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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 [66] had the largest ratio of [.3333]

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 2 1 1.00 17 0.059
2 A 2 1 1.00 17 0.059
3 A 2 1 1.00 17 0.059
4 A 2 1 1.00 15 0.067
5 A 2 2 1.00 17 0.118
6 A 2 2 1.00 17 0.118
7 A 3 3 1.00 17 0.176
8 A 2 1 1.00 19 0.053
9 A 2 1 1.00 19 0.053
10 A 2 1 1.00 17 0.059
11 A 3 2 1.00 19 0.105
12 A 4 3 1.00 19 0.158
13 A 3 3 1.00 19 0.158
14 A 2 1 1.00 19 0.053
15 A 2 1 1.00 19 0.053
16 A 2 1 1.00 17 0.059
17 A 3 2 1.00 19 0.105
18 A 4 3 1.00 19 0.158
19 A 5 4 1.00 19 0.210
20 A 3 2 1.00 19 0.105
21 A 3 2 1.00 19 0.105
22 A 3 2 1.00 19 0.105
23 A 2 2 1.00 17 0.118
24 A 3 2 1.00 19 0.105
25 A 4 3 1.00 19 0.158
26 A 5 4 1.00 19 0.210
27 A 4 3 1.00 19 0.158
28 A 4 3 1.00 19 0.158
29 A 4 3 1.00 19 0.158
30 A 4 3 1.00 19 0.158
31 A 2 2 1.00 17 0.118
32 A 4 3 1.00 19 0.158
33 A 5 4 1.00 19 0.210
34 A 6 4 1.00 19 0.210
35 A 5 4 1.00 19 0.210
36 A 5 4 1.00 19 0.210
37 A 5 4 1.00 19 0.210
38 A 3 3 1.00 19 0.158
39 A 3 3 1.00 17 0.176
40 A 5 4 1.00 19 0.210
41 A 6 4 1.00 19 0.210
42 A 7 4 1.00 19 0.210
43 A 3 3 1.00 15 0.200
44 A 5 3 1.00 15 0.200
45 A 6 6 1.00 21 0.286
46 A 5 5 1.00 21 0.238
47 A 4 4 1.00 19 0.210
48 A 3 3 1.00 11 0.273
49 A 5 5 1.00 21 0.238
50 A 3 3 1.00 21 0.143
51 A 4 4 1.00 21 0.190
52 A 6 5 1.00 21 0.238
53 A 7 6 1.00 21 0.286
54 A 6 5 1.00 21 0.238
55 A 5 4 1.00 19 0.210
56 A 4 3 1.00 11 0.273
57 A 6 6 1.00 21 0.286
58 A 6 6 1.00 21 0.286
59 A 4 3 1.00 21 0.143
60 A 5 4 1.00 21 0.190
61 A 7 5 1.00 21 0.238
62 A 8 6 1.00 21 0.286
63 A 7 5 1.00 21 0.238
64 A 6 4 1.00 19 0.210
65 A 5 3 1.00 11 0.273
66 A 7 7 1.00 21 0.333
67 A 7 7 1.00 21 0.333
68 A 7 7 1.00 21 0.333
69 A 5 3 1.00 21 0.143
70 A 6 4 1.00 21 0.190
71 A 4 4 1.00 19 0.210
72 A 4 4 1.00 17 0.235
73 A 4 4 1.00 21 0.190
74 A 5 5 1.00 21 0.238
75 A 4 4 1.00 21 0.190
76 A 3 3 1.00 19 0.158
77 A 2 2 1.00 11 0.182
78 A 2 2 1.00 21 0.095
79 A 3 3 1.00 21 0.143
80 A 5 5 1.00 21 0.238
81 A 6 5 1.00 21 0.238
82 A 5 5 1.00 21 0.238
83 A 4 4 1.17 21 0.190
84 A 3 3 1.00 19 0.158
85 A 1 1 1.00 11 0.091
86 A 3 3 1.00 21 0.143
87 A 5 5 1.00 21 0.238
88 A 6 5 1.00 21 0.238
89 A 6 6 1.00 21 0.286
90 A 5 5 1.00 21 0.238
91 A 4 4 1.00 21 0.190
92 A 2 2 1.00 19 0.105
93 A 2 2 1.00 11 0.182
94 A 5 5 1.00 21 0.238
95 A 6 5 1.00 21 0.238
96 A 7 5 1.00 21 0.238
97 A 5 3 1.00 21 0.143
98 A 4 3 1.00 21 0.143
99 A 3 3 1.00 19 0.158
100 A 2 2 1.00 11 0.182
101 A 3 3 1.00 21 0.143
102 A 3 3 1.00 21 0.143
103 A 4 4 1.00 21 0.190
104 A 5 4 1.00 21 0.190
105 A 2 2 1.00 26 0.077
106 A 2 2 1.00 19 0.105
107 A 2 2 1.00 21 0.095
108 A 2 2 1.00 15 0.133
109 A 1 1 1.00 24 0.042
110 A 2 2 1.00 24 0.083
111 A 1 1 1.00 26 0.038
112 A 1 1 1.00 24 0.042
113 A 1 1 1.00 23 0.043
114 A 1 1 1.00 24 0.042
115 A 1 1 1.00 22 0.045
116 A 1 1 1.00 19 0.053
117 A 1 1 1.00 19 0.053
118 A 1 1 1.00 24 0.042
119 A 1 1 1.00 22 0.045
120 A 1 1 1.00 27 0.037
121 A 1 1 1.00 28 0.036
122 A 1 1 1.00 29 0.034
123 A 1 1 1.00 30 0.033
124 A 1 1 1.00 26 0.038
125 A 1 1 1.00 26 0.038
126 A 1 1 1.00 23 0.043
127 A 1 1 1.00 23 0.043
128 A 1 1 1.00 23 0.043
129 A 1 1 1.00 23 0.043
130 A 1 1 1.00 17 0.059
131 A 1 1 1.00 21 0.048
132 A 1 1 1.00 21 0.048
133 A 3 3 1.15 29 0.103
134 A 3 3 1.23 29 0.103
135 A 3 3 1.20 29 0.103
136 A 2 1 1.00 23 0.043
137 A 2 2 1.00 23 0.087
138 A 2 2 1.00 21 0.095
139 A 2 2 1.00 21 0.095
140 A 2 2 1.00 23 0.087
141 A 1 1 1.00 21 0.048
142 A 1 1 1.00 21 0.048
143 A 1 1 1.00 21 0.048
144 A 1 1 1.00 23 0.043
145 A 1 1 1.00 23 0.043
146 A 1 1 1.00 23 0.043
147 A 1 1 1.00 23 0.043
148 A 1 1 1.00 25 0.040
149 A 1 1 1.00 21 0.048
150 A 1 1 1.00 21 0.048
151 A 1 1 1.00 21 0.048
152 A 1 1 1.00 23 0.043
153 A 1 1 1.00 25 0.040
154 A 1 1 1.00 25 0.040
155 A 1 1 1.00 25 0.040
156 A 1 1 1.00 27 0.037
157 A 1 1 1.00 19 0.053
158 A 1 1 1.00 50 0.020

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