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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 [45] had the largest ratio of [.714285999999999976]

# 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 10 9 0.92 21 0.429
2 A 10 9 1.41 13 0.692
3 A 13 12 1.37 19 0.632
4 A 9 8 1.28 21 0.381
5 A 8 7 1.15 21 0.333
6 A 6 5 1.18 19 0.263
7 A 5 4 1.00 11 0.364
8 A 8 7 1.09 21 0.333
9 A 11 10 1.10 21 0.476
10 A 13 12 1.17 21 0.571
11 A 10 9 1.14 21 0.429
12 A 9 8 1.05 21 0.381
13 A 7 6 1.07 19 0.316
14 A 6 5 1.05 11 0.455
15 A 8 7 1.08 21 0.333
16 A 10 9 1.21 21 0.429
17 A 12 11 1.08 21 0.524
18 A 11 10 1.07 21 0.476
19 A 10 9 0.99 21 0.429
20 A 8 7 0.98 19 0.368
21 A 7 6 1.03 11 0.545
22 A 10 9 1.09 21 0.429
23 A 10 9 1.12 21 0.429
24 A 12 11 1.16 21 0.524
25 A 7 6 1.25 21 0.286
26 A 7 6 1.12 21 0.286
27 A 5 4 1.00 19 0.211
28 A 5 4 1.00 11 0.364
29 A 8 7 1.11 21 0.333
30 A 10 9 1.19 21 0.429
31 A 12 11 1.18 21 0.524
32 A 7 6 1.36 21 0.286
33 A 7 6 1.19 21 0.286
34 A 6 5 1.00 19 0.263
35 A 6 5 1.12 11 0.455
36 A 10 9 1.24 21 0.429
37 A 12 11 1.23 21 0.524
38 A 14 13 1.18 21 0.619
39 A 7 6 1.32 21 0.286
40 A 8 7 1.11 21 0.333
41 A 7 6 0.96 19 0.316
42 A 7 6 1.14 11 0.545
43 A 12 11 1.24 21 0.524
44 A 14 13 1.22 21 0.619
45 A 16 15 1.17 21 0.714
46 A 8 7 1.05 23 0.304
47 A 5 4 1.00 23 0.174
48 A 6 5 1.01 23 0.217
49 A 4 3 1.01 19 0.158
50 A 3 3 1.00 17 0.176
51 A 8 7 1.06 23 0.304
52 A 8 7 1.24 23 0.304
53 A 11 10 1.20 23 0.435
54 A 5 4 1.00 19 0.211
55 A 11 10 0.90 17 0.588
56 A 4 3 1.08 21 0.143
57 A 5 4 1.23 17 0.235
58 A 6 5 1.41 17 0.294
59 A 12 11 1.06 17 0.647
60 A 5 4 1.13 17 0.235
61 A 3 3 1.00 23 0.130
62 A 2 2 1.00 19 0.105
63 A 2 2 1.00 23 0.087
64 A 3 3 1.00 24 0.125
65 A 3 3 1.00 24 0.125
66 A 3 3 1.00 20 0.150
67 A 2 2 1.00 17 0.118
68 A 2 2 1.00 17 0.118
69 A 2 2 1.00 17 0.118
70 A 2 2 1.00 15 0.133
71 A 2 2 1.00 17 0.118
72 A 2 2 1.03 17 0.118
73 A 2 2 1.28 17 0.118
74 A 2 2 1.28 17 0.118
75 A 2 2 1.00 19 0.105
76 A 2 2 1.00 19 0.105
77 A 2 2 1.00 17 0.118
78 A 4 4 1.11 19 0.211
79 A 3 3 1.02 19 0.158
80 A 3 3 1.01 19 0.158
81 A 8 8 1.35 19 0.421
82 A 6 6 1.19 19 0.316
83 A 4 4 1.11 19 0.211
84 A 2 2 1.00 17 0.118
85 A 2 2 1.00 19 0.105
86 A 3 3 1.15 19 0.158
87 A 4 4 1.18 19 0.211
88 A 5 5 1.30 19 0.263
89 A 4 4 1.13 19 0.211
90 A 3 3 1.02 19 0.158
91 A 2 2 1.01 17 0.118
92 A 3 3 1.16 19 0.158
93 A 4 4 1.16 19 0.211
94 A 5 5 1.15 19 0.263
95 A 5 5 1.00 21 0.238
96 A 3 3 1.00 19 0.158
97 A 2 2 1.00 21 0.095
98 A 2 2 1.00 21 0.095
99 A 5 5 1.00 21 0.238
100 A 3 3 1.00 19 0.158
101 A 2 2 1.00 21 0.095
102 A 2 2 1.00 21 0.095
103 A 5 5 0.98 21 0.238
104 A 3 3 1.11 19 0.158
105 A 2 2 1.00 21 0.095
106 A 2 2 1.00 21 0.095
107 A 5 5 1.00 21 0.238
108 A 3 3 1.00 19 0.158
109 A 2 2 1.00 21 0.095
110 A 2 2 1.00 21 0.095
111 A 5 5 1.00 21 0.238
112 A 3 3 1.00 19 0.158
113 A 2 2 1.00 21 0.095
114 A 2 2 1.00 21 0.095
115 A 5 5 0.98 21 0.238
116 A 3 3 1.11 19 0.158
117 A 2 2 1.00 21 0.095
118 A 2 2 1.00 21 0.095
119 A 7 7 0.97 19 0.368
120 A 5 5 0.95 19 0.263
121 A 3 3 1.00 17 0.176
122 A 2 2 1.00 9 0.222
123 A 2 2 1.00 19 0.105
124 A 2 2 1.00 19 0.105
125 A 2 2 1.00 19 0.105
126 A 1 1 1.00 28 0.036
127 A 4 4 0.83 25 0.160
128 A 3 3 0.86 25 0.120
129 A 2 2 0.81 23 0.087
130 A 1 1 1.00 15 0.067
131 A 1 1 1.00 23 0.043
132 A 1 1 1.00 25 0.040
133 A 1 1 1.00 25 0.040
134 A 2 2 1.10 28 0.071
135 A 1 1 1.00 69 0.014
136 A 5 5 0.91 25 0.200
137 A 3 3 0.89 23 0.130
138 A 2 2 1.00 15 0.133
139 A 2 2 1.01 25 0.080
140 A 2 2 1.00 23 0.087
141 A 2 2 1.01 25 0.080
142 A 2 2 1.01 25 0.080
143 A 3 3 1.00 19 0.158
144 A 1 1 1.00 21 0.048
145 A 1 1 1.00 21 0.048
146 A 2 2 1.00 21 0.095
147 A 2 2 1.00 21 0.095

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