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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 [83] had the largest ratio of [.423099999999999976]

# 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 22 0.045
2 A 2 1 1.00 22 0.045
3 A 2 1 1.00 22 0.045
4 A 2 1 1.00 22 0.045
5 A 2 1 1.00 20 0.050
6 A 8 8 1.00 22 0.364
7 A 8 8 1.00 22 0.364
8 A 8 8 1.00 22 0.364
9 A 7 6 1.00 25 0.240
10 A 6 6 1.00 25 0.240
11 A 5 5 1.00 25 0.200
12 A 7 6 1.00 25 0.240
13 A 7 6 1.00 25 0.240
14 A 14 8 1.00 25 0.320
15 A 14 8 1.00 25 0.320
16 A 13 7 1.00 23 0.304
17 A 13 7 1.00 22 0.318
18 A 14 8 1.00 25 0.320
19 A 14 8 1.00 25 0.320
20 A 7 6 1.00 23 0.261
21 A 4 4 1.00 23 0.174
22 A 5 5 1.00 23 0.217
23 A 7 6 1.00 23 0.261
24 A 5 4 1.00 23 0.174
25 A 15 9 1.00 23 0.391
26 A 15 9 1.00 23 0.391
27 A 14 8 1.00 23 0.348
28 A 13 7 1.00 21 0.333
29 A 13 7 1.00 20 0.350
30 A 14 8 1.00 23 0.348
31 A 15 9 1.00 23 0.391
32 A 5 5 1.00 21 0.238
33 A 7 6 1.00 21 0.286
34 A 8 7 1.00 18 0.389
35 A 6 4 1.00 24 0.167
36 A 5 4 1.00 24 0.167
37 A 4 4 1.00 24 0.167
38 A 3 3 1.00 24 0.125
39 A 3 3 1.00 24 0.125
40 A 3 3 1.00 24 0.125
41 A 4 4 1.00 24 0.167
42 A 5 4 1.00 24 0.167
43 A 8 5 1.00 25 0.200
44 A 5 5 1.00 25 0.200
45 A 7 4 1.00 25 0.160
46 A 4 3 1.00 23 0.130
47 A 7 4 1.00 22 0.182
48 A 7 6 1.00 25 0.240
49 A 8 5 1.00 25 0.200
50 A 5 4 1.00 25 0.160
51 A 8 5 1.00 25 0.200
52 A 20 7 1.00 23 0.304
53 A 5 5 1.00 23 0.217
54 A 21 7 1.00 23 0.304
55 A 4 3 1.00 21 0.143
56 A 19 6 1.00 20 0.300
57 A 7 6 1.00 23 0.261
58 A 20 7 1.00 23 0.304
59 A 11 8 1.00 23 0.348
60 A 21 9 1.00 23 0.391
61 A 7 6 1.00 25 0.240
62 A 7 6 1.00 25 0.240
63 A 7 6 1.00 23 0.261
64 A 7 6 1.00 22 0.273
65 A 7 6 1.00 25 0.240
66 A 7 7 1.00 25 0.280
67 A 7 6 1.01 25 0.240
68 A 7 6 1.00 25 0.240
69 A 7 6 1.00 25 0.240
70 A 7 6 1.00 25 0.240
71 A 7 6 1.00 25 0.240
72 A 7 6 1.00 23 0.261
73 A 7 6 1.00 22 0.273
74 A 7 6 1.00 25 0.240
75 A 8 7 1.00 25 0.280
76 A 7 6 1.00 25 0.240
77 A 7 6 1.00 25 0.240
78 A 7 6 1.00 25 0.240
79 A 11 7 1.00 29 0.241
80 A 10 7 1.00 29 0.241
81 A 8 7 1.00 29 0.241
82 A 8 7 1.00 27 0.259
83 A 16 11 1.00 26 0.423
84 A 16 11 1.00 29 0.379
85 A 24 12 1.00 29 0.414
86 N/A 0 0 1.00 26 0.000
87 A 13 4 1.00 26 0.154
88 A 10 4 1.00 26 0.154
89 A 7 4 1.00 24 0.167
90 A 6 3 1.00 26 0.115
91 A 8 3 1.00 26 0.115
92 A 10 3 1.00 26 0.115
93 A 1 1 1.00 19 0.053
94 A 2 2 1.00 24 0.083
95 A 2 2 1.00 26 0.077
96 A 2 2 1.00 30 0.067
97 A 1 1 1.00 21 0.048
98 A 2 2 1.00 26 0.077
99 A 2 2 1.00 28 0.071
100 A 2 2 1.00 32 0.062
101 A 1 1 1.00 18 0.056
102 A 3 3 1.00 23 0.130
103 A 3 3 1.00 25 0.120
104 A 3 3 1.00 29 0.103
105 A 1 1 1.00 19 0.053
106 A 2 2 1.00 24 0.083
107 A 2 2 1.00 26 0.077
108 A 2 2 1.00 30 0.067
109 A 1 1 1.00 19 0.053
110 A 2 2 1.00 24 0.083
111 A 2 2 1.00 26 0.077
112 A 2 2 1.00 30 0.067
113 A 1 1 1.00 21 0.048
114 A 2 2 1.00 26 0.077
115 A 2 2 1.00 28 0.071
116 A 2 2 1.00 32 0.062
117 A 1 1 1.00 21 0.048
118 A 2 2 1.00 26 0.077
119 A 2 2 1.00 28 0.071
120 A 2 2 1.00 32 0.062
121 A 1 1 1.00 18 0.056
122 A 4 3 0.94 23 0.130
123 A 4 3 0.94 25 0.120
124 A 4 3 1.00 29 0.103
125 A 1 1 1.00 18 0.056
126 A 3 3 1.00 23 0.130
127 A 3 3 1.00 25 0.120
128 A 3 3 1.00 29 0.103
129 A 1 1 1.00 19 0.053
130 A 2 2 1.00 24 0.083
131 A 2 2 1.00 26 0.077
132 A 2 2 1.00 30 0.067
133 A 1 1 1.00 21 0.048
134 A 2 2 1.00 26 0.077
135 A 2 2 1.00 28 0.071
136 A 2 2 1.00 32 0.062
137 A 1 1 1.00 18 0.056
138 A 1 1 1.00 23 0.043
139 A 1 1 1.00 25 0.040
140 A 2 2 1.00 29 0.069
141 A 4 2 1.00 29 0.069
142 A 5 3 1.00 29 0.103
143 A 6 3 1.00 29 0.103
144 A 3 3 1.00 59 0.051
145 A 5 3 1.00 31 0.097
146 A 5 3 1.00 29 0.103
147 A 5 3 1.00 27 0.111
148 A 5 3 1.00 26 0.115
149 A 8 5 1.00 29 0.172
150 A 5 3 1.00 29 0.103
151 A 5 3 1.00 29 0.103
152 A 10 4 1.00 31 0.129
153 A 7 4 1.00 29 0.138
154 A 2 2 1.00 22 0.091
155 N/A 0 0 1.00 31 0.000
156 N/A 0 0 1.00 31 0.000

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