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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 [81] had the largest ratio of [28]

# 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 2 1.00 14 0.143
2 A 4 2 1.00 14 0.143
3 A 3 2 1.00 14 0.143
4 A 2 2 1.00 12 0.167
5 A 3 3 1.00 14 0.214
6 A 4 4 1.00 14 0.286
7 A 5 4 1.00 14 0.286
8 A 6 4 1.00 14 0.286
9 A 6 4 1.00 16 0.250
10 A 4 3 1.00 16 0.188
11 A 4 4 1.00 16 0.250
12 A 2 1 1.00 14 0.071
13 A 5 4 1.00 16 0.250
14 A 5 5 1.00 16 0.312
15 A 7 6 1.00 16 0.375
16 A 12 4 1.00 16 0.250
17 A 8 4 1.00 16 0.250
18 A 6 4 1.00 16 0.250
19 A 3 3 1.00 14 0.214
20 A 8 4 1.00 16 0.250
21 A 8 4 1.00 16 0.250
22 A 12 5 1.00 16 0.312
23 A 8 3 1.00 12 0.250
24 A 8 4 1.00 12 0.333
25 A 3 2 1.00 10 0.200
26 A 8 4 1.00 12 0.333
27 A 8 4 1.00 12 0.333
28 A 14 5 1.00 12 0.417
29 A 9 5 1.00 14 0.357
30 A 7 4 1.00 14 0.286
31 A 5 3 1.00 12 0.250
32 A 0 0 0.00 0 0.000
33 A 6 6 1.00 16 0.375
34 A 5 5 1.00 16 0.312
35 A 2 2 1.00 14 0.143
36 A 0 0 0.00 0 0.000
37 A 15 8 1.00 16 0.500
38 A 9 6 1.00 16 0.375
39 A 6 4 1.00 14 0.286
40 A 0 0 0.00 0 0.000
41 A 8 6 1.00 16 0.375
42 A 7 6 1.00 16 0.375
43 A 6 6 1.00 16 0.375
44 A 5 5 1.00 16 0.312
45 A 6 6 1.00 16 0.375
46 A 7 6 1.00 16 0.375
47 A 8 6 1.00 16 0.375
48 A 10 9 1.00 18 0.500
49 A 9 8 1.00 18 0.444
50 A 8 7 1.00 18 0.389
51 A 7 6 1.00 18 0.333
52 A 7 7 1.00 18 0.389
53 A 9 8 1.00 18 0.444
54 A 9 9 1.00 18 0.500
55 A 11 8 1.00 18 0.444
56 A 23 8 1.00 18 0.444
57 A 20 8 1.00 18 0.444
58 A 14 7 1.00 18 0.389
59 A 12 6 1.00 18 0.333
60 A 12 6 1.00 18 0.333
61 A 18 7 1.00 18 0.389
62 A 19 8 1.00 18 0.444
63 A 4 3 1.00 8 0.375
64 A 3 3 1.00 8 0.375
65 A 2 2 1.00 8 0.250
66 A 3 3 1.00 8 0.375
67 A 5 3 1.00 16 0.188
68 A 4 3 1.00 16 0.188
69 A 4 3 1.00 16 0.188
70 A 3 2 1.00 16 0.125
71 A 3 2 1.00 16 0.125
72 A 4 3 1.00 16 0.188
73 A 4 3 1.00 16 0.188
74 A 5 3 1.00 16 0.188
75 A 0 0 0.00 0 0.000
76 A 1 1 1.00 10 0.100
77 A 0 0 0.00 0 0.000
78 A 0 0 0.00 0 0.000
79 A 2 2 1.00 10 0.200
80 A 0 0 0.00 0 0.000
81 A 2 1 1.00 28 0.036
82 A 0 0 0.00 0 0.000
83 A 0 0 0.00 0 0.000
84 A 1 1 1.00 10 0.100
85 A 0 0 0.00 0 0.000
86 A 0 0 0.00 0 0.000
87 A 2 2 1.00 10 0.200
88 A 0 0 0.00 0 0.000
89 A 2 1 1.00 25 0.040
90 A 2 1 1.00 17 0.059
91 A 2 1 1.00 20 0.050
92 A 3 1 1.00 20 0.050
93 A 3 2 1.00 21 0.095
94 A 4 2 1.00 20 0.100
