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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 [35] had the largest ratio of [.615384999999999960]

# 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 7 6 1.16 13 0.462
2 A 7 6 1.12 15 0.400
3 A 6 5 1.11 15 0.333
4 A 5 4 1.07 15 0.267
5 A 4 3 1.00 15 0.200
6 A 7 6 1.17 13 0.462
7 A 6 5 1.15 13 0.385
8 A 5 4 1.12 13 0.308
9 A 4 3 1.06 13 0.231
10 A 4 3 1.06 13 0.231
11 A 4 3 1.06 13 0.231
12 A 5 4 1.10 11 0.364
13 A 4 3 1.00 11 0.273
14 A 4 3 1.00 11 0.273
15 A 4 3 1.00 11 0.273
16 A 3 3 1.07 13 0.231
17 A 3 2 1.00 15 0.133
18 A 1 1 1.00 15 0.067
19 A 2 2 1.00 15 0.133
20 A 3 3 1.06 15 0.200
21 A 3 2 1.17 13 0.154
22 A 1 1 1.00 13 0.077
23 A 2 2 1.00 13 0.154
24 A 3 3 1.07 13 0.231
25 A 3 2 1.50 16 0.125
26 A 3 2 1.00 15 0.133
27 A 3 2 1.20 13 0.154
28 A 3 2 1.00 11 0.182
29 A 3 2 1.00 11 0.182
30 A 7 6 0.78 13 0.462
31 A 6 5 0.81 13 0.385
32 A 5 4 0.86 13 0.308
33 A 6 5 0.80 13 0.385
34 A 7 6 0.77 13 0.462
35 A 9 8 0.86 13 0.615
36 A 8 7 0.88 13 0.538
37 A 7 6 0.92 13 0.462
38 A 8 7 0.88 13 0.538
39 A 9 8 0.86 13 0.615
40 A 6 5 1.17 13 0.385
41 A 5 4 1.13 13 0.308
42 A 5 4 1.13 13 0.308
43 A 4 3 1.22 13 0.231
44 A 4 3 1.20 13 0.231
45 A 5 4 1.14 13 0.308
46 A 6 5 1.13 13 0.385
47 A 7 6 1.13 13 0.462
48 A 1 1 1.00 11 0.091
49 A 2 2 1.00 9 0.222
50 A 2 2 1.00 9 0.222
51 A 2 2 1.00 9 0.222
52 A 1 1 1.00 7 0.143
53 A 1 1 1.00 9 0.111
54 A 2 2 1.00 9 0.222
55 A 3 3 1.13 9 0.333
56 A 6 5 1.07 11 0.455
57 A 5 4 1.05 11 0.364
58 A 4 3 1.00 11 0.273
59 A 3 2 1.00 11 0.182
60 A 1 1 1.00 11 0.091
61 A 2 2 1.00 11 0.182
62 A 3 3 1.14 11 0.273
63 A 4 4 1.21 11 0.364
64 A 2 2 1.09 14 0.143
65 A 2 2 1.00 14 0.143
66 A 2 2 1.00 14 0.143
67 A 1 1 1.00 14 0.071
68 A 2 2 1.00 14 0.143
69 A 2 2 1.00 14 0.143
70 A 2 2 1.00 14 0.143
71 A 2 2 1.00 14 0.143
72 A 2 2 1.00 14 0.143
73 A 2 2 1.00 14 0.143
74 A 2 2 1.04 23 0.087
75 A 2 2 1.04 23 0.087
76 A 2 2 1.04 23 0.087
77 A 2 2 1.04 23 0.087
78 A 3 2 1.17 12 0.167
79 A 3 2 1.33 15 0.133
80 B 2 2 2.37 12 0.167
81 A 2 2 1.62 12 0.167
82 A 2 2 1.10 12 0.167
83 B 2 2 2.83 10 0.200
84 A 3 2 1.00 12 0.167
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 3 2 1.00 12 0.167
89 A 3 2 1.17 13 0.154
90 A 3 2 1.16 14 0.143
91 A 4 3 1.07 12 0.250
92 A 3 3 1.60 12 0.250
93 A 2 2 1.21 12 0.167
94 A 2 2 1.07 12 0.167
95 A 4 3 1.00 12 0.250
96 A 4 3 1.08 13 0.231
97 A 4 3 1.07 14 0.214
98 A 3 2 1.23 40 0.050
99 A 2 2 1.91 30 0.067
100 B 2 2 2.03 31 0.065
101 A 3 2 1.41 14 0.143
102 A 3 2 1.30 16 0.125
103 A 4 3 1.00 14 0.214
104 A 4 3 1.20 14 0.214
105 A 4 3 1.00 14 0.214
106 A 4 3 1.07 14 0.214
107 A 4 3 1.07 14 0.214
108 A 4 3 1.00 14 0.214
109 A 4 3 1.00 14 0.214
110 A 4 3 1.00 14 0.214
111 A 4 3 1.00 14 0.214
112 A 4 3 1.00 14 0.214
113 A 4 3 1.00 14 0.214
114 A 3 2 1.00 14 0.143
115 A 3 2 1.40 14 0.143
116 A 3 2 1.00 14 0.143
117 A 3 2 1.17 14 0.143
118 A 3 2 1.16 14 0.143
119 A 3 2 1.00 14 0.143
120 A 3 2 1.00 14 0.143
121 A 3 2 1.00 14 0.143
122 A 3 2 1.00 14 0.143
123 A 3 2 1.00 14 0.143
124 A 3 2 1.00 14 0.143
125 A 3 2 1.00 27 0.074
126 A 3 2 1.00 30 0.067
127 A 3 2 1.00 28 0.071
128 A 1 1 1.00 12 0.083
129 A 1 1 1.00 14 0.071
130 A 1 1 1.00 16 0.062
131 A 2 2 1.00 14 0.143
132 A 1 1 1.00 12 0.083
133 A 3 2 1.08 12 0.167
134 A 3 2 1.00 12 0.167
135 A 3 2 1.08 12 0.167
136 A 3 2 1.43 12 0.167
137 A 1 1 1.00 10 0.100
138 A 1 1 1.00 7 0.143
139 A 3 2 1.06 12 0.167
140 A 3 2 1.06 12 0.167
141 A 3 2 1.05 12 0.167
142 A 3 2 1.00 12 0.167
143 A 3 2 1.05 12 0.167

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