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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 [85] had the largest ratio of [.620689999999999964]

# 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 2 1.00 22 0.091
2 A 2 2 1.00 22 0.091
3 A 2 2 1.00 22 0.091
4 A 2 2 1.00 22 0.091
5 A 2 2 1.00 20 0.100
6 A 12 11 0.86 22 0.500
7 A 11 10 0.86 22 0.455
8 A 11 10 0.90 22 0.455
9 A 4 3 0.99 25 0.120
10 A 4 3 0.98 25 0.120
11 A 6 5 1.03 25 0.200
12 A 4 3 1.04 25 0.120
13 A 4 3 1.02 25 0.120
14 A 13 12 0.80 25 0.480
15 A 12 11 0.77 25 0.440
16 A 11 10 0.84 23 0.435
17 A 11 10 0.81 22 0.455
18 A 12 11 0.84 25 0.440
19 A 13 12 0.81 25 0.480
20 A 4 3 1.04 23 0.130
21 A 4 3 1.00 23 0.130
22 A 7 6 1.03 23 0.261
23 A 4 3 1.07 23 0.130
24 A 4 3 1.00 23 0.130
25 A 11 10 0.85 23 0.435
26 A 11 10 0.95 23 0.435
27 A 11 10 0.90 23 0.435
28 A 9 8 0.89 21 0.381
29 A 9 8 0.85 20 0.400
30 A 10 9 0.89 23 0.391
31 A 11 10 0.85 23 0.435
32 A 8 7 1.14 21 0.333
33 A 4 3 1.15 21 0.143
34 A 5 4 1.15 18 0.222
35 A 7 7 0.90 24 0.292
36 A 6 6 0.94 24 0.250
37 A 5 5 0.99 24 0.208
38 A 4 4 1.03 24 0.167
39 A 4 4 1.02 24 0.167
40 A 4 4 1.03 24 0.167
41 A 5 5 0.99 24 0.208
42 A 6 6 0.95 24 0.250
43 A 5 5 0.85 25 0.200
44 A 6 5 1.03 25 0.200
45 A 5 5 0.88 25 0.200
46 A 4 3 0.99 23 0.130
47 A 4 4 0.87 22 0.182
48 A 4 3 1.04 25 0.120
49 A 6 6 0.88 25 0.240
50 A 5 4 0.98 25 0.160
51 A 6 6 0.88 25 0.240
52 A 10 9 1.49 23 0.391
53 A 7 6 1.03 23 0.261
54 A 11 10 1.01 23 0.435
55 A 5 4 1.08 21 0.190
56 A 9 8 0.98 20 0.400
57 A 4 3 1.07 23 0.130
58 A 9 8 1.49 23 0.348
59 A 10 9 1.07 23 0.391
60 A 11 10 1.00 23 0.435
61 A 3 3 1.00 25 0.120
62 A 3 3 1.00 25 0.120
63 A 3 3 1.00 23 0.130
64 A 3 3 1.00 22 0.136
65 A 3 3 0.98 25 0.120
66 A 7 6 0.86 25 0.240
67 A 3 3 1.01 25 0.120
68 A 3 3 1.00 25 0.120
69 A 3 3 1.00 25 0.120
70 A 3 3 1.00 25 0.120
71 A 3 3 1.00 25 0.120
72 A 3 3 1.00 23 0.130
73 A 3 3 1.00 22 0.136
74 A 3 3 1.00 25 0.120
75 A 4 4 1.11 25 0.160
76 A 3 3 1.00 25 0.120
77 A 3 3 1.00 25 0.120
78 A 3 3 1.00 25 0.120
79 A 16 15 1.04 29 0.517
80 A 14 13 1.03 29 0.448
81 A 10 9 1.00 29 0.310
82 A 9 8 1.01 27 0.296
83 A 14 13 0.90 26 0.500
84 A 13 12 0.91 29 0.414
85 A 19 18 1.15 29 0.621
86 N/A 1 0 1.00 26 0.000
87 A 2 2 1.00 26 0.077
88 A 2 2 1.00 26 0.077
89 A 2 2 1.00 24 0.083
90 A 2 2 1.03 26 0.077
91 A 2 2 1.01 26 0.077
92 A 2 2 1.00 26 0.077
93 A 1 1 1.00 19 0.053
94 A 3 2 1.00 24 0.083
95 A 3 2 1.00 26 0.077
96 A 3 2 1.00 30 0.067
97 A 1 1 1.00 21 0.048
98 A 4 3 1.00 26 0.115
99 A 4 3 1.00 28 0.107
100 A 4 3 1.00 32 0.094
101 A 1 1 1.00 18 0.056
102 A 4 3 1.00 23 0.130
103 A 4 3 1.00 25 0.120
104 A 4 3 1.00 29 0.103
105 A 1 1 1.00 19 0.053
106 A 3 2 1.00 24 0.083
107 A 3 2 1.00 26 0.077
108 A 3 2 1.00 30 0.067
109 A 1 1 1.00 19 0.053
110 A 3 2 1.00 24 0.083
111 A 3 2 1.00 26 0.077
112 A 3 2 1.00 30 0.067
113 A 1 1 1.00 21 0.048
114 A 4 3 1.00 26 0.115
115 A 4 3 1.00 28 0.107
116 A 4 3 1.00 32 0.094
117 A 1 1 1.00 21 0.048
118 A 3 2 1.00 26 0.077
119 A 3 2 1.00 28 0.071
120 A 3 2 1.00 32 0.062
121 A 1 1 1.00 18 0.056
122 A 5 4 1.06 23 0.174
123 A 5 4 1.06 25 0.160
124 A 5 4 1.13 29 0.138
125 A 1 1 1.00 18 0.056
126 A 4 3 1.00 23 0.130
127 A 4 3 1.00 25 0.120
128 A 4 3 1.00 29 0.103
129 A 1 1 1.00 19 0.053
130 A 3 2 1.00 24 0.083
131 A 3 2 1.00 26 0.077
132 A 3 2 1.00 30 0.067
133 A 1 1 1.00 21 0.048
134 A 3 2 1.00 26 0.077
135 A 3 2 1.00 28 0.071
136 A 3 2 1.00 32 0.062
137 A 1 1 1.00 18 0.056
138 A 3 2 1.00 23 0.087
139 A 3 2 1.00 25 0.080
140 A 3 2 1.00 29 0.069
141 A 2 2 1.00 29 0.069
142 A 4 4 0.96 29 0.138
143 A 6 6 1.00 29 0.207
144 A 4 3 1.00 59 0.051
145 A 3 3 1.00 31 0.097
146 A 3 3 1.04 29 0.103
147 A 3 3 1.04 27 0.111
148 A 3 3 1.05 26 0.115
149 A 4 3 0.98 29 0.103
150 A 3 3 1.04 29 0.103
151 A 3 3 1.05 29 0.103
152 A 2 2 1.00 31 0.065
153 A 2 2 1.00 29 0.069
154 A 2 2 1.00 22 0.091
155 N/A 1 0 1.00 31 0.000
156 N/A 1 0 1.00 31 0.000

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