95 A 4 2 1.00 20 0.100
96 A 5 2 1.00 20 0.100
97 A 7 5 1.00 24 0.208
98 A 0 0 0.00 0 0.000
99 A 8 3 1.00 16 0.188
100 A 5 3 1.00 16 0.188
101 A 3 2 1.00 14 0.143
102 A 0 0 0.00 0 0.000
103 A 0 0 0.00 0 0.000
104 A 3 2 1.00 12 0.167
105 A 3 2 1.00 12 0.167
106 A 3 2 1.00 12 0.167
107 A 3 2 1.00 10 0.200
108 A 3 2 1.00 12 0.167
109 A 3 2 1.00 12 0.167
110 A 3 2 1.00 12 0.167
111 A 5 3 1.00 14 0.214
112 A 5 3 1.00 14 0.214
113 A 5 3 1.00 14 0.214
114 A 5 3 1.00 12 0.250
115 A 5 3 1.00 14 0.214
116 A 5 3 1.00 14 0.214
117 A 5 3 1.00 14 0.214
118 A 6 3 1.00 18 0.167
119 A 5 3 1.00 18 0.167
120 A 4 3 1.00 16 0.188
121 A 5 4 1.00 18 0.222
122 A 6 5 1.00 18 0.278
123 A 10 6 1.00 20 0.300
124 A 9 7 1.00 20 0.350
125 A 6 4 1.00 18 0.222
126 A 9 5 1.00 20 0.250
127 A 9 5 1.00 20 0.250
128 A 7 7 1.00 20 0.350
129 A 6 6 1.00 20 0.300
130 A 3 3 1.00 18 0.167
131 A 0 0 0.00 0 0.000
132 A 0 0 0.00 0 0.000
133 A 10 9 1.00 20 0.450
134 A 9 9 1.00 20 0.450
135 A 4 4 1.00 18 0.222
136 A 0 0 0.00 0 0.000
137 A 0 0 0.00 0 0.000
138 A 7 7 1.00 21 0.333
139 A 6 6 1.00 21 0.286
140 A 3 3 1.00 19 0.158
141 A 0 0 0.00 0 0.000
142 A 0 0 0.00 0 0.000
143 A 5 3 1.00 18 0.167
144 A 4 3 1.00 18 0.167
145 A 3 3 1.00 16 0.188
146 A 1 1 1.00 14 0.071
147 A 4 4 1.00 18 0.222
148 A 5 5 1.00 18 0.278
149 A 6 5 1.00 18 0.278
150 A 5 3 1.00 14 0.214
151 A 4 3 1.00 14 0.214
152 A 3 3 1.00 12 0.250
153 A 1 1 1.00 10 0.100
154 A 2 2 1.00 14 0.143
155 A 3 3 1.00 14 0.214
156 A 4 3 1.00 14 0.214
157 A 5 3 1.00 15 0.200
158 A 4 3 1.00 15 0.200
159 A 3 3 1.00 13 0.231
160 A 1 1 1.00 11 0.091
161 A 2 2 1.00 15 0.133
162 A 3 3 1.00 15 0.200
163 A 4 3 1.00 15 0.200
164 A 9 5 1.00 14 0.357
165 A 7 5 1.00 14 0.357
166 A 4 4 1.00 12 0.333
167 A 5 3 1.00 14 0.214
168 A 5 3 1.00 14 0.214
169 A 7 4 1.00 14 0.286
170 A 10 6 1.00 18 0.333
171 A 8 5 1.00 18 0.278
172 A 6 4 1.00 16 0.250
173 A 2 2 1.00 14 0.143
174 A 0 0 0.00 0 0.000
175 A 10 6 1.00 15 0.400
176 A 8 5 1.00 15 0.333
177 A 6 4 1.00 13 0.308
178 A 2 2 1.00 11 0.182
179 A 0 0 0.00 0 0.000
180 A 16 9 1.00 14 0.643
181 A 10 7 1.00 14 0.500
182 A 7 5 1.00 12 0.417
183 A 0 0 0.00 0 0.000
184 A 0 0 0.00 0 0.000
185 A 12 7 1.00 12 0.583
186 A 10 6 1.00 16 0.375
187 A 8 5 1.00 14 0.357
188 A 0 0 0.00 0 0.000
189 A 11 8 1.00 18 0.444

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