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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 [235] had the largest ratio of [.933332999999999968]

# 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 0.89 18 0.333
2 A 7 6 0.89 18 0.333
3 A 7 6 0.91 18 0.333
4 A 7 6 0.91 18 0.333
5 A 7 6 0.97 18 0.333
6 A 7 6 0.97 18 0.333
7 A 2 2 1.00 16 0.125
8 A 4 4 1.00 16 0.250
9 A 8 7 0.82 18 0.389
10 A 8 7 1.10 18 0.389
11 A 8 7 1.00 18 0.389
12 A 10 9 1.09 18 0.500
13 A 8 7 0.95 20 0.350
14 A 10 9 1.13 20 0.450
15 A 7 6 1.03 20 0.300
16 A 8 7 1.10 20 0.350
17 A 6 5 1.00 18 0.278
18 A 4 4 1.00 18 0.222
19 A 6 5 1.00 20 0.250
20 A 7 6 0.90 20 0.300
21 A 7 6 0.86 20 0.300
22 A 8 7 0.82 20 0.350
23 A 7 6 0.91 20 0.300
24 A 7 6 0.89 20 0.300
25 A 7 6 0.97 20 0.300
26 A 7 6 0.91 20 0.300
27 A 6 5 1.00 18 0.278
28 A 7 6 0.82 18 0.333
29 A 6 5 1.00 20 0.250
30 A 6 6 1.12 20 0.300
31 A 8 7 0.81 20 0.350
32 A 10 9 1.21 20 0.450
33 A 7 6 0.89 18 0.333
34 A 7 6 0.89 18 0.333
35 A 7 6 0.91 18 0.333
36 A 7 6 0.91 18 0.333
37 A 7 6 0.97 18 0.333
38 A 7 6 0.97 18 0.333
39 A 6 5 1.00 18 0.278
40 A 4 4 1.00 16 0.250
41 A 8 7 0.82 16 0.438
42 A 8 7 1.10 18 0.389
43 A 8 7 1.00 18 0.389
44 A 10 9 1.09 18 0.500
45 A 17 17 1.21 20 0.850
46 A 8 7 0.95 20 0.350
47 A 13 13 1.20 20 0.650
48 A 7 6 1.03 20 0.300
49 A 9 9 1.32 20 0.450
50 A 6 5 1.00 20 0.250
51 A 5 5 1.29 20 0.250
52 A 5 5 1.17 18 0.278
53 A 7 6 0.90 18 0.333
54 A 7 6 0.81 20 0.300
55 A 8 7 0.78 20 0.350
56 A 7 6 0.83 20 0.300
57 A 8 7 0.81 20 0.350
58 A 7 6 0.78 20 0.300
59 A 7 6 0.89 20 0.300
60 A 7 6 0.87 20 0.300
61 A 7 6 0.91 20 0.300
62 A 7 6 0.89 20 0.300
63 A 7 6 0.97 20 0.300
64 A 7 6 0.91 20 0.300
65 A 6 5 1.00 20 0.250
66 A 6 5 0.96 20 0.250
67 A 8 7 0.88 20 0.350
68 A 7 6 1.00 18 0.333
69 A 8 7 0.81 18 0.389
70 A 10 9 1.21 20 0.450
71 A 8 7 0.96 20 0.350
72 A 10 9 1.14 20 0.450
73 A 8 8 1.11 20 0.400
74 A 6 6 1.09 20 0.300
75 A 4 4 1.06 20 0.200
76 A 2 2 1.00 20 0.100
77 A 2 2 1.00 20 0.100
78 A 4 4 1.00 20 0.200
79 A 6 6 1.06 20 0.300
80 A 8 8 1.10 20 0.400
81 A 8 8 1.10 22 0.364
82 A 6 6 1.07 22 0.273
83 A 6 6 1.07 22 0.273
84 A 4 4 1.00 22 0.182
85 A 4 4 1.00 22 0.182
86 A 4 4 1.00 22 0.182
87 A 4 4 1.00 22 0.182
88 A 6 6 1.01 22 0.273
89 A 8 8 1.11 22 0.364
90 A 6 6 1.09 22 0.273
91 A 4 4 1.06 22 0.182
92 A 6 6 1.06 22 0.273
93 A 2 2 1.00 22 0.091
94 A 4 4 1.00 22 0.182
95 A 6 6 1.06 22 0.273
96 A 8 8 1.09 22 0.364
97 A 10 10 1.12 20 0.500
98 A 8 8 1.11 20 0.400
99 A 6 6 1.12 20 0.300
100 A 4 4 1.13 20 0.200
101 A 2 2 1.00 20 0.100
102 A 6 6 1.04 20 0.300
103 A 8 8 1.09 20 0.400
104 A 10 10 1.11 20 0.500
105 A 8 8 1.09 22 0.364
106 A 8 8 1.09 22 0.364
107 A 6 6 1.09 22 0.273
108 A 6 6 1.10 22 0.273
109 A 4 4 1.00 22 0.182
110 A 4 4 1.00 22 0.182
111 A 6 6 1.01 22 0.273
112 A 6 6 1.06 22 0.273
113 A 8 8 1.06 22 0.364
114 A 8 8 1.09 22 0.364
115 A 14 14 1.13 22 0.636
116 A 12 12 1.11 22 0.545
117 A 10 10 1.17 22 0.455
118 A 8 8 1.13 22 0.364
119 A 2 2 1.00 22 0.091
120 A 4 4 1.00 22 0.182
121 A 8 8 1.06 22 0.364
122 A 10 10 1.09 22 0.455
123 A 4 4 1.00 20 0.200
124 A 4 4 1.00 20 0.200
125 A 4 4 1.00 18 0.222
126 A 4 4 1.00 18 0.222
