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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 [90] had the largest ratio of [20]

# 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 4 3 1.00 12 0.250
2 A 4 3 1.00 12 0.250
3 A 4 3 1.00 12 0.250
4 A 4 3 1.00 12 0.250
5 A 3 3 1.00 10 0.300
6 A 3 2 1.00 8 0.250
7 A 1 1 1.00 12 0.083
8 A 5 5 1.00 12 0.417
9 A 3 3 1.00 12 0.250
10 A 4 3 1.00 12 0.250
11 A 4 3 1.00 12 0.250
12 A 4 3 1.00 12 0.250
13 A 16 7 1.00 14 0.500
14 A 14 9 1.00 14 0.643
15 A 11 7 1.00 14 0.500
16 A 9 8 1.00 14 0.571
17 A 6 5 1.00 12 0.417
18 A 5 5 1.00 10 0.500
19 A 6 5 1.00 14 0.357
20 A 4 4 1.00 14 0.286
21 A 8 7 1.00 14 0.500
22 A 8 7 1.00 14 0.500
23 A 13 8 1.00 14 0.571
24 A 33 11 1.00 14 0.786
25 A 24 11 1.00 14 0.786
26 A 18 10 1.00 14 0.714
27 A 12 9 1.00 14 0.643
28 A 8 8 1.00 12 0.667
29 A 5 6 1.00 10 0.600
30 A 8 6 1.00 14 0.429
31 A 5 6 1.00 14 0.429
32 A 7 6 1.00 14 0.429
33 A 14 11 1.00 14 0.786
34 A 16 8 1.00 14 0.571
35 A 7 6 1.00 16 0.375
36 A 6 6 1.00 16 0.375
37 A 6 6 1.00 16 0.375
38 A 5 5 1.00 16 0.312
39 A 5 5 1.00 16 0.312
40 A 6 6 1.00 16 0.375
41 A 6 6 1.00 16 0.375
42 A 7 6 1.00 16 0.375
43 A 0 0 0.00 0 0.000
44 A 0 0 0.00 0 0.000
45 A 2 2 1.00 14 0.143
46 A 0 0 0.00 0 0.000
47 A 0 0 0.00 0 0.000
48 A 0 0 0.00 0 0.000
49 A 0 0 0.00 0 0.000
50 A 5 4 1.00 14 0.286
51 A 4 3 1.00 14 0.214
52 A 4 4 1.00 14 0.286
53 A 2 2 1.00 12 0.167
54 A 2 2 1.00 14 0.143
55 A 5 5 1.00 14 0.357
56 A 4 4 1.00 14 0.286
57 A 4 3 1.00 14 0.214
58 A 5 5 1.00 14 0.357
59 A 5 5 1.00 14 0.357
60 A 5 4 1.00 10 0.400
61 A 4 4 1.00 14 0.286
62 A 5 5 1.00 14 0.357
63 A 5 5 1.00 14 0.357
64 A 12 8 1.00 16 0.500
65 A 10 9 1.00 16 0.562
66 A 7 6 1.00 16 0.375
67 A 6 6 1.00 14 0.429
68 A 7 6 1.00 16 0.375
69 A 5 5 1.00 16 0.312
70 A 9 8 1.00 16 0.500
71 A 102 26 1.00 16 1.625
72 A 86 26 1.00 16 1.625
73 A 69 21 1.00 12 1.750
74 A 47 21 1.00 16 1.313
75 A 64 24 1.00 16 1.500
76 A 77 24 1.00 16 1.500
77 A 9 9 1.00 16 0.562
78 A 6 7 1.00 14 0.500
79 A 9 7 1.00 16 0.438
80 A 6 7 1.00 16 0.438
81 A 8 7 1.00 16 0.438
82 A 16 13 1.00 18 0.722
83 A 16 13 1.00 18 0.722
84 A 15 12 1.00 18 0.667
85 A 15 12 1.00 18 0.667
86 A 15 12 1.00 18 0.667
87 A 15 12 1.00 18 0.667
88 A 16 13 1.00 18 0.722
89 A 16 13 1.00 18 0.722
90 A 238 34 1.00 20 1.700
91 A 241 33 1.00 20 1.650
92 A 197 33 1.00 20 1.650
93 A 197 33 1.00 20 1.650
94 A 0 0 0.00 0 0.000
95 A 0 0 0.00 0 0.000
96 A 2 2 1.00 16 0.125
97 A 0 0 0.00 0 0.000
98 A 0 0 0.00 0 0.000
99 A 5 4 1.00 14 0.286
100 A 4 3 1.00 14 0.214
101 A 4 4 1.00 14 0.286
102 A 2 2 1.00 14 0.143
103 A 2 2 1.00 14 0.143
104 A 5 5 1.00 14 0.357
105 A 4 4 1.00 14 0.286
106 A 4 3 1.00 14 0.214
107 A 12 8 1.00 14 0.571
108 A 9 8 1.00 10 0.800
109 A 11 7 1.00 14 0.500
110 A 9 9 1.00 14 0.643
111 A 12 8 1.00 14 0.571
112 A 9 9 1.00 14 0.643
113 A 11 7 1.00 12 0.583
114 A 8 8 1.00 14 0.571
115 A 12 8 1.00 14 0.571
116 A 12 8 1.00 16 0.500
117 A 10 9 1.00 16 0.562
118 A 7 6 1.00 16 0.375
119 A 6 6 1.00 16 0.375
120 A 7 6 1.00 16 0.375
