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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 [9] had the largest ratio of [23]

# 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 5 5 1.00 21 0.238
2 A 3 2 1.00 21 0.095
3 A 4 4 1.00 21 0.190
4 A 3 2 1.00 19 0.105
5 A 3 3 1.00 19 0.158
6 A 3 2 1.00 21 0.095
7 A 4 4 1.00 21 0.190
8 A 3 2 1.00 21 0.095
9 A 6 5 1.00 23 0.217
10 A 3 2 1.00 23 0.087
11 A 5 5 1.00 23 0.217
12 A 3 2 1.00 21 0.095
13 A 4 3 1.00 21 0.143
14 A 3 2 1.00 23 0.087
15 A 5 5 1.00 23 0.217
16 A 3 2 1.00 23 0.087
17 A 6 5 1.00 23 0.217
18 A 3 2 1.00 23 0.087
19 A 6 5 1.14 23 0.217
20 A 3 2 1.00 21 0.095
21 A 4 3 1.00 21 0.143
22 A 3 2 1.00 23 0.087
23 A 6 5 1.00 23 0.217
24 A 3 2 1.00 23 0.087
25 A 6 6 1.00 23 0.261
26 A 4 4 1.00 23 0.174
27 A 5 5 1.00 23 0.217
28 A 3 3 1.00 21 0.143
29 A 4 4 1.00 21 0.190
30 A 3 3 1.00 23 0.130
31 A 5 5 1.00 23 0.217
32 A 4 4 1.00 23 0.174
33 A 7 6 1.00 23 0.261
34 A 5 4 1.00 23 0.174
35 A 6 6 1.00 23 0.261
36 A 4 4 1.00 21 0.190
37 A 5 5 1.00 21 0.238
38 A 4 4 1.00 23 0.174
39 A 6 6 1.00 23 0.261
40 A 5 4 1.00 23 0.174
41 A 8 6 1.00 23 0.261
42 A 6 5 1.00 23 0.217
43 A 7 6 1.00 23 0.261
44 A 5 4 1.00 21 0.190
45 A 6 6 1.00 21 0.286
46 A 5 4 1.00 23 0.174
47 A 7 6 1.00 23 0.261
48 A 6 5 1.00 23 0.217
49 A 8 5 1.00 21 0.238
50 A 9 6 1.00 21 0.286
51 A 7 5 1.00 21 0.238
52 A 7 6 1.00 19 0.316
53 A 5 3 1.00 19 0.158
54 A 3 2 1.00 21 0.095
55 A 6 3 1.00 21 0.143
56 A 3 2 1.00 21 0.095
57 A 8 5 1.21 23 0.217
58 A 12 8 1.00 23 0.348
59 A 7 5 1.23 23 0.217
60 A 10 8 1.00 21 0.381
61 A 8 5 1.00 21 0.238
62 A 3 2 1.00 23 0.087
63 A 9 5 1.00 23 0.217
64 A 3 2 1.00 23 0.087
65 A 8 5 1.11 23 0.217
66 A 20 8 1.00 23 0.348
67 A 7 5 1.10 23 0.217
68 A 17 8 1.00 21 0.381
69 A 13 5 1.00 21 0.238
70 A 3 2 1.00 23 0.087
71 A 14 6 1.00 23 0.261
72 A 3 2 1.00 23 0.087
73 A 11 10 1.00 23 0.435
74 A 0 0 0.00 0 0.000
75 A 11 10 1.00 23 0.435
76 A 0 0 0.00 0 0.000
77 A 0 0 0.00 0 0.000
78 A 8 8 1.00 23 0.348
79 A 0 0 0.00 0 0.000
80 A 12 11 1.00 23 0.478
81 A 4 4 1.00 21 0.190
82 A 2 1 1.00 21 0.048
83 A 3 3 1.00 21 0.143
84 A 3 3 1.00 19 0.158
85 A 3 3 1.00 19 0.158
