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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 [109] had the largest ratio of [.777800000000000047]

# 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 1.00 12 0.500
2 A 6 6 1.00 12 0.500
3 A 6 6 1.00 12 0.500
4 A 5 5 1.00 12 0.417
5 A 5 5 1.00 12 0.417
6 A 6 6 1.00 12 0.500
7 A 6 6 1.00 12 0.500
8 A 7 6 1.00 12 0.500
9 A 13 9 1.00 12 0.750
10 A 12 8 1.00 12 0.667
11 A 9 9 1.00 12 0.750
12 A 9 9 1.00 12 0.750
13 A 12 8 1.00 12 0.667
14 A 13 9 1.00 12 0.750
15 A 2 2 1.00 8 0.250
16 A 2 2 1.00 10 0.200
17 A 3 3 1.00 12 0.250
18 A 3 3 1.00 14 0.214
19 A 2 2 1.00 14 0.143
20 A 2 2 1.00 14 0.143
21 A 3 3 1.00 14 0.214
22 A 14 10 1.00 14 0.714
23 A 14 10 1.00 14 0.714
24 A 13 9 1.00 14 0.643
25 A 13 9 1.00 14 0.643
26 A 14 10 1.00 14 0.714
27 A 14 10 1.00 14 0.714
28 A 3 3 1.00 12 0.250
29 A 8 7 1.00 14 0.500
30 A 7 7 1.00 14 0.500
31 A 7 7 1.00 14 0.500
32 A 8 7 1.00 14 0.500
33 A 4 3 1.00 14 0.214
34 A 3 3 1.00 14 0.214
35 A 2 2 1.00 14 0.143
36 A 2 2 1.00 14 0.143
37 A 3 3 1.00 14 0.214
38 A 4 3 1.00 14 0.214
39 A 3 3 1.00 12 0.250
40 A 5 3 1.00 14 0.214
41 A 3 3 1.00 14 0.214
42 A 3 3 1.00 14 0.214
43 A 5 3 1.00 14 0.214
44 A 16 10 1.00 14 0.714
45 A 14 10 1.00 14 0.714
46 A 14 10 1.00 14 0.714
47 A 14 10 1.00 14 0.714
48 A 14 10 1.00 14 0.714
49 A 16 10 1.00 14 0.714
50 A 3 3 1.00 12 0.250
51 A 3 3 1.00 14 0.214
52 A 3 3 1.00 14 0.214
53 A 3 3 1.00 14 0.214
54 A 3 3 1.00 14 0.214
55 A 3 3 1.00 14 0.214
56 A 3 3 1.00 14 0.214
57 A 3 3 1.00 14 0.214
58 A 3 3 1.00 14 0.214
59 A 3 3 1.00 14 0.214
60 A 3 3 1.00 14 0.214
61 A 5 3 1.00 6 0.500
62 A 4 3 1.00 6 0.500
63 A 3 3 1.00 6 0.500
64 A 2 2 1.00 6 0.333
65 A 2 2 1.00 6 0.333
66 A 3 2 1.00 6 0.333
67 A 4 2 1.00 6 0.333
68 A 5 2 1.00 6 0.333
69 A 6 2 1.00 6 0.333
70 A 5 3 1.00 8 0.375
71 A 4 3 1.00 8 0.375
72 A 3 3 1.00 8 0.375
73 A 2 2 1.00 8 0.250
74 A 3 3 1.00 8 0.375
75 A 4 3 1.00 8 0.375
76 A 5 3 1.00 8 0.375
77 A 5 4 1.00 12 0.333
78 A 4 4 1.00 12 0.333
79 A 3 3 1.00 12 0.250
80 A 2 2 1.00 12 0.167
81 A 2 2 1.00 12 0.167
82 A 3 3 1.00 12 0.250
83 A 4 4 1.00 12 0.333
84 A 5 4 1.00 12 0.333
85 A 2 2 1.00 12 0.167
86 A 2 2 1.00 12 0.167
87 A 5 4 1.00 14 0.286
88 A 5 4 1.00 14 0.286
89 A 4 3 1.00 11 0.273
90 A 3 2 1.00 11 0.182
91 A 4 3 1.00 11 0.273
92 A 2 2 1.00 9 0.222
93 A 1 1 1.00 9 0.111
94 A 2 2 1.00 11 0.182
95 A 2 2 1.00 11 0.182
96 A 2 1 1.00 11 0.091
97 A 5 4 1.00 13 0.308
98 A 9 6 1.00 13 0.462
99 A 4 3 1.00 13 0.231
100 A 5 5 1.00 11 0.454
101 A 2 2 1.00 11 0.182
102 A 2 2 1.00 13 0.154
103 A 5 5 1.00 13 0.385
104 A 3 2 1.00 13 0.154
105 A 5 4 1.00 11 0.364
106 A 9 7 1.00 11 0.636
107 A 5 4 1.00 11 0.364
108 A 8 6 1.00 9 0.667
109 A 8 7 1.00 9 0.778
110 A 3 2 1.00 11 0.182
111 A 8 7 1.00 11 0.636
