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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 [198] had the largest ratio of [.565216999999999969]

# 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 2 2 1.00 13 0.154
2 A 1 1 1.00 18 0.056
3 A 1 1 1.00 13 0.077
4 A 6 5 0.91 21 0.238
5 A 5 4 0.92 21 0.190
6 A 3 2 0.90 21 0.095
7 A 5 4 0.92 21 0.190
8 A 6 5 0.91 21 0.238
9 A 4 3 1.00 17 0.176
10 A 1 1 1.31 17 0.059
11 A 2 2 1.00 21 0.095
12 A 2 2 1.00 21 0.095
13 A 2 2 1.00 19 0.105
14 A 1 1 1.00 7 0.143
15 A 3 3 1.00 21 0.143
16 A 3 3 1.00 21 0.143
17 A 2 2 1.00 17 0.118
18 A 2 2 1.00 17 0.118
19 A 2 2 1.00 17 0.118
20 A 2 2 1.00 15 0.133
21 A 1 1 1.00 9 0.111
22 A 2 2 1.00 17 0.118
23 A 2 2 1.00 17 0.118
24 A 2 2 1.00 17 0.118
25 A 2 2 1.00 17 0.118
26 A 2 2 1.00 17 0.118
27 A 2 2 1.00 19 0.105
28 A 2 2 1.00 19 0.105
29 A 2 2 1.00 19 0.105
30 A 2 2 1.00 17 0.118
31 A 2 2 1.00 11 0.182
32 A 2 2 1.00 19 0.105
33 A 2 2 1.00 19 0.105
34 A 2 2 1.00 19 0.105
35 A 2 2 1.00 19 0.105
36 A 2 2 1.00 19 0.105
37 A 2 2 1.00 19 0.105
38 A 2 2 1.00 19 0.105
39 A 2 2 1.00 19 0.105
40 A 2 2 1.00 19 0.105
41 A 2 2 1.00 19 0.105
42 A 2 2 1.00 19 0.105
43 A 2 2 1.00 17 0.118
44 A 2 2 1.00 11 0.182
45 A 2 2 1.00 19 0.105
46 A 2 2 1.00 19 0.105
47 A 2 2 1.00 19 0.105
48 A 2 2 1.00 19 0.105
49 A 2 2 1.00 19 0.105
50 A 2 2 1.00 19 0.105
51 A 2 2 1.00 19 0.105
52 A 2 2 1.00 19 0.105
53 A 2 2 1.00 19 0.105
54 A 2 2 1.00 19 0.105
55 A 2 2 1.05 19 0.105
56 A 2 2 1.08 19 0.105
57 A 2 2 1.12 19 0.105
58 A 2 2 1.17 17 0.118
59 A 2 2 1.00 11 0.182
60 A 2 2 1.13 19 0.105
61 A 2 2 1.10 19 0.105
62 A 2 2 1.10 19 0.105
63 A 2 2 1.08 19 0.105
64 A 2 2 1.11 19 0.105
65 A 2 2 1.11 19 0.105
66 A 2 2 1.18 19 0.105
67 A 2 2 1.25 17 0.118
68 A 2 2 1.00 11 0.182
69 A 2 2 1.06 19 0.105
70 A 2 2 1.08 19 0.105
71 A 2 2 1.06 19 0.105
72 A 2 2 1.07 19 0.105
73 A 2 2 1.08 19 0.105
74 A 2 2 1.12 19 0.105
75 A 2 2 1.14 19 0.105
76 A 2 2 1.15 19 0.105
77 A 2 2 1.16 17 0.118
78 A 2 2 1.00 11 0.182
79 A 2 2 1.04 19 0.105
80 A 2 2 1.06 19 0.105
81 A 2 2 1.00 19 0.105
82 A 2 2 1.00 19 0.105
83 A 2 2 1.00 19 0.105
84 A 2 2 1.00 19 0.105
85 A 2 2 1.00 19 0.105