86 A 2 1 1.00 21 0.048
87 A 4 4 1.00 21 0.190
88 A 3 2 1.00 21 0.095
89 A 4 4 1.00 23 0.174
90 A 4 3 1.00 23 0.130
91 A 5 4 1.00 23 0.174
92 A 5 4 1.00 21 0.190
93 A 4 4 1.00 21 0.190
94 A 3 2 1.00 23 0.087
95 A 5 5 1.00 23 0.217
96 A 3 2 1.00 23 0.087
97 A 6 5 1.00 23 0.217
98 A 5 4 1.00 23 0.174
99 A 5 4 1.00 23 0.174
100 A 6 5 1.00 21 0.238
101 A 5 5 1.00 21 0.238
102 A 3 2 1.00 23 0.087
103 A 6 6 1.00 23 0.261
104 A 3 2 1.00 23 0.087
105 A 6 6 1.00 23 0.261
106 A 4 3 1.00 23 0.130
107 A 5 5 1.00 23 0.217
108 A 3 3 1.00 21 0.143
109 A 2 2 1.00 21 0.095
110 A 2 2 1.00 23 0.087
111 A 4 4 1.00 23 0.174
112 A 3 3 1.00 23 0.130
113 A 5 5 1.00 23 0.217
114 A 4 3 1.00 23 0.130
115 A 5 4 1.00 23 0.174
116 A 6 6 1.00 23 0.261
117 A 5 4 1.00 21 0.190
118 A 3 3 1.00 21 0.143
119 A 3 3 1.00 23 0.130
120 A 3 3 1.00 23 0.130
121 A 3 3 1.00 23 0.130
122 A 5 5 1.00 23 0.217
123 A 5 4 1.00 23 0.174
124 A 6 6 1.00 23 0.261
125 A 7 6 1.00 23 0.261
126 A 6 5 1.00 21 0.238
127 A 4 4 1.00 21 0.190
128 A 4 3 1.00 23 0.130
129 A 4 4 1.00 23 0.174
130 A 4 4 1.00 23 0.174
131 A 4 3 1.00 23 0.130
132 A 4 4 1.00 23 0.174
133 A 6 6 1.00 23 0.261
134 A 4 3 1.00 21 0.143
135 A 3 3 1.00 21 0.143
136 A 3 3 1.00 21 0.143
137 A 2 2 1.00 19 0.105
138 A 3 2 1.00 12 0.167
139 A 3 2 1.00 19 0.105
140 A 2 2 1.00 21 0.095
141 A 3 3 1.00 21 0.143
142 A 4 4 1.00 21 0.190
143 A 4 4 1.00 21 0.190
144 A 4 3 1.00 23 0.130
145 A 4 3 1.00 23 0.130
146 A 4 3 1.00 23 0.130
147 A 4 3 1.00 21 0.143
148 A 4 3 1.00 14 0.214
149 A 4 3 1.00 21 0.143
150 A 4 3 1.00 23 0.130
151 A 4 3 1.00 23 0.130
152 A 4 3 1.00 23 0.130
153 A 4 3 1.00 23 0.130
154 A 4 3 1.00 23 0.130
155 A 4 3 1.00 23 0.130
156 A 4 3 1.00 23 0.130
157 A 4 3 1.00 23 0.130
158 A 4 3 1.00 23 0.130
159 A 4 3 1.00 21 0.143
160 A 4 3 1.00 14 0.214
161 A 4 3 1.00 21 0.143
162 A 4 3 1.00 23 0.130
163 A 4 3 1.00 23 0.130
164 A 4 3 1.00 23 0.130
165 A 4 3 1.00 23 0.130
166 A 4 3 1.00 23 0.130
167 A 4 3 1.00 23 0.130
168 A 4 3 1.00 14 0.214
169 A 4 3 1.00 14 0.214
170 A 4 3 1.00 23 0.130
171 A 5 5 1.00 23 0.217
172 A 4 3 1.00 23 0.130
173 A 4 4 1.00 23 0.174
174 A 5 4 1.00 21 0.190
175 A 3 3 1.00 14 0.214
