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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 [91] 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 3 2 1.00 19 0.105
2 A 3 2 1.00 19 0.105
3 A 3 2 1.00 17 0.118
4 A 3 2 1.00 17 0.118
5 A 3 2 1.00 19 0.105
6 A 3 2 1.00 19 0.105
7 A 3 2 1.00 19 0.105
8 A 9 5 1.00 19 0.263
9 A 8 5 1.00 19 0.263
10 A 5 5 1.00 19 0.263
11 A 7 6 1.00 19 0.316
12 A 9 7 1.00 19 0.368
13 A 11 7 1.00 19 0.368
14 A 3 2 1.00 21 0.095
15 A 3 2 1.00 21 0.095
16 A 3 2 1.00 19 0.105
17 A 2 2 1.00 21 0.095
18 A 3 2 1.00 21 0.095
19 A 14 9 1.00 21 0.429
20 A 4 4 1.00 21 0.190
21 A 6 5 1.00 21 0.238
22 A 1 1 1.00 12 0.083
23 A 8 6 1.00 21 0.286
24 A 12 7 1.00 21 0.333
25 A 3 2 1.00 21 0.095
26 A 3 2 1.00 21 0.095
27 A 3 2 1.00 19 0.105
28 A 3 2 1.00 21 0.095
29 A 9 7 1.00 21 0.333
30 A 10 7 1.00 21 0.333
31 A 8 6 1.00 21 0.286
32 A 7 5 1.00 12 0.417
33 A 10 7 1.00 21 0.333
34 A 3 2 1.00 21 0.095
35 A 3 2 1.00 21 0.095
36 A 3 2 1.00 19 0.105
37 A 3 2 1.00 21 0.095
38 A 13 7 1.00 21 0.333
39 A 11 6 1.00 21 0.286
40 A 10 5 1.00 12 0.417
41 A 12 6 1.00 21 0.286
42 A 17 8 1.00 21 0.381
43 A 21 8 1.00 21 0.381
44 A 8 5 1.00 21 0.238
45 A 7 5 1.00 21 0.238
46 A 6 5 1.00 21 0.238
47 A 5 5 1.57 19 0.263
48 A 4 4 1.00 19 0.210
49 A 5 4 1.00 21 0.190
50 A 5 4 1.00 21 0.190
51 A 6 5 1.00 21 0.238
52 A 6 5 1.00 21 0.238
53 A 6 5 1.00 21 0.238
54 A 6 5 1.00 21 0.238
55 A 5 4 1.00 21 0.190
56 A 1 1 1.00 12 0.083
57 A 4 4 1.00 21 0.190
58 A 5 5 1.00 21 0.238
59 A 6 5 1.00 21 0.238
60 A 7 5 1.00 21 0.238
61 A 4 3 1.00 21 0.143
62 A 4 3 1.00 21 0.143
63 A 4 3 1.00 21 0.143
64 A 4 3 1.00 19 0.158
65 A 3 2 1.00 19 0.105
66 A 3 2 1.00 21 0.095
67 A 3 2 1.00 21 0.095
68 A 3 2 1.00 21 0.095
69 A 3 2 1.00 21 0.095
70 A 3 2 1.00 21 0.095
71 A 3 2 1.00 21 0.095
72 A 4 3 1.00 21 0.143
73 A 4 3 1.00 21 0.143
74 A 4 3 1.00 19 0.158
75 A 3 2 1.00 19 0.105
76 A 3 2 1.00 21 0.095
77 A 3 2 1.00 21 0.095
78 A 3 2 1.00 21 0.095
79 A 3 2 1.00 21 0.095
80 A 3 2 1.00 21 0.095
81 A 3 2 1.00 21 0.095
82 A 4 3 1.00 21 0.143
83 A 3 2 1.00 21 0.095
84 A 4 3 1.00 19 0.158
85 A 3 2 1.00 21 0.095
86 A 3 2 1.00 21 0.095
87 A 17 5 1.00 21 0.238
88 A 14 8 1.00 21 0.381
89 A 14 8 1.00 21 0.381
90 A 16 6 1.00 21 0.286
91 A 15 10 1.20 23 0.435
92 A 4 4 1.00 23 0.174
93 A 4 4 1.00 23 0.174
94 A 7 7 1.00 23 0.304
95 A 14 9 1.17 23 0.391
96 A 3 3 1.00 23 0.130
97 A 5 5 1.00 23 0.217
98 A 8 8 1.00 23 0.348
99 A 10 7 1.38 23 0.304
100 A 4 4 1.00 23 0.174
101 A 6 5 1.00 23 0.217
102 A 10 8 1.00 23 0.348
103 A 17 9 1.61 23 0.391
104 A 4 4 1.00 23 0.174