86 A 2 2 1.00 19 0.105
87 A 2 2 1.00 19 0.105
88 A 2 2 1.00 19 0.105
89 A 2 2 1.00 21 0.095
90 A 2 2 1.00 21 0.095
91 A 2 2 1.00 21 0.095
92 A 2 2 1.00 21 0.095
93 A 2 2 1.00 21 0.095
94 A 2 2 1.00 21 0.095
95 A 2 2 1.00 21 0.095
96 A 2 2 1.00 21 0.095
97 A 2 2 1.00 21 0.095
98 A 2 2 1.00 21 0.095
99 A 2 2 1.00 21 0.095
100 A 2 2 1.00 21 0.095
101 A 2 2 1.00 21 0.095
102 A 2 2 1.00 21 0.095
103 A 2 2 1.00 21 0.095
104 A 2 2 1.00 21 0.095
105 A 9 8 1.16 21 0.381
106 A 8 7 1.17 21 0.333
107 A 7 6 1.14 21 0.286
108 A 4 3 1.10 21 0.143
109 A 4 3 1.10 21 0.143
110 A 6 5 1.30 21 0.238
111 A 7 6 1.36 21 0.286
112 A 8 7 1.35 21 0.333
113 A 10 9 1.11 21 0.429
114 A 9 8 1.12 21 0.381
115 A 8 7 1.13 21 0.333
116 A 7 6 0.99 21 0.286
117 A 7 6 0.99 21 0.286
118 A 7 6 1.15 21 0.286
119 A 8 7 1.20 21 0.333
120 A 9 8 1.20 21 0.381
121 A 11 10 1.03 21 0.476
122 A 10 9 1.04 21 0.429
123 A 9 8 0.87 21 0.381
124 A 9 8 0.88 21 0.381
125 A 9 8 1.03 21 0.381
126 A 9 8 0.98 21 0.381
127 A 9 8 1.09 21 0.381
128 A 10 9 1.10 21 0.429
129 A 7 6 0.71 21 0.286
130 A 7 6 0.79 21 0.286
131 A 5 4 0.79 19 0.211
132 A 4 3 0.82 13 0.231
133 A 7 6 1.22 21 0.286
134 A 7 6 1.21 21 0.286
135 A 4 3 0.95 21 0.143
136 A 5 4 0.93 21 0.190
137 A 7 6 0.93 21 0.286
138 A 9 8 0.92 21 0.381
139 A 8 7 0.59 21 0.333
140 A 8 7 0.65 21 0.333
141 A 6 5 0.71 19 0.263
142 A 5 4 0.79 13 0.308
143 A 9 8 1.10 21 0.381
144 A 10 9 1.07 21 0.429
145 A 8 7 0.99 21 0.333
146 A 9 8 1.17 21 0.381
147 A 5 4 0.93 21 0.190
148 A 9 8 0.53 21 0.381
149 A 9 8 0.58 21 0.381
150 A 7 6 0.66 19 0.316
151 A 6 5 0.77 13 0.385
152 A 11 10 1.02 21 0.476
153 A 12 11 1.02 21 0.524
154 A 10 9 0.90 21 0.429
155 A 10 9 0.86 21 0.429
156 A 10 9 1.01 21 0.429
157 A 6 5 0.95 21 0.238
158 A 6 5 1.05 21 0.238
159 A 4 3 1.00 19 0.158
160 A 3 2 1.00 13 0.154
161 A 3 2 1.31 21 0.095
162 A 4 3 1.21 21 0.143
163 A 6 5 1.20 21 0.238
164 A 6 5 1.10 21 0.238
165 A 7 6 1.13 21 0.286
166 A 1 1 0.69 19 0.053
167 A 1 1 0.60 13 0.077
168 A 5 4 1.06 21 0.190
169 A 6 5 1.13 21 0.238
170 A 8 7 1.12 21 0.333
171 A 7 6 0.94 21 0.286
172 A 2 2 0.62 21 0.095
173 A 2 2 0.46 21 0.095
174 A 2 2 0.63 19 0.105
175 A 2 2 0.61 13 0.154
