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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 [35] had the largest ratio of [.4643]

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 26 0.038
2 A 2 1 1.00 24 0.042
3 A 2 1 1.00 23 0.043
4 A 2 1 1.00 26 0.038
5 A 2 1 1.00 26 0.038
6 A 2 1 1.00 26 0.038
7 A 2 1 1.00 26 0.038
8 A 2 1 1.00 26 0.038
9 A 2 1 1.00 26 0.038
10 A 2 1 1.00 26 0.038
11 A 2 1 1.00 28 0.036
12 A 2 1 1.00 26 0.038
13 A 2 1 1.00 25 0.040
14 A 2 1 1.00 28 0.036
15 A 2 1 1.00 28 0.036
16 A 2 1 1.00 28 0.036
17 A 2 1 1.00 28 0.036
18 A 2 1 1.00 28 0.036
19 A 2 1 1.00 28 0.036
20 A 2 1 1.00 28 0.036
21 A 13 11 1.00 28 0.393
22 A 12 11 1.00 28 0.393
23 A 11 10 1.00 28 0.357
24 A 10 9 1.00 26 0.346
25 A 8 7 1.00 25 0.280
26 A 12 10 1.00 28 0.357
27 A 13 12 1.00 28 0.429
28 A 13 11 1.00 28 0.393
29 A 11 10 1.00 28 0.357
30 A 10 9 1.00 28 0.321
31 A 10 9 1.00 28 0.321
32 A 10 9 1.00 26 0.346
33 A 10 9 1.00 25 0.360
34 A 14 12 1.00 28 0.429
35 A 15 13 1.00 28 0.464
36 A 15 13 1.00 28 0.464
37 A 2 1 1.00 30 0.033
38 A 2 1 1.00 30 0.033
39 A 2 1 1.00 28 0.036
40 A 10 9 1.00 28 0.321
41 A 11 10 1.00 30 0.333
42 A 11 10 1.00 31 0.323
43 A 11 10 1.00 34 0.294
44 A 11 10 1.00 34 0.294
45 A 7 6 1.00 30 0.200
46 A 7 6 1.00 30 0.200
47 A 7 6 1.00 30 0.200
48 A 7 6 1.00 28 0.214
49 A 7 6 1.00 30 0.200
50 A 7 6 1.00 30 0.200
51 A 7 6 1.00 30 0.200
52 A 7 6 1.00 30 0.200
53 A 5 3 1.00 30 0.100
54 A 5 3 1.00 30 0.100
55 A 5 3 1.00 27 0.111
56 A 5 3 1.00 30 0.100
57 A 5 3 1.00 30 0.100
58 A 5 3 1.00 30 0.100
59 A 8 7 1.00 30 0.233
60 A 7 7 1.00 30 0.233
61 A 6 6 1.00 30 0.200
62 A 5 5 1.00 28 0.179
63 A 8 7 1.00 30 0.233
64 A 8 7 1.00 30 0.233
65 A 8 7 1.00 30 0.233
66 A 6 4 1.00 30 0.133
67 A 6 4 1.00 30 0.133
68 A 4 3 1.00 30 0.100
69 A 4 3 1.00 27 0.111
70 A 6 4 1.00 30 0.133
71 A 6 4 1.00 30 0.133
72 A 7 5 1.00 31 0.161
73 A 7 5 1.00 31 0.161
74 A 7 5 1.00 31 0.161
75 A 7 5 1.00 31 0.161
76 A 5 4 1.00 29 0.138
77 A 4 3 1.00 31 0.097
78 A 4 3 1.00 31 0.097
79 A 4 3 1.00 31 0.097
80 A 6 4 1.00 31 0.129
81 A 6 4 1.00 31 0.129
82 A 6 4 1.00 31 0.129
83 A 6 4 1.00 31 0.129
84 A 4 3 1.00 28 0.107
85 A 5 3 1.00 31 0.097
86 A 5 3 1.00 31 0.097
87 A 5 3 1.00 31 0.097
88 A 5 3 1.00 31 0.097
89 A 7 5 1.00 31 0.161
90 A 7 5 1.00 31 0.161
91 A 7 5 1.00 31 0.161
92 A 5 4 1.00 31 0.129
93 A 5 4 1.00 31 0.129
94 A 5 4 1.00 28 0.143
95 A 6 3 1.00 31 0.097
96 A 6 3 1.00 31 0.097
97 A 6 3 1.00 31 0.097
98 A 8 7 1.00 31 0.226
99 A 8 7 1.00 31 0.226
100 A 8 7 1.00 31 0.226
101 A 8 7 1.00 31 0.226
102 A 6 6 1.00 29 0.207
103 A 8 7 1.00 31 0.226
104 A 8 7 1.00 31 0.226
105 A 8 7 1.00 31 0.226
106 A 8 7 1.00 31 0.226
107 A 12 7 1.00 31 0.226
108 A 12 7 1.00 31 0.226
109 A 12 7 1.00 31 0.226
110 A 12 7 1.00 31 0.226
111 A 10 6 1.00 28 0.214
112 A 12 7 1.00 31 0.226
113 A 12 7 1.00 31 0.226
114 A 12 7 1.00 31 0.226
115 A 13 8 1.00 31 0.258
116 A 13 8 1.00 31 0.258
117 A 13 8 1.00 31 0.258
118 A 11 7 1.00 31 0.226
119 A 11 7 1.00 31 0.226
120 A 11 7 1.00 28 0.250
121 A 13 7 1.00 31 0.226
122 A 13 7 1.00 31 0.226
123 A 7 6 1.00 33 0.182
124 A 6 4 1.00 35 0.114
125 A 6 4 1.00 35 0.114
126 A 4 3 1.00 32 0.094
127 A 6 4 1.00 35 0.114
128 A 6 4 1.00 35 0.114
129 A 1 1 1.00 42 0.024
130 A 5 4 1.32 35 0.114
131 A 4 3 1.34 35 0.086
132 A 4 3 1.37 33 0.091
133 A 6 5 1.62 35 0.143
134 A 6 6 1.57 35 0.171
135 A 6 6 1.44 35 0.171
136 A 7 7 1.17 35 0.200
137 A 6 6 1.13 35 0.171
138 A 5 5 1.40 32 0.156
139 A 5 5 1.52 35 0.143
140 A 5 5 1.00 35 0.143
141 A 4 4 1.00 35 0.114
142 A 5 5 1.00 35 0.143
143 A 6 5 1.00 35 0.143

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