127 A 4 4 1.00 20 0.200
128 A 4 4 1.00 20 0.200
129 A 7 6 0.89 18 0.333
130 A 7 6 0.89 18 0.333
131 A 7 6 0.91 18 0.333
132 A 7 6 0.91 18 0.333
133 A 7 6 0.97 18 0.333
134 A 7 6 0.97 18 0.333
135 A 2 2 1.00 16 0.125
136 A 4 4 1.00 16 0.250
137 A 8 7 0.82 18 0.389
138 A 8 7 1.10 18 0.389
139 A 8 7 1.00 18 0.389
140 A 10 9 1.09 18 0.500
141 A 8 7 0.95 20 0.350
142 A 10 9 1.13 20 0.450
143 A 7 6 1.07 20 0.300
144 A 8 7 1.10 20 0.350
145 A 6 5 1.00 18 0.278
146 A 5 5 1.14 18 0.278
147 A 6 5 1.00 20 0.250
148 A 7 6 0.90 20 0.300
149 A 7 6 0.81 20 0.300
150 A 8 7 0.78 20 0.350
151 A 7 6 0.91 20 0.300
152 A 7 6 0.89 20 0.300
153 A 7 6 0.97 20 0.300
154 A 7 6 0.91 20 0.300
155 A 6 5 1.00 18 0.278
156 A 8 7 0.82 18 0.389
157 A 7 6 1.00 20 0.300
158 A 6 6 1.12 20 0.300
159 A 8 7 0.81 20 0.350
160 A 10 9 1.21 20 0.450
161 A 8 8 1.11 20 0.400
162 A 6 6 1.09 20 0.300
163 A 4 4 1.06 20 0.200
164 A 2 2 1.00 20 0.100
165 A 2 2 1.00 20 0.100
166 A 4 4 1.00 20 0.200
167 A 6 6 1.06 20 0.300
168 A 8 8 1.10 20 0.400
169 A 8 8 1.10 22 0.364
170 A 6 6 1.07 22 0.273
171 A 6 6 1.07 22 0.273
172 A 4 4 1.00 22 0.182
173 A 4 4 1.00 22 0.182
174 A 4 4 1.00 22 0.182
175 A 4 4 1.00 22 0.182
176 A 6 6 1.01 22 0.273
177 A 8 8 1.11 22 0.364
178 A 6 6 1.09 22 0.273
179 A 4 4 1.06 22 0.182
180 A 6 6 1.06 22 0.273
181 A 2 2 1.00 22 0.091
182 A 4 4 1.00 22 0.182
183 A 6 6 1.06 22 0.273
184 A 8 8 1.09 22 0.364
185 A 2 2 1.00 11 0.182
186 A 4 4 1.32 11 0.364
187 A 4 4 1.00 20 0.200
188 A 4 4 1.00 20 0.200
189 A 4 4 1.00 18 0.222
190 A 7 6 0.91 28 0.214
191 A 2 2 0.98 15 0.133
192 A 2 2 1.00 15 0.133
193 A 2 2 1.00 15 0.133
194 A 2 2 1.00 13 0.154
195 A 5 5 1.08 13 0.385
196 A 7 6 1.00 15 0.400
197 A 8 7 1.00 15 0.467
198 A 9 8 0.94 15 0.533
199 A 8 7 0.87 15 0.467
200 A 11 10 0.95 15 0.667
201 A 2 2 0.97 17 0.118
202 A 2 2 1.00 15 0.133
203 A 2 2 1.00 17 0.118
204 A 2 2 1.00 17 0.118
205 A 2 2 0.97 17 0.118
206 A 2 2 1.00 15 0.133
207 A 2 2 1.00 17 0.118
208 A 2 2 1.00 17 0.118
209 A 2 2 0.98 15 0.133
210 A 2 2 1.00 15 0.133
211 A 2 2 1.00 15 0.133
212 A 2 2 1.00 13 0.154
213 A 4 4 1.00 13 0.308
214 A 6 5 1.00 15 0.333
215 A 7 6 1.00 15 0.400
216 A 8 7 0.94 15 0.467
217 A 7 6 0.92 15 0.400
218 A 10 9 0.95 15 0.600
219 A 2 2 0.97 17 0.118
220 A 2 2 1.00 15 0.133
221 A 2 2 1.00 17 0.118
222 A 2 2 1.00 17 0.118
223 A 2 2 0.96 17 0.118
224 A 2 2 1.00 15 0.133
225 A 2 2 1.00 17 0.118
226 A 2 2 1.00 17 0.118
227 A 5 5 1.07 13 0.385
228 A 7 6 1.00 15 0.400
229 A 8 7 1.00 15 0.467
230 A 14 13 1.19 15 0.867
231 A 9 8 1.00 15 0.533
232 A 4 4 1.00 13 0.308
233 A 4 4 1.00 13 0.308
234 A 10 9 1.00 15 0.600
235 A 15 14 1.18 15 0.933
236 A 2 2 1.00 13 0.154
237 A 2 2 1.00 13 0.154
238 A 2 2 1.00 15 0.133
239 A 2 2 1.00 15 0.133
240 A 2 2 1.00 13 0.154
241 A 4 4 1.00 13 0.308
242 A 6 5 1.00 15 0.333
243 A 7 6 1.00 15 0.400
244 A 2 2 1.00 17 0.118
245 A 2 2 1.00 17 0.118
246 A 2 2 1.00 17 0.118
247 A 14 13 1.19 15 0.867
248 A 9 8 1.00 15 0.533
249 A 4 4 1.00 13 0.308
250 A 4 4 1.00 13 0.308
251 A 10 9 1.00 15 0.600
252 A 15 14 1.18 15 0.933
253 A 2 2 1.00 13 0.154
254 A 2 2 1.00 13 0.154

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