176 A 4 3 1.00 21 0.143
177 A 5 5 1.00 23 0.217
178 A 4 3 1.00 23 0.130
179 A 6 6 1.00 23 0.261
180 A 4 3 1.00 23 0.130
181 A 5 5 1.00 23 0.217
182 A 4 3 1.00 23 0.130
183 A 5 5 1.00 23 0.217
184 A 4 3 1.00 21 0.143
185 A 5 5 1.00 14 0.357
186 A 4 3 1.00 21 0.143
187 A 6 6 1.00 23 0.261
188 A 4 3 1.00 23 0.130
189 A 7 6 1.00 23 0.261
190 A 6 6 1.00 23 0.261
191 A 4 3 1.00 23 0.130
192 A 6 6 1.00 23 0.261
193 A 4 3 1.00 23 0.130
194 A 6 6 1.00 23 0.261
195 A 4 3 1.00 21 0.143
196 A 6 6 1.00 14 0.429
197 A 4 3 1.00 21 0.143
198 A 7 7 1.00 23 0.304
199 A 4 3 1.00 23 0.130
200 A 8 7 1.00 23 0.304
201 A 7 6 1.00 14 0.429
202 A 3 3 1.00 12 0.250
203 A 4 4 1.00 10 0.400
204 A 4 4 1.00 12 0.333
205 A 5 5 1.00 10 0.500
206 A 3 3 1.00 12 0.250
207 A 3 3 1.00 10 0.300
208 A 7 6 1.00 17 0.353
209 A 8 7 1.00 17 0.412
210 A 6 6 1.00 17 0.353
211 A 7 6 1.00 17 0.353
212 A 5 5 1.00 15 0.333
213 A 6 5 1.00 12 0.417
214 A 7 5 1.00 15 0.333
215 A 5 5 1.00 17 0.294
216 A 8 6 1.00 17 0.353
217 A 6 6 1.00 17 0.353
218 A 9 7 1.00 17 0.412
219 A 7 6 1.00 17 0.353
220 A 8 7 1.00 17 0.412
221 A 6 5 1.00 15 0.333
222 A 7 6 1.00 12 0.500
223 A 8 6 1.00 15 0.400
224 A 7 6 1.00 17 0.353
225 A 5 5 1.00 10 0.500
226 A 6 5 1.00 12 0.417
227 A 6 6 1.00 10 0.600
228 A 7 6 1.00 12 0.500
229 A 6 5 1.00 17 0.294
230 A 7 6 1.00 17 0.353
231 A 5 5 1.00 17 0.294
232 A 6 5 1.00 17 0.294
233 A 4 4 1.00 15 0.267
234 A 3 3 1.00 12 0.250
235 A 7 5 1.00 15 0.333
236 A 5 5 1.00 17 0.294
237 A 8 6 1.00 17 0.353
238 A 6 5 1.00 17 0.294
239 A 7 6 1.00 17 0.353
240 A 5 5 1.00 17 0.294
241 A 4 4 1.00 17 0.235
242 A 5 5 1.00 15 0.333
243 A 4 4 1.00 12 0.333
244 A 8 6 1.00 15 0.400
245 A 6 6 1.00 17 0.353
246 A 8 7 1.00 17 0.412
247 A 6 5 1.00 17 0.294
248 A 6 6 1.00 17 0.353
249 A 6 6 1.00 17 0.353
250 A 6 6 1.00 17 0.353
251 A 6 5 1.00 15 0.333
252 A 6 6 1.00 12 0.500
253 A 9 7 1.00 15 0.467
254 A 7 7 1.00 17 0.412
255 A 3 3 1.00 10 0.300
256 A 3 3 1.00 12 0.250
257 A 6 4 1.26 14 0.286
258 A 6 5 1.00 8 0.625
259 A 9 8 1.00 15 0.533
260 A 8 7 1.00 15 0.467
261 A 4 4 1.00 15 0.267
262 A 6 6 1.00 15 0.400
263 A 7 7 1.00 15 0.467

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