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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 [76] had the largest ratio of [.470588000000000006]

# 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 3 0.98 15 0.200
2 A 3 3 1.00 15 0.200
3 A 2 2 1.03 13 0.154
4 A 1 1 1.00 5 0.200
5 A 3 3 1.00 15 0.200
6 A 2 2 1.00 15 0.133
7 A 3 3 1.09 15 0.200
8 A 6 5 1.03 17 0.294
9 A 5 4 1.01 17 0.235
10 A 4 3 1.00 17 0.176
11 A 1 1 1.00 17 0.059
12 A 2 2 1.00 17 0.118
13 A 3 3 1.10 17 0.176
14 A 4 4 1.15 17 0.235
15 A 6 5 1.01 17 0.294
16 A 5 4 1.00 17 0.235
17 A 4 3 1.00 17 0.176
18 A 4 3 1.00 17 0.176
19 A 7 6 1.07 17 0.353
20 A 6 5 1.08 17 0.294
21 A 6 5 1.08 17 0.294
22 A 3 3 1.00 15 0.200
23 A 3 3 1.00 20 0.150
24 A 3 3 1.00 20 0.150
25 A 2 2 1.00 18 0.111
26 A 1 1 1.00 10 0.100
27 A 2 2 1.00 20 0.100
28 A 4 4 1.00 20 0.200
29 A 5 5 1.00 20 0.250
30 A 6 6 0.98 20 0.300
31 A 7 6 0.90 22 0.273
32 A 6 5 0.95 22 0.227
33 A 5 4 1.04 22 0.182
34 A 6 5 1.00 22 0.227
35 A 4 4 1.00 22 0.182
36 A 5 5 0.97 22 0.227
37 A 6 6 0.95 22 0.273
38 A 7 6 0.98 22 0.273
39 A 6 5 1.01 22 0.227
40 A 5 4 1.00 22 0.182
41 A 9 8 1.03 22 0.364
42 A 8 7 1.04 22 0.318
43 A 7 6 1.05 22 0.273
44 A 8 7 1.03 22 0.318
45 A 5 5 1.11 20 0.250
46 A 3 3 1.00 25 0.120
47 A 3 3 1.00 25 0.120
48 A 2 2 1.00 23 0.087
49 A 1 1 1.00 15 0.067
50 A 2 2 1.00 25 0.080
51 A 6 6 1.06 25 0.240
52 A 5 5 1.09 25 0.200
53 A 6 5 1.10 17 0.294
54 A 9 8 0.98 27 0.296
55 A 8 7 1.04 27 0.259
56 A 7 6 1.13 27 0.222
57 A 7 6 1.06 27 0.222
58 A 4 4 1.00 27 0.148
59 A 5 5 1.07 27 0.185
60 A 6 6 1.03 27 0.222
61 A 6 5 1.26 17 0.294
62 A 9 8 1.01 27 0.296
63 A 8 7 1.04 27 0.259
64 A 6 5 1.02 27 0.185
65 A 6 5 1.03 27 0.185
66 A 7 6 1.02 27 0.222
67 A 11 10 1.04 27 0.370
68 A 10 9 1.06 27 0.333
69 A 8 7 1.06 27 0.259
70 A 8 7 1.05 27 0.259
71 A 9 8 1.04 27 0.296
72 A 8 8 1.22 25 0.320
73 A 5 4 0.94 29 0.138
74 A 4 4 1.32 21 0.190
75 A 3 3 1.00 15 0.200
76 A 8 8 1.15 17 0.471
77 A 8 8 1.15 32 0.250
78 A 9 9 1.15 35 0.257
79 A 2 2 1.00 17 0.118
80 A 2 2 1.00 17 0.118
81 A 2 2 1.00 17 0.118
82 A 2 2 1.00 15 0.133
83 A 1 1 1.00 7 0.143
84 A 2 2 1.00 17 0.118
85 A 2 2 1.00 17 0.118
86 A 3 3 1.00 17 0.176
87 A 4 4 0.98 17 0.235
88 A 7 6 0.85 19 0.316
89 A 6 5 0.89 19 0.263
90 A 5 4 0.95 19 0.211
91 A 4 3 1.00 19 0.158
92 A 4 3 1.00 19 0.158
93 A 2 2 0.77 19 0.105
94 A 3 3 0.97 19 0.158
95 A 4 4 0.95 19 0.211
96 A 1 1 1.00 22 0.045
97 B 2 2 3.82 18 0.111
98 B 2 2 2.82 18 0.111
99 A 2 2 1.82 16 0.125
100 A 1 1 1.00 18 0.056
101 A 1 1 1.00 18 0.056
102 A 1 1 1.00 20 0.050
103 A 1 1 1.00 20 0.050
104 A 1 1 1.00 20 0.050
105 A 1 1 1.00 20 0.050
106 B 2 2 3.62 20 0.100
107 A 1 1 1.00 20 0.050
108 A 3 3 1.00 17 0.176
109 A 2 2 1.00 22 0.091
110 A 2 2 1.00 22 0.091
111 A 2 2 1.00 20 0.100
112 A 2 2 1.00 22 0.091
113 A 5 5 1.17 22 0.227
114 A 5 5 1.06 22 0.227
115 A 7 6 0.87 24 0.250
116 A 7 6 0.98 24 0.250
117 A 5 4 1.08 24 0.167
118 A 7 6 1.07 24 0.250
119 A 7 6 1.07 24 0.250
120 A 4 4 0.86 24 0.167
121 A 5 5 0.83 24 0.208
122 A 7 6 0.99 24 0.250
123 A 6 5 1.03 24 0.208
124 A 9 8 1.00 24 0.333
125 A 8 7 1.02 24 0.292
126 A 4 4 0.95 22 0.182
127 A 2 2 1.00 27 0.074
128 A 2 2 1.00 27 0.074
129 A 2 2 1.00 25 0.080
130 A 2 2 1.00 27 0.074
131 A 4 4 1.07 27 0.148
132 A 7 7 1.09 27 0.259
133 A 9 8 0.87 29 0.276
134 A 8 7 0.98 29 0.241
135 A 7 6 1.11 29 0.207
136 A 8 7 1.09 29 0.241
137 A 8 7 1.03 29 0.241
138 A 9 8 1.08 29 0.276
139 A 8 8 0.96 29 0.276
140 A 8 8 0.89 29 0.276
141 A 9 9 0.88 29 0.310
142 A 8 8 0.98 29 0.276
143 A 8 8 0.97 29 0.276
144 A 7 7 1.09 29 0.241
145 A 8 8 1.25 29 0.276
146 A 7 7 1.08 29 0.241
147 A 8 8 1.30 29 0.276
148 A 7 7 1.07 29 0.241
149 A 8 8 1.35 29 0.276
150 A 7 7 1.07 29 0.241
151 A 5 5 0.96 27 0.185

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