176 A 7 6 1.07 21 0.286
177 A 8 7 1.10 21 0.333
178 A 3 3 0.51 21 0.143
179 A 4 4 0.64 21 0.190
180 A 3 3 0.69 21 0.143
181 A 3 3 0.60 19 0.158
182 A 3 3 0.64 13 0.231
183 A 9 8 1.02 21 0.381
184 A 10 9 1.08 21 0.429
185 A 10 10 0.88 23 0.435
186 A 9 9 0.95 23 0.391
187 A 7 7 0.93 23 0.304
188 A 7 7 1.13 23 0.304
189 A 9 9 1.28 23 0.391
190 A 11 11 1.31 23 0.478
191 A 12 12 0.88 23 0.522
192 A 11 11 0.86 23 0.478
193 A 9 9 0.86 23 0.391
194 A 9 9 0.86 23 0.391
195 A 9 9 1.02 23 0.391
196 A 9 9 1.12 23 0.391
197 A 11 11 1.18 23 0.478
198 A 13 13 0.85 23 0.565
199 A 11 11 0.83 23 0.478
200 A 11 11 0.82 23 0.478
201 A 11 11 0.93 23 0.478
202 A 11 11 0.93 23 0.478
203 A 11 11 1.05 23 0.478
204 A 11 11 1.04 23 0.478
205 A 12 12 0.92 23 0.522
206 A 10 10 0.89 23 0.435
207 A 8 8 0.90 23 0.348
208 A 3 3 0.46 23 0.130
209 A 3 3 1.01 23 0.130
210 A 5 5 0.71 23 0.217
211 A 10 10 1.23 23 0.435
212 A 12 12 1.26 23 0.522
213 A 12 12 0.93 23 0.522
214 A 10 10 0.96 23 0.435
215 A 8 8 0.97 23 0.348
216 A 8 8 1.15 23 0.348
217 A 8 8 1.20 23 0.348
218 A 10 10 1.20 23 0.435
219 A 12 12 1.19 23 0.522
220 A 12 12 1.01 23 0.522
221 A 10 10 1.05 23 0.435
222 A 10 10 1.02 23 0.435
223 A 10 10 1.17 23 0.435
224 A 10 10 1.11 23 0.435
225 A 10 10 1.12 23 0.435
226 A 12 12 1.14 23 0.522
227 A 6 6 1.00 23 0.261
228 A 6 6 1.00 23 0.261
229 A 6 6 0.29 23 0.261
230 A 6 6 0.65 23 0.261
231 A 2 2 1.00 19 0.105
232 A 2 2 1.00 19 0.105
233 A 1 1 1.00 24 0.042
234 B 8 7 2.92 24 0.292
235 A 2 2 1.00 23 0.087
236 A 1 1 1.00 24 0.042
237 A 6 5 1.81 23 0.217
238 A 2 2 1.00 19 0.105
239 A 2 2 1.00 19 0.105
240 A 2 2 1.00 17 0.118
241 A 2 2 1.00 19 0.105
242 A 3 3 1.09 19 0.158
243 A 4 4 1.05 19 0.211
244 A 3 2 1.33 21 0.095
245 A 3 2 1.38 21 0.095
246 A 3 2 1.42 21 0.095
247 A 3 2 1.38 21 0.095
248 A 3 2 1.30 21 0.095
249 A 4 4 1.07 19 0.211
250 A 2 2 1.19 17 0.118
251 A 1 1 1.41 11 0.091
252 A 3 2 1.67 19 0.105
253 A 3 2 1.86 19 0.105
254 A 3 2 1.28 21 0.095
255 A 3 2 1.29 21 0.095
256 A 3 2 1.27 21 0.095
257 A 3 2 1.22 21 0.095
258 A 3 2 1.74 19 0.105
259 A 3 2 1.75 19 0.105
260 A 3 2 1.35 19 0.105
261 A 3 2 1.36 19 0.105

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