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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 1.28 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 5 4 1.00 23 0.174
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 7 1.00 23 0.304
48 A 6 5 1.00 23 0.217
49 A 3 3 1.00 21 0.143
50 A 3 2 1.00 21 0.095
51 A 2 2 1.00 21 0.095
52 A 2 2 1.00 19 0.105
53 A 2 2 1.00 19 0.105
54 A 3 3 1.43 21 0.143
55 A 3 3 1.00 21 0.143
56 A 3 2 1.30 21 0.095
57 A 4 4 1.00 23 0.174
58 A 4 3 1.00 23 0.130
59 A 5 4 1.00 23 0.174
60 A 5 4 1.00 21 0.190
61 A 4 4 1.00 21 0.190
62 A 3 2 1.00 23 0.087
63 A 5 5 1.00 23 0.217
64 A 3 2 1.00 23 0.087
65 A 6 5 1.00 23 0.217
66 A 5 4 1.00 23 0.174
67 A 5 4 1.00 23 0.174
68 A 6 5 1.00 21 0.238
69 A 5 5 1.00 21 0.238
70 A 3 2 1.00 23 0.087
71 A 6 6 1.00 23 0.261
72 A 3 2 1.00 23 0.087
73 A 6 6 1.00 23 0.261
74 A 4 3 1.00 23 0.130
75 A 5 5 1.00 23 0.217
76 A 3 3 1.00 21 0.143
77 A 2 2 1.00 21 0.095
78 A 2 2 1.00 23 0.087
79 A 4 4 1.00 23 0.174
80 A 3 3 1.00 23 0.130
81 A 5 5 1.00 23 0.217
82 A 4 3 1.00 23 0.130
83 A 5 4 1.00 23 0.174
84 A 6 6 1.00 23 0.261
85 A 5 4 1.00 21 0.190
86 A 3 3 1.00 21 0.143
87 A 3 3 1.00 23 0.130
88 A 3 3 1.00 23 0.130
89 A 3 3 1.00 23 0.130
90 A 5 5 1.00 23 0.217
91 A 5 4 1.00 23 0.174
92 A 6 6 1.00 23 0.261
93 A 7 6 1.00 23 0.261
94 A 6 5 1.00 21 0.238
95 A 4 4 1.00 21 0.190
96 A 4 3 1.00 23 0.130
97 A 4 4 1.00 23 0.174
98 A 4 4 1.00 23 0.174
99 A 4 3 1.00 23 0.130
100 A 4 4 1.00 23 0.174
101 A 6 6 1.00 23 0.261
102 A 4 3 1.00 21 0.143
103 A 4 3 1.00 21 0.143
104 A 4 3 1.00 21 0.143
105 A 3 2 1.00 19 0.105
106 A 3 2 1.00 12 0.167
107 A 4 3 1.00 19 0.158
108 A 4 3 1.00 21 0.143
109 A 4 3 1.00 21 0.143
110 A 4 3 1.00 21 0.143
111 A 4 3 1.00 21 0.143
112 A 4 3 1.00 23 0.130
113 A 4 3 1.00 23 0.130
114 A 4 3 1.00 23 0.130
115 A 4 3 1.00 21 0.143
116 A 4 3 1.00 14 0.214
117 A 4 3 1.00 21 0.143
118 A 4 3 1.00 23 0.130
119 A 4 3 1.00 23 0.130
120 A 4 3 1.00 23 0.130
121 A 4 3 1.00 23 0.130
122 A 4 3 1.00 23 0.130
123 A 5 4 1.00 23 0.174
124 A 4 3 1.00 23 0.130
125 A 5 4 1.00 23 0.174
126 A 4 3 1.00 23 0.130
127 A 4 3 1.00 21 0.143
128 A 4 3 1.00 14 0.214
129 A 4 3 1.00 21 0.143
130 A 4 3 1.00 23 0.130
