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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 [71] had the largest ratio of [.375000000000000000]

# 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 9 8 1.02 38 0.211
2 A 7 6 1.04 38 0.158
3 A 5 4 1.06 36 0.111
4 A 5 4 1.12 35 0.114
5 A 8 7 1.18 38 0.184
6 A 8 7 1.18 38 0.184
7 A 8 7 1.19 38 0.184
8 A 5 4 1.12 38 0.105
9 A 7 6 1.08 38 0.158
10 A 9 8 1.05 38 0.211
11 A 9 8 1.12 40 0.200
12 A 7 6 1.10 40 0.150
13 A 5 4 1.11 38 0.105
14 A 4 3 1.15 37 0.081
15 A 8 7 1.18 40 0.175
16 A 5 4 1.16 40 0.100
17 A 7 6 1.14 40 0.150
18 A 9 8 1.14 40 0.200
19 A 11 10 1.13 40 0.250
20 A 9 8 1.04 40 0.200
21 A 8 7 0.98 40 0.175
22 A 6 5 1.12 38 0.132
23 A 6 5 1.13 37 0.135
24 A 6 5 1.13 40 0.125
25 A 7 6 1.00 40 0.150
26 A 8 7 1.02 40 0.175
27 A 10 9 0.98 40 0.225
28 A 10 9 1.03 40 0.225
29 A 8 7 1.03 40 0.175
30 A 6 5 1.05 38 0.132
31 A 5 4 1.16 37 0.108
32 A 9 8 1.17 40 0.200
33 A 9 8 1.18 40 0.200
34 A 9 8 1.17 40 0.200
35 A 6 5 1.16 40 0.125
36 A 8 7 1.09 40 0.175
37 A 10 9 1.06 40 0.225
38 A 12 11 1.05 40 0.275
39 A 12 11 1.15 40 0.275
40 A 9 8 1.14 40 0.200
41 A 8 7 1.12 38 0.184
42 A 6 5 1.18 37 0.135
43 A 9 8 1.18 40 0.200
44 A 7 6 1.08 40 0.150
45 A 8 7 0.99 40 0.175
46 A 10 9 1.05 40 0.225
47 A 12 11 1.02 40 0.275
48 A 11 10 0.97 40 0.250
49 A 9 8 0.99 40 0.200
50 A 7 6 1.04 38 0.158
51 A 6 5 1.17 37 0.135
52 A 11 10 1.14 40 0.250
53 A 11 10 1.14 40 0.250
54 A 11 10 1.11 40 0.250
55 A 11 10 1.12 40 0.250
56 A 11 10 1.14 40 0.250
57 A 7 6 1.17 40 0.150
58 A 9 8 1.07 40 0.200
59 A 11 10 1.02 40 0.250
60 A 13 12 1.00 40 0.300
61 A 13 12 1.21 40 0.300
62 A 12 11 1.20 40 0.275
63 A 9 8 1.21 38 0.211
64 A 8 7 1.40 37 0.189
65 A 10 9 1.17 40 0.225
66 A 10 9 1.11 40 0.225
67 A 8 7 1.10 40 0.175
68 A 10 9 1.03 40 0.225
69 A 12 11 1.04 40 0.275
70 A 14 13 1.01 40 0.325
71 A 16 15 1.01 40 0.375
72 A 8 7 1.10 38 0.184
73 A 6 5 1.11 38 0.132
74 A 4 3 1.10 36 0.083
75 A 4 3 1.16 35 0.086
76 A 7 6 1.18 38 0.158
77 A 4 3 1.19 38 0.079
78 A 6 5 1.12 38 0.132
79 A 8 7 1.13 38 0.184
80 A 8 7 1.07 40 0.175
81 A 5 4 1.13 40 0.100
82 A 5 4 1.11 38 0.105
83 A 1 1 1.00 37 0.027
84 A 6 5 1.14 40 0.125
85 A 7 6 1.03 40 0.150
86 A 8 7 0.95 40 0.175
87 A 3 3 1.00 21 0.143
88 A 7 6 1.08 38 0.158
89 A 7 6 1.12 38 0.158
90 A 4 3 1.11 36 0.083
91 A 2 2 1.00 35 0.057
92 A 6 5 1.13 38 0.132
93 A 7 6 0.99 38 0.158
94 A 8 7 0.94 38 0.184
95 A 9 8 1.14 40 0.200
96 A 8 7 1.11 40 0.175
97 A 6 5 1.12 38 0.132
98 A 4 3 1.13 37 0.081
99 A 6 5 1.15 40 0.125
100 A 7 6 1.13 40 0.150
101 A 8 7 1.17 40 0.175
102 A 10 9 1.18 40 0.225
103 A 11 10 1.14 40 0.250
104 A 10 9 1.14 40 0.225
105 A 7 6 1.09 38 0.158
106 A 6 5 1.17 37 0.135
107 A 9 8 1.21 40 0.200
108 A 7 6 1.12 40 0.150
109 A 8 7 1.18 40 0.175
110 A 10 9 1.21 40 0.225
111 A 12 11 1.20 40 0.275
112 A 8 7 1.17 40 0.175
113 A 8 7 1.21 40 0.175
114 A 6 5 1.02 40 0.125
115 A 2 2 0.68 40 0.050
116 A 2 2 1.00 38 0.053
117 A 2 2 1.00 37 0.054
118 A 7 6 1.06 40 0.150
119 A 8 7 1.10 40 0.175
120 A 10 9 1.10 40 0.225
121 A 12 11 1.08 40 0.275
122 A 4 4 1.41 40 0.100
123 A 9 8 0.99 40 0.200
124 A 7 7 1.51 40 0.175
125 A 5 5 1.28 40 0.125
126 A 3 3 1.02 38 0.079
127 A 3 3 1.08 37 0.081
128 A 2 2 1.24 40 0.050
129 A 2 2 1.48 40 0.050
130 A 11 10 0.99 40 0.250
131 A 10 10 1.73 40 0.250
132 A 8 8 1.25 40 0.200
133 A 6 6 1.17 40 0.150
134 A 4 4 1.01 38 0.105
135 A 4 4 1.12 37 0.108
136 A 2 2 1.44 40 0.050
137 A 2 2 1.56 40 0.050
138 A 8 7 1.17 38 0.184
139 A 7 6 1.11 38 0.158
140 A 2 2 1.00 38 0.053
141 A 2 2 1.00 36 0.056
142 A 2 2 1.00 35 0.057
143 A 7 6 1.20 38 0.158
144 A 8 7 1.20 38 0.184
145 A 4 4 0.67 40 0.100
146 A 4 4 1.00 34 0.118
147 A 4 4 1.00 32 0.125
148 A 3 2 1.00 27 0.074
149 A 4 4 1.00 34 0.118
150 A 4 4 1.00 34 0.118
151 A 4 4 1.00 34 0.118

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