.000
143 A 0 0 0.00 0 0.000
144 A 0 0 0.00 0 0.000
145 A 0 0 0.00 0 0.000
146 A 0 0 0.00 0 0.000
147 A 4 4 1.00 26 0.154
148 A 0 0 0.00 0 0.000
149 A 0 0 0.00 0 0.000
150 A 18 12 1.00 32 0.375
151 A 16 12 1.00 32 0.375
152 A 14 11 1.00 30 0.367
153 A 15 12 1.00 32 0.375
154 A 16 12 1.00 32 0.375
155 A 18 12 1.00 32 0.375
156 A 3 3 1.00 24 0.125
157 A 3 3 1.00 22 0.136
158 A 3 2 1.00 21 0.095
159 A 4 5 1.00 24 0.208
160 A 2 2 1.00 24 0.083
161 A 3 3 1.00 24 0.125
162 A 3 3 1.00 24 0.125
163 A 7 5 1.00 26 0.192
164 A 7 5 1.00 24 0.208
165 A 6 3 1.00 23 0.130
166 A 4 4 1.00 26 0.154
167 A 6 4 1.00 26 0.154
168 A 7 5 1.00 26 0.192
169 A 7 5 1.00 26 0.192
170 A 6 6 1.00 26 0.231
171 A 6 6 1.00 24 0.250
172 A 6 6 1.00 23 0.261
173 A 5 6 1.00 26 0.231
174 A 6 6 1.00 26 0.231
175 A 6 6 1.00 26 0.231
176 A 7 4 1.52 23 0.174
177 A 2 4 1.00 18 0.222
178 A 8 7 1.00 28 0.250
179 A 7 7 1.00 26 0.269
180 A 7 7 1.00 24 0.292
181 A 7 7 1.00 23 0.304
182 A 4 4 1.00 26 0.154
183 A 7 7 1.00 26 0.269
184 A 7 7 1.00 26 0.269
185 A 7 7 1.00 26 0.269
186 A 17 11 1.00 18 0.611
187 A 17 11 1.00 18 0.611
188 A 9 10 1.00 18 0.556
189 A 9 10 1.00 18 0.556
190 A 17 11 1.00 18 0.611
191 A 12 11 1.00 18 0.611
192 A 9 10 1.00 18 0.556
193 A 9 10 1.00 18 0.556
194 A 21 14 1.00 20 0.700
195 A 21 14 1.00 20 0.700
196 A 21 14 1.00 20 0.700
197 A 22 15 1.00 20 0.750
198 A 0 0 0.00 0 0.000
199 A 4 2 1.00 23 0.087
200 A 3 2 1.00 23 0.087
201 A 2 2 1.00 21 0.095
202 A 0 0 0.00 0 0.000
203 A 0 0 0.00 0 0.000
204 A 0 0 0.00 0 0.000
205 A 2 2 1.00 11 0.182
206 A 3 2 1.00 13 0.154
207 A 2 1 1.00 57 0.018
208 A 10 5 1.00 19 0.263
209 A 10 5 1.00 17 0.294
210 A 10 8 1.00 16 0.500
211 A 2 2 1.00 19 0.105
212 A 13 8 1.00 19 0.421
213 A 11 6 1.00 19 0.316
214 A 15 6 1.00 19 0.316
215 A 15 6 1.00 17 0.353
216 A 14 9 1.00 16 0.562
217 A 2 2 1.00 19 0.105
218 A 19 9 1.00 19 0.474
219 A 16 7 1.00 19 0.368
220 A 0 0 0.00 0 0.000
221 A 0 0 0.00 0 0.000
222 A 0 0 0.00 0 0.000
223 A 2 2 1.00 14 0.143
224 A 2 2 1.00 12 0.167
225 A 2 2 1.00 10 0.200
226 A 2 2 1.00 14 0.143
227 A 2 2 1.00 14 0.143
228 A 2 2 1.00 14 0.143
229 A 2 2 1.00 14 0.143
230 A 3 3 1.00 16 0.188
231 A 3 3 1.00 14 0.214
232 A 3 3 1.00 12 0.250
233 A 3 3 1.00 16 0.188
234 A 3 3 1.00 16 0.188
235 A 3 3 1.00 16 0.188
236 A 3 3 1.00 16 0.188
237 A 4 3 1.00 22 0.136
238 A 3 3 1.00 22 0.136
239 A 2 2 1.00 20 0.100
240 A 3 3 1.00 22 0.136
241 A 4 4 1.00 22 0.182
242 A 3 3 1.00 22 0.136
243 A 3 3 1.00 20 0.150
244 A 3 3 1.00 18 0.167
245 A 3 3 1.00 16 0.188
246 A 3 3 1.00 20 0.150
247 A 3 3 1.00 20 0.150
248 A 3 3 1.00 20 0.150
249 A 6 6 1.00 24 0.250

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