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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 [144] had the largest ratio of [.642900000000000027]

# 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 16 0.250
9 A 4 3 1.00 16 0.188
10 A 4 4 1.00 16 0.250
11 A 2 1 1.00 14 0.071
12 A 5 4 1.00 16 0.250
13 A 5 5 1.00 16 0.312
14 A 7 6 1.00 16 0.375
15 A 7 7 1.00 16 0.438
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 9 5 1.00 14 0.357
27 A 7 4 1.00 14 0.286
28 A 5 3 1.00 12 0.250
29 N/A 0 0 1.00 14 0.000
30 N/A 0 0 1.00 14 0.000
31 A 6 6 1.00 16 0.375
32 A 5 5 1.00 16 0.312
33 A 2 2 1.00 14 0.143
34 N/A 0 0 1.00 16 0.000
35 N/A 0 0 1.00 16 0.000
36 A 15 8 1.00 16 0.500
37 A 9 6 1.00 16 0.375
38 A 6 4 1.00 14 0.286
39 N/A 0 0 1.00 16 0.000
40 N/A 0 0 1.00 16 0.000
41 A 8 5 1.00 16 0.312
42 A 7 5 1.00 16 0.312
43 A 6 5 1.00 16 0.312
44 A 5 4 1.00 16 0.250
45 A 6 5 1.00 16 0.312
46 A 7 5 1.00 16 0.312
47 A 8 5 1.00 16 0.312
48 A 10 8 1.00 18 0.444
49 A 9 7 1.00 18 0.389
50 A 8 6 1.00 18 0.333
51 A 7 5 1.00 18 0.278
52 A 7 6 1.00 18 0.333
53 A 9 7 1.00 18 0.389
54 A 9 8 1.00 18 0.444
55 A 11 7 1.00 18 0.389
56 A 23 7 1.00 18 0.389
57 A 20 7 1.00 18 0.389
58 A 14 6 1.00 18 0.333
59 A 12 5 1.00 18 0.278
60 A 12 5 1.00 18 0.278
61 A 18 6 1.00 18 0.333
62 A 19 7 1.00 18 0.389
63 A 7 5 1.00 12 0.417
64 A 6 5 1.00 12 0.417
65 A 5 4 1.00 12 0.333
66 A 6 5 1.00 12 0.417
67 A 7 5 1.00 12 0.417
68 N/A 0 0 1.00 16 0.000
69 N/A 0 0 1.00 16 0.000
70 N/A 0 0 1.00 10 0.000
71 A 2 1 1.00 17 0.059
72 A 2 1 1.00 20 0.050
73 A 3 1 1.00 20 0.050
74 A 3 2 1.00 21 0.095
75 N/A 0 0 1.00 18 0.000
76 A 8 3 1.00 16 0.188
77 A 5 3 1.00 16 0.188
78 A 3 2 1.00 14 0.143
79 N/A 0 0 1.00 14 0.000
80 N/A 0 0 1.00 16 0.000
81 A 3 2 1.00 12 0.167
82 A 3 2 1.00 12 0.167
83 A 3 2 1.00 12 0.167
84 A 3 2 1.00 10 0.200
85 A 3 2 1.00 12 0.167
86 A 3 2 1.00 12 0.167
87 A 3 2 1.00 12 0.167
88 A 5 3 1.00 14 0.214
89 A 5 3 1.00 14 0.214
90 A 5 3 1.00 14 0.214
91 A 5 3 1.00 12 0.250
92 A 5 3 1.00 14 0.214
93 A 5 3 1.00 14 0.214
94 A 5 3 1.00 14 0.214
95 A 4 2 1.00 20 0.100
96 A 4 2 1.00 20 0.100
97 A 5 2 1.00 20 0.100
98 A 7 5 1.00 24 0.208
99 A 6 3 1.00 18 0.167
100 A 5 3 1.00 18 0.167
101 A 4 3 1.00 16 0.188
102 A 5 4 1.00 18 0.222
103 A 6 5 1.00 18 0.278
104 A 7 5 1.00 18 0.278
105 A 10 6 1.00 20 0.300
106 A 9 7 1.00 20 0.350
107 A 6 4 1.00 18 0.222
108 A 9 5 1.00 20 0.250
109 A 9 5 1.00 20 0.250
110 A 15 6 1.00 20 0.300
111 A 7 7 1.00 20 0.350
112 A 6 6 1.00 20 0.300
113 A 3 3 1.00 18 0.167
114 N/A 0 0 1.00 20 0.000
115 N/A 0 0 1.00 20 0.000
116 A 10 9 1.00 20 0.450
117 A 9 9 1.00 20 0.450
118 A 4 4 1.00 18 0.222
119 N/A 0 0 1.00 20 0.000
120 N/A 0 0 1.00 20 0.000
121 A 5 3 1.00 18 0.167
122 A 4 3 1.00 18 0.167
123 A 3 3 1.00 16 0.188
124 A 4 4 1.00 18 0.222
125 A 5 5 1.00 18 0.278
126 A 6 5 1.00 18 0.278
127 A 5 3 1.00 14 0.214
128 A 4 3 1.00 14 0.214
129 A 3 3 1.00 12 0.250
130 A 2 2 1.00 14 0.143
131 A 3 3 1.00 14 0.214
132 A 4 3 1.00 14 0.214
133 A 9 5 1.00 14 0.357
134 A 7 5 1.00 14 0.357
135 A 4 4 1.00 12 0.333
136 A 5 3 1.00 14 0.214
137 A 5 3 1.00 14 0.214
138 A 7 4 1.00 14 0.286
139 A 10 6 1.00 18 0.333
140 A 8 5 1.00 18 0.278
141 A 6 4 1.00 16 0.250
142 N/A 0 0 1.00 18 0.000
143 N/A 0 0 1.00 18 0.000
144 A 16 9 1.00 14 0.643
145 A 10 7 1.00 14 0.500
146 A 7 5 1.00 12 0.417
147 N/A 0 0 1.00 14 0.000
148 N/A 0 0 1.00 14 0.000
149 N/A 0 0 1.00 18 0.000
150 N/A 0 0 1.00 20 0.000
151 A 12 4 1.00 20 0.200
152 A 9 4 1.00 20 0.200
153 A 5 3 1.00 18 0.167
154 N/A 0 0 1.00 20 0.000
155 N/A 0 0 1.00 20 0.000
156 A 6 3 1.00 18 0.167
157 A 5 3 1.00 18 0.167
158 A 4 3 1.00 16 0.188
159 A 5 4 1.00 18 0.222
160 A 6 5 1.00 18 0.278
161 A 7 5 1.00 18 0.278
162 A 10 6 1.00 20 0.300
163 A 9 7 1.00 20 0.350
164 A 6 4 1.00 18 0.222
165 A 10 5 1.00 20 0.250
166 A 11 7 1.00 20 0.350
167 A 14 8 1.00 20 0.400
168 A 12 7 1.00 20 0.350
169 A 10 6 1.00 20 0.300
170 A 8 5 1.00 18 0.278
171 N/A 0 0 1.00 20 0.000
172 N/A 0 0 1.00 20 0.000
173 A 22 9 1.00 20 0.450
174 A 18 10 1.00 20 0.500
175 A 11 8 1.00 18 0.444
176 N/A 0 0 1.00 20 0.000
177 N/A 0 0 1.00 20 0.000
178 N/A 0 0 1.00 20 0.000
179 A 18 4 1.00 20 0.200
180 A 10 4 1.00 20 0.200
181 A 5 3 1.00 18 0.167
182 N/A 0 0 1.00 20 0.000
183 N/A 0 0 1.00 20 0.000

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