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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [13] had the largest ratio of [.4000]

Table 2.1:Rubi specific breakdown of results for each integral
# 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 6 5 1.00 20 0.250
2 A 5 5 1.00 20 0.250
3 A 4 4 1.00 18 0.222
4 A 4 4 1.00 17 0.235
5 A 7 7 1.00 20 0.350
6 A 7 7 1.00 20 0.350
7 A 7 7 1.00 20 0.350
8 A 7 5 1.00 20 0.250
9 A 6 5 1.00 20 0.250
10 A 5 4 1.00 18 0.222
11 A 5 4 1.00 17 0.235
12 A 8 7 1.00 20 0.350
13 A 8 8 1.00 20 0.400
14 A 8 7 1.00 20 0.350
15 A 8 5 1.00 20 0.250
16 A 7 5 1.00 20 0.250
17 A 6 4 1.00 18 0.222
18 A 6 4 1.00 17 0.235
19 A 9 7 1.00 20 0.350
20 A 9 8 1.00 20 0.400
21 A 9 8 1.00 20 0.400
22 A 5 4 1.00 20 0.200
23 A 4 4 1.00 20 0.200
24 A 3 3 1.00 18 0.167
25 A 3 3 1.00 17 0.176
26 A 6 6 1.00 20 0.300
27 A 4 4 1.00 20 0.200
28 A 5 5 1.00 20 0.250
29 A 4 4 1.00 20 0.200
30 A 4 4 1.00 20 0.200
31 A 3 3 1.00 18 0.167
32 A 1 1 1.00 17 0.059
33 A 5 5 1.00 20 0.250
34 A 5 5 1.00 20 0.250
35 A 6 6 1.00 20 0.300
36 A 4 4 1.00 20 0.200
37 A 2 2 1.00 20 0.100
38 A 2 2 0.94 18 0.111
39 A 2 2 1.00 17 0.118
40 A 6 5 1.00 20 0.250
41 A 6 5 1.00 20 0.250
42 A 7 6 1.00 20 0.300
43 A 2 2 1.00 18 0.111
44 A 3 3 1.00 19 0.158
45 A 2 2 1.00 13 0.154
46 A 2 2 1.00 13 0.154
47 A 7 5 1.00 25 0.200
48 A 6 5 1.00 25 0.200
49 A 5 4 1.00 25 0.160
50 A 4 4 1.00 25 0.160
51 A 4 4 1.00 25 0.160
52 A 4 4 1.00 25 0.160
53 A 4 4 1.00 23 0.174
54 A 5 4 1.00 22 0.182
55 A 8 6 1.00 25 0.240
56 A 8 5 1.00 25 0.200
57 A 9 6 1.00 25 0.240
58 A 2 1 1.00 26 0.038
59 A 2 1 1.00 26 0.038
60 A 2 1 1.00 24 0.042
61 A 2 1 1.00 23 0.043
62 A 2 1 1.00 26 0.038
63 A 2 1 1.00 26 0.038
64 A 2 1 1.00 26 0.038
65 A 2 1 1.00 26 0.038
66 A 2 1 1.00 28 0.036
67 A 2 1 1.00 28 0.036
68 A 3 2 1.00 26 0.077
69 A 3 2 1.00 25 0.080
70 A 3 2 1.00 28 0.071
71 A 3 2 1.00 28 0.071
72 A 2 1 1.00 28 0.036
73 A 2 1 1.00 28 0.036
74 A 2 1 1.00 28 0.036
75 A 2 1 1.00 28 0.036
76 A 3 2 1.00 26 0.077
77 A 3 2 1.00 25 0.080
78 A 3 2 1.00 28 0.071
79 A 3 2 1.00 28 0.071
80 A 2 1 1.00 28 0.036
81 A 2 1 1.00 28 0.036
82 A 5 4 1.00 28 0.143