131 A 4 3 1.00 23 0.130
132 A 4 3 1.00 23 0.130
133 A 4 3 1.00 23 0.130
134 A 4 3 1.00 23 0.130
135 A 4 3 1.00 23 0.130
136 A 4 3 1.00 14 0.214
137 A 4 3 1.00 14 0.214
138 A 4 3 1.00 23 0.130
139 A 6 6 1.00 23 0.261
140 A 4 3 1.00 23 0.130
141 A 5 5 1.00 23 0.217
142 A 2 2 1.00 21 0.095
143 A 3 3 1.00 14 0.214
144 A 4 3 1.00 21 0.143
145 A 6 6 1.00 23 0.261
146 A 4 3 1.00 23 0.130
147 A 7 7 1.00 23 0.304
148 A 4 3 1.00 23 0.130
149 A 6 6 1.00 23 0.261
150 A 4 3 1.00 23 0.130
151 A 6 6 1.00 23 0.261
152 A 4 3 1.00 21 0.143
153 A 5 5 1.00 14 0.357
154 A 4 3 1.00 21 0.143
155 A 7 7 1.00 23 0.304
156 A 4 3 1.00 23 0.130
157 A 8 7 1.00 23 0.304
158 A 7 7 1.00 23 0.304
159 A 4 3 1.00 23 0.130
160 A 7 7 1.00 23 0.304
161 A 4 3 1.00 23 0.130
162 A 7 7 1.00 23 0.304
163 A 4 3 1.00 21 0.143
164 A 6 6 1.00 14 0.429
165 A 4 3 1.00 21 0.143
166 A 8 8 1.00 23 0.348
167 A 4 3 1.00 23 0.130
168 A 9 8 1.00 23 0.348
169 A 7 6 1.00 14 0.429
170 A 4 4 1.00 12 0.333
171 A 3 3 1.00 12 0.250
172 A 3 3 1.00 12 0.250
173 A 4 4 1.00 10 0.400
174 A 3 3 1.00 10 0.300
175 A 3 3 1.00 10 0.300
176 A 7 6 1.00 17 0.353
177 A 9 9 1.00 17 0.529
178 A 6 6 1.00 17 0.353
179 A 8 8 1.00 17 0.471
180 A 5 5 1.00 15 0.333
181 A 6 6 1.00 12 0.500
182 A 7 5 1.00 15 0.333
183 A 6 6 1.00 17 0.353
184 A 8 6 1.00 17 0.353
185 A 7 7 1.00 17 0.412
186 A 9 7 1.00 17 0.412
187 A 7 6 1.00 17 0.353
188 A 9 9 1.00 17 0.529
189 A 6 5 1.00 15 0.333
190 A 7 7 1.00 12 0.583
191 A 8 6 1.00 15 0.400
192 A 8 8 1.00 17 0.471
193 A 8 8 1.00 16 0.500
194 A 6 5 1.00 17 0.294
195 A 8 8 1.00 17 0.471
196 A 5 5 1.00 17 0.294
197 A 7 7 1.00 17 0.412
198 A 4 4 1.00 15 0.267
199 A 3 3 1.00 12 0.250
200 A 7 5 1.00 15 0.333
201 A 6 6 1.00 17 0.353
202 A 8 6 1.00 17 0.353
203 A 6 5 1.00 17 0.294
204 A 8 8 1.00 17 0.471
205 A 5 5 1.00 17 0.294
206 A 5 5 1.00 17 0.294
207 A 5 5 1.00 15 0.333
208 A 4 4 1.00 12 0.333
209 A 8 6 1.00 15 0.400
210 A 7 7 1.00 17 0.412
211 A 9 9 1.00 17 0.529
212 A 6 5 1.00 17 0.294
213 A 7 7 1.00 17 0.412
214 A 6 6 1.00 17 0.353
215 A 7 7 1.00 17 0.412
216 A 6 5 1.00 15 0.333
217 A 6 6 1.00 12 0.500
218 A 9 7 1.00 15 0.467
219 A 8 8 1.00 17 0.471
220 A 7 6 1.00 16 0.375

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