105 A 4 4 1.00 23 0.174
106 A 11 7 1.00 23 0.304
107 A 20 9 1.10 23 0.391
108 A 5 5 1.00 23 0.217
109 A 6 5 1.00 23 0.217
110 A 10 6 1.00 23 0.261
111 A 23 9 1.26 23 0.391
112 A 6 6 1.00 23 0.261
113 A 7 6 1.00 23 0.261
114 A 16 8 1.00 23 0.348
115 A 10 9 1.00 23 0.391
116 A 4 4 1.00 23 0.174
117 A 3 3 1.00 23 0.130
118 A 3 3 1.00 23 0.130
119 A 8 7 1.00 23 0.304
120 A 4 4 1.00 23 0.174
121 A 3 3 1.00 23 0.130
122 A 3 3 1.00 23 0.130
123 A 10 6 1.00 23 0.261
124 A 8 6 1.00 23 0.261
125 A 6 5 1.00 21 0.238
126 A 4 4 1.00 23 0.174
127 A 10 6 1.00 23 0.261
128 A 13 6 1.00 23 0.261
129 A 4 3 1.00 23 0.130
130 A 4 4 1.00 21 0.190
131 A 3 3 1.00 19 0.158
132 A 2 2 1.00 19 0.105
133 A 3 3 1.00 21 0.143
134 A 4 4 1.00 21 0.190
135 A 6 6 1.00 21 0.286
136 A 5 5 1.00 21 0.238
137 A 2 2 1.00 12 0.167
138 A 3 3 1.00 21 0.143
139 A 3 3 1.00 21 0.143
140 A 6 5 1.00 19 0.263
141 A 5 4 1.00 17 0.235
142 A 3 2 1.00 17 0.118
143 A 3 2 1.00 19 0.105
144 A 3 2 1.00 19 0.105
145 A 8 5 1.00 19 0.263
146 A 7 5 1.00 19 0.263
147 A 7 6 1.00 19 0.316
148 A 9 7 1.00 19 0.368
149 A 11 7 1.00 19 0.368
150 A 7 5 1.00 21 0.238
151 A 6 4 1.00 19 0.210
152 A 3 2 1.00 19 0.105
153 A 3 2 1.00 21 0.095
154 A 3 2 1.00 21 0.095
155 A 13 9 1.00 21 0.429
156 A 11 9 1.00 21 0.429
157 A 9 7 1.00 21 0.333
158 A 13 9 1.00 21 0.429
159 A 16 10 1.00 21 0.476
160 A 7 5 1.00 21 0.238
161 A 6 4 1.00 19 0.210
162 A 3 2 1.00 19 0.105
163 A 3 2 1.00 21 0.095
164 A 3 2 1.00 21 0.095
165 A 16 9 1.00 21 0.429
166 A 14 10 1.00 21 0.476
167 A 11 9 1.00 21 0.429
168 A 17 10 1.00 21 0.476
169 A 21 10 1.00 21 0.476
170 A 5 3 1.00 21 0.143
171 A 4 3 1.00 21 0.143
172 A 3 2 1.00 19 0.105
173 A 4 4 1.00 19 0.210
174 A 3 2 1.00 21 0.095
175 A 3 2 1.00 21 0.095
176 A 13 9 1.00 21 0.429
177 A 8 7 1.00 21 0.333
178 A 7 7 1.00 21 0.333
179 A 7 7 1.00 21 0.333
180 A 9 7 1.00 21 0.333
181 A 5 3 1.00 21 0.143
182 A 4 3 1.00 21 0.143
183 A 3 2 1.00 19 0.105
184 A 3 2 1.00 19 0.105
185 A 3 2 1.00 21 0.095
186 A 3 2 1.00 21 0.095
187 A 16 8 1.00 21 0.381
188 A 12 7 1.00 21 0.333
189 A 8 7 1.00 21 0.333
190 A 8 7 1.00 21 0.333
191 A 10 7 1.00 21 0.333
192 A 5 3 1.00 21 0.143
193 A 4 3 1.00 21 0.143
194 A 3 2 1.00 19 0.105
195 A 3 2 1.00 19 0.105
196 A 3 2 1.00 21 0.095
197 A 3 2 1.00 21 0.095
198 A 22 9 1.00 21 0.429
199 A 18 8 1.00 21 0.381
200 A 9 8 1.00 21 0.381
201 A 9 7 1.00 21 0.333
202 A 11 7 1.00 21 0.333
203 A 10 6 1.00 23 0.261
204 A 8 6 1.00 23 0.261
205 A 6 5 1.00 21 0.238
206 F 0 0 N/A 0. N/A
207 F 0 0 N/A 0. N/A
208 A 0 0 0.00 0 0.000

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