83 A 5 4 1.00 28 0.143
84 A 5 4 1.00 28 0.143
85 A 5 4 1.00 26 0.154
86 A 5 4 1.00 25 0.160
87 A 5 4 1.00 28 0.143
88 A 5 4 1.00 28 0.143
89 A 5 4 1.00 28 0.143
90 A 6 5 1.00 28 0.179
91 A 6 5 1.00 28 0.179
92 A 6 5 1.00 28 0.179
93 A 6 5 1.00 26 0.192
94 A 4 4 1.00 25 0.160
95 A 6 5 1.00 28 0.179
96 A 6 5 1.00 28 0.179
97 A 6 5 1.00 28 0.179
98 A 7 5 1.00 28 0.179
99 A 6 5 1.00 28 0.179
100 A 5 4 1.00 28 0.143
101 A 4 4 1.00 26 0.154
102 A 3 3 1.00 25 0.120
103 A 7 6 1.00 28 0.214
104 A 7 5 1.00 28 0.179
105 A 7 5 1.00 28 0.179
106 A 4 3 1.00 17 0.176
107 A 4 3 1.00 17 0.176
108 A 4 4 1.00 21 0.190
109 A 6 5 1.00 15 0.333
110 A 3 2 1.00 30 0.067
111 A 3 2 1.00 30 0.067
112 A 3 2 1.00 30 0.067
113 A 3 2 1.00 27 0.074
114 A 3 2 1.00 30 0.067
115 A 3 2 1.00 30 0.067
116 A 3 2 1.00 30 0.067
117 A 3 2 1.00 30 0.067
118 A 3 2 1.00 30 0.067
119 A 3 2 1.00 30 0.067
120 A 5 4 1.00 30 0.133
121 A 5 4 1.00 30 0.133
122 A 5 4 1.00 30 0.133
123 A 4 3 1.00 27 0.111
124 A 4 3 1.00 30 0.100
125 A 4 3 1.00 30 0.100
126 A 4 3 1.00 30 0.100
127 A 4 3 1.00 30 0.100
128 A 4 3 1.00 30 0.100
129 A 6 5 1.00 30 0.167
130 A 6 5 1.00 30 0.167
131 A 6 5 1.00 30 0.167
132 A 6 5 1.00 30 0.167
133 A 4 4 1.00 27 0.148
134 A 4 4 1.00 30 0.133
135 A 5 4 1.00 30 0.133
136 A 5 3 1.00 30 0.100
137 A 5 3 1.00 30 0.100
138 A 5 3 1.00 30 0.100
139 A 3 2 1.00 32 0.062
140 A 3 2 1.00 32 0.062
141 A 3 2 1.00 30 0.067
142 A 5 4 1.00 32 0.125
143 A 6 5 1.00 32 0.156
144 A 6 6 1.00 32 0.188
145 A 6 6 1.00 32 0.188
146 A 7 7 1.00 32 0.219
147 A 7 6 1.00 32 0.188
148 A 6 6 1.00 32 0.188
149 A 5 5 1.00 29 0.172
150 A 6 6 1.00 32 0.188
151 A 6 6 1.00 32 0.188
152 A 6 6 1.00 32 0.188
153 A 5 3 1.00 32 0.094
154 A 6 4 1.00 32 0.125
155 A 11 9 1.00 32 0.281
156 A 10 9 1.00 32 0.281
157 A 9 9 1.00 32 0.281
158 A 8 8 1.07 32 0.250
159 A 5 4 1.00 29 0.138
160 A 6 5 0.97 32 0.156
161 A 7 5 1.00 32 0.156
162 A 8 4 0.98 32 0.125
163 A 9 5 1.00 32 0.156
164 A 10 5 0.97 32 0.156
165 A 4 3 1.00 33 0.091
166 A 4 3 1.00 33 0.091
167 A 4 3 1.00 31 0.097
168 A 10 9 0.98 37 0.243
169 A 6 5 1.17 34 0.147
170 A 6 4 1.00 37 0.108

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