121 A 5 5 1.00 16 0.312
122 A 9 8 1.00 16 0.500
123 A 9 8 1.00 16 0.500
124 A 13 10 1.00 16 0.625
125 A 9 9 1.00 16 0.562
126 A 6 7 1.00 16 0.438
127 A 9 7 1.00 16 0.438
128 A 6 7 1.00 16 0.438
129 A 8 7 1.00 16 0.438
130 A 0 0 0.00 0 0.000
131 A 0 0 0.00 0 0.000
132 A 2 2 1.00 16 0.125
133 A 0 0 0.00 0 0.000
134 A 0 0 0.00 0 0.000
135 A 5 4 1.00 14 0.286
136 A 5 4 1.00 14 0.286
137 A 4 4 1.00 12 0.333
138 A 4 3 1.00 10 0.300
139 A 2 2 1.00 14 0.143
140 A 2 2 1.00 14 0.143
141 A 4 4 1.00 14 0.286
142 A 5 4 1.00 14 0.286
143 A 14 9 1.00 16 0.562
144 A 9 8 1.00 16 0.500
145 A 9 8 1.00 14 0.571
146 A 6 6 1.00 12 0.500
147 A 7 6 1.00 16 0.375
148 A 6 6 1.00 16 0.375
149 A 7 6 1.00 16 0.375
150 A 17 9 1.00 16 0.562
151 A 15 12 1.00 16 0.750
152 A 8 7 1.00 14 0.500
153 A 6 7 1.00 12 0.583
154 A 9 7 1.00 16 0.438
155 A 6 7 1.00 16 0.438
156 A 9 9 1.00 16 0.562
157 A 6 5 1.00 14 0.357
158 A 5 4 1.00 14 0.286
159 A 5 5 1.00 14 0.357
160 A 3 3 1.00 12 0.250
161 A 2 2 1.00 14 0.143
162 A 2 2 1.00 14 0.143
163 A 5 5 1.00 14 0.357
164 A 5 4 1.00 14 0.286
165 A 6 6 1.00 14 0.429
166 A 6 6 1.00 14 0.429
167 A 6 5 1.00 10 0.500
168 A 5 5 1.00 14 0.357
169 A 6 6 1.00 14 0.429
170 A 6 6 1.00 14 0.429
171 A 9 8 1.00 16 0.500
172 A 5 5 1.00 14 0.357
173 A 7 6 1.00 16 0.375
174 A 6 6 1.00 16 0.375
175 A 7 6 1.00 16 0.375
176 A 98 34 1.00 16 2.125
177 A 80 34 1.00 16 2.125
178 A 100 30 1.00 12 2.500
179 A 72 30 1.00 16 1.875
180 A 105 31 1.00 16 1.938
181 A 130 31 1.00 16 1.938
182 A 0 0 0.00 0 0.000
183 A 0 0 0.00 0 0.000
184 A 3 3 1.00 16 0.188
185 A 0 0 0.00 0 0.000
186 A 0 0 0.00 0 0.000
187 A 7 4 1.00 16 0.250
188 A 6 4 1.00 16 0.250
189 A 5 4 1.00 14 0.286
190 A 5 4 1.00 12 0.333
191 A 2 2 1.00 16 0.125
192 A 4 4 1.00 16 0.250
193 A 5 4 1.00 16 0.250
194 A 6 4 1.00 16 0.250
195 A 22 8 1.00 18 0.444
196 A 17 8 1.00 18 0.444
197 A 12 8 1.00 16 0.500
198 A 7 6 1.00 14 0.429
199 A 7 6 1.00 18 0.333
200 A 9 8 1.00 18 0.444
201 A 14 9 1.00 18 0.500
202 A 54 12 1.00 18 0.667
203 A 34 12 1.00 18 0.667
204 A 19 11 1.00 16 0.688
205 A 9 9 1.00 14 0.643
206 A 9 7 1.00 18 0.389
207 A 8 7 1.00 18 0.389
208 A 17 9 1.00 18 0.500
209 A 3 2 1.00 12 0.167
210 A 3 2 1.00 12 0.167
211 A 2 2 1.00 12 0.167
212 A 4 4 1.00 12 0.333
213 A 13 9 1.00 16 0.562
214 A 5 5 1.00 16 0.312
215 A 13 9 1.00 14 0.643
216 A 13 8 1.00 12 0.667
217 A 2 2 1.00 16 0.125
218 A 12 8 1.00 16 0.500
219 A 13 9 1.00 16 0.562
220 A 5 5 1.00 16 0.312
221 A 7 6 1.00 18 0.333
222 A 7 6 1.00 18 0.333
223 A 9 8 1.00 18 0.444
224 A 2 2 1.00 14 0.143
225 A 2 2 1.00 12 0.167
226 A 3 2 1.00 10 0.200
227 A 2 2 1.00 14 0.143
228 A 2 2 1.00 14 0.143
229 A 2 2 1.00 14 0.143
230 A 2 2 1.00 14 0.143
231 A 0 0 0.00 0 0.000
232 A 0 0 0.00 0 0.000
233 A 7 6 1.00 16 0.375
234 A 0 0 0.00 0 0.000
235 A 0 0 0.00 0 0.000
236 A 2 2 1.00 10 0.200
237 A 2 2 1.00 10 0.200
238 A 3 3 1.00 4 0.750
239 A 0 0 0.00 0 0.000
240 A 0 0 0.00 0 0.000
241 A 3 3 1.00 16 0.188
242 A 0 0 0.00 0 0.000
243 A 0 0 0.00 0 0.000

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