112 A 4 3 1.00 11 0.273
113 A 4 4 1.00 13 0.308
114 A 5 3 1.00 13 0.231
115 A 10 9 1.00 13 0.692
116 A 4 3 1.00 13 0.231
117 A 6 6 1.00 11 0.546
118 A 6 5 1.00 11 0.454
119 A 3 2 1.00 13 0.154
120 A 9 7 1.00 13 0.538
121 A 3 2 1.00 13 0.154
122 A 6 5 1.00 13 0.385
123 A 6 4 1.00 11 0.364
124 A 5 4 1.00 11 0.364
125 A 4 4 1.00 11 0.364
126 A 4 4 1.00 9 0.444
127 A 2 2 1.00 6 0.333
128 A 2 2 1.00 9 0.222
129 A 3 2 1.00 11 0.182
130 A 3 3 1.00 11 0.273
131 A 4 4 1.00 11 0.364
132 A 4 4 1.00 11 0.364
133 A 3 3 1.00 11 0.273
134 A 3 3 1.00 11 0.273
135 A 4 4 1.00 11 0.364
136 A 4 4 1.00 13 0.308
137 A 3 3 1.00 13 0.231
138 A 4 4 1.00 13 0.308
139 A 4 4 1.00 13 0.308
140 A 6 6 1.00 13 0.462
141 A 5 5 1.00 13 0.385
142 A 4 4 1.00 13 0.308
143 A 3 3 1.00 11 0.273
144 A 2 2 1.00 8 0.250
145 A 2 2 1.00 11 0.182
146 A 4 4 1.00 13 0.308
147 A 5 5 1.00 13 0.385
148 A 6 6 1.00 13 0.462
149 A 7 7 1.00 13 0.538
150 A 3 3 1.00 14 0.214
151 A 4 3 1.00 11 0.273
152 A 5 5 1.00 11 0.454
153 A 4 4 1.00 9 0.444
154 A 5 5 1.00 7 0.714
155 A 2 1 1.00 11 0.091
156 A 5 5 1.00 11 0.454
157 A 4 4 1.00 11 0.364
158 A 4 3 1.00 13 0.231
159 A 6 6 1.00 13 0.462
160 A 5 5 1.00 11 0.454
161 A 7 6 1.00 9 0.667
162 A 3 2 1.00 13 0.154
163 A 6 6 1.00 13 0.462
164 A 5 5 1.00 13 0.385
165 A 3 3 1.00 13 0.231
166 A 4 4 1.00 15 0.267
167 A 5 5 1.00 15 0.333
168 A 3 3 1.00 9 0.333
169 A 3 3 1.00 15 0.200
170 A 2 2 1.00 11 0.182
171 A 4 4 1.00 11 0.364
172 A 5 5 1.00 11 0.454
173 A 5 5 1.00 11 0.454
174 A 3 3 1.00 7 0.429
175 A 3 3 1.00 9 0.333
176 A 3 3 1.00 9 0.333
177 A 4 4 1.00 17 0.235
178 A 4 4 1.00 17 0.235
179 A 4 4 1.00 15 0.267
180 A 4 4 1.00 13 0.308
181 A 2 1 1.00 17 0.059
182 A 4 4 1.00 17 0.235
183 A 4 4 1.00 17 0.235
184 A 5 5 1.00 19 0.263
185 A 5 5 1.00 19 0.263
186 A 5 5 1.00 17 0.294
187 A 5 5 1.00 15 0.333
188 A 3 2 1.00 19 0.105
189 A 5 5 1.00 19 0.263
190 A 5 5 1.00 19 0.263
191 A 3 2 1.00 17 0.118
192 A 4 2 1.00 17 0.118
193 A 4 2 1.00 17 0.118
194 A 4 4 1.00 19 0.210
195 A 5 5 1.00 21 0.238
196 A 6 6 1.00 21 0.286
197 A 4 4 1.00 15 0.267
198 A 4 4 1.00 21 0.190
199 A 7 6 1.00 19 0.316
200 A 7 6 1.00 19 0.316
201 A 6 5 1.00 19 0.263
202 A 6 5 1.00 19 0.263
203 A 7 6 1.00 19 0.316
204 A 7 6 1.00 19 0.316
205 A 8 7 1.00 23 0.304
206 A 7 6 1.00 23 0.261
207 A 4 4 1.00 21 0.190
208 A 8 5 1.00 21 0.238
209 A 11 6 1.00 23 0.261
210 A 8 7 1.00 21 0.333
211 A 9 7 1.00 25 0.280
212 A 8 7 1.00 25 0.280
213 A 4 4 1.00 25 0.160
214 A 4 4 1.00 25 0.160
215 A 8 7 1.00 25 0.280
216 A 9 7 1.00 25 0.280
217 A 19 5 1.00 9 0.556
218 A 13 5 1.00 9 0.556
219 A 9 4 1.00 7 0.571
220 N/A 0 0 1.00 7 0.000
221 A 19 5 1.00 9 0.556
222 A 13 5 1.00 9 0.556
223 A 9 4 1.00 7 0.571
224 N/A 0 0 1.00 7 0.000

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