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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 [130] had the largest ratio of [.714285999999999976]

# 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 20 0.100
2 A 3 3 1.00 19 0.158
3 A 7 7 1.15 29 0.241
4 A 5 5 1.10 29 0.172
5 A 3 3 1.00 27 0.111
6 A 4 3 1.00 29 0.103
7 A 5 4 1.00 29 0.138
8 A 9 8 1.10 29 0.276
9 A 7 7 1.30 29 0.241
10 A 5 5 1.20 29 0.172
11 A 3 3 1.00 27 0.111
12 A 5 4 1.00 29 0.138
13 A 8 7 1.06 29 0.241
14 A 7 6 1.32 28 0.214
15 A 6 5 1.44 28 0.179
16 A 2 2 1.00 26 0.077
17 A 4 3 1.00 28 0.107
18 A 5 4 0.97 28 0.143
19 A 7 6 1.04 28 0.214
20 A 9 8 1.48 28 0.286
21 A 6 6 1.47 28 0.214
22 A 2 2 1.00 26 0.077
23 A 5 4 0.97 28 0.143
24 A 8 7 1.00 28 0.250
25 A 12 12 1.02 31 0.387
26 A 10 10 1.00 31 0.323
27 A 8 8 1.16 31 0.258
28 B 11 11 2.56 31 0.355
29 A 13 13 1.04 31 0.419
30 A 15 15 1.04 31 0.484
31 A 3 3 1.00 25 0.120
32 A 4 4 1.00 24 0.167
33 A 4 4 1.00 25 0.160
34 A 4 4 1.00 28 0.143
35 A 2 2 1.00 24 0.083
36 A 2 2 1.00 24 0.083
37 A 2 2 1.00 22 0.091
38 A 2 2 1.00 17 0.118
39 A 5 4 1.03 24 0.167
40 A 6 5 1.16 24 0.208
41 A 9 8 1.27 24 0.333
42 A 2 2 1.00 24 0.083
43 A 2 2 1.00 24 0.083
44 A 2 2 1.00 22 0.091
45 A 2 2 1.00 17 0.118
46 A 5 4 1.04 24 0.167
47 A 5 4 1.18 24 0.167
48 A 7 6 1.32 24 0.250
49 A 2 2 1.00 24 0.083
50 A 2 2 1.00 24 0.083
51 A 2 2 1.00 22 0.091
52 A 2 2 1.00 17 0.118
53 A 5 4 1.02 24 0.167
54 A 6 5 1.30 24 0.208
55 A 7 6 1.21 24 0.250
56 A 2 2 1.00 24 0.083
57 A 2 2 1.00 24 0.083
58 A 2 2 1.00 22 0.091
59 A 2 2 1.00 17 0.118
60 A 5 4 1.00 24 0.167
61 A 7 6 1.19 24 0.250
62 A 10 9 1.21 24 0.375
63 A 2 2 1.00 26 0.077
64 A 2 2 1.00 26 0.077
65 A 2 2 1.00 24 0.083
66 A 2 2 1.00 19 0.105
67 A 5 4 0.99 26 0.154
68 A 6 5 1.08 26 0.192
69 A 9 8 1.23 26 0.308
70 A 2 2 1.00 26 0.077
71 A 2 2 1.00 26 0.077
72 A 2 2 1.00 24 0.083
73 A 2 2 1.00 19 0.105
74 A 5 4 1.00 26 0.154
75 A 5 4 1.11 26 0.154
76 A 7 6 1.26 26 0.231
77 A 2 2 1.00 26 0.077
78 A 2 2 1.00 26 0.077
79 A 2 2 1.00 24 0.083
80 A 2 2 1.00 19 0.105
81 A 5 4 0.98 26 0.154
82 A 6 5 1.24 26 0.192
83 A 9 8 1.27 26 0.308
84 A 2 2 1.00 26 0.077
85 A 2 2 1.00 26 0.077
86 A 2 2 1.00 24 0.083
87 A 2 2 1.00 19 0.105
88 A 5 4 0.97 26 0.154
89 A 6 5 1.21 26 0.192
90 A 9 8 1.20 26 0.308
91 A 6 5 1.06 25 0.200
92 A 5 4 1.05 25 0.160
93 A 12 11 1.68 24 0.458
94 A 10 9 1.61 24 0.375
95 A 6 5 1.02 26 0.192
96 A 1 1 1.00 22 0.045
97 A 7 6 0.97 28 0.214
98 A 6 5 1.00 28 0.179
99 A 2 2 1.00 28 0.071
100 A 4 4 0.97 28 0.143
101 A 5 5 1.33 28 0.179
102 A 2 2 1.00 28 0.071
103 A 2 2 1.00 28 0.071
104 A 2 2 1.00 28 0.071
105 A 2 2 1.02 28 0.071
106 A 7 6 1.39 28 0.214
107 A 4 4 0.97 28 0.143
108 A 2 2 1.02 28 0.071
109 A 2 2 1.31 28 0.071
110 A 16 15 1.23 28 0.536
111 A 12 11 1.29 28 0.393
112 A 10 9 1.31 26 0.346
113 A 9 8 1.36 21 0.381
114 F 0 0 N/A 0.000 N/A
115 B 13 12 2.15 28 0.429
116 B 19 18 2.87 28 0.643
117 A 13 12 1.25 28 0.429
118 A 12 11 1.31 28 0.393
119 A 8 7 1.34 26 0.269
120 A 7 6 1.38 21 0.286
121 B 13 12 2.23 28 0.429
122 B 14 13 2.10 28 0.464
123 B 20 19 2.87 28 0.679
124 A 12 11 1.23 28 0.393
125 A 10 9 1.28 28 0.321
126 A 7 6 1.40 26 0.231
127 A 5 4 1.38 21 0.190
128 B 9 8 2.68 28 0.286
129 B 14 13 2.08 28 0.464
130 B 21 20 2.83 28 0.714
131 A 2 2 1.79 28 0.071
132 B 2 2 2.50 28 0.071
133 A 10 9 1.37 28 0.321
134 A 8 7 1.43 28 0.250
135 A 5 4 1.45 26 0.154
136 A 3 2 1.21 21 0.095
137 B 6 5 3.80 28 0.179
138 B 14 13 2.04 28 0.464
139 B 19 18 2.81 28 0.643
140 B 6 5 4.21 28 0.179
141 A 2 2 1.59 28 0.071
142 B 2 2 2.01 28 0.071
143 A 3 2 1.00 28 0.071
144 F 0 0 N/A 0.000 N/A
145 C 1 1 0.22 28 0.036
146 A 3 2 0.98 30 0.067
147 A 4 4 1.68 26 0.154
148 F 0 0 N/A 0.000 N/A
149 F 0 0 N/A 0.000 N/A
150 A 2 2 1.00 22 0.091
151 A 2 2 1.00 20 0.100
152 A 2 2 1.00 22 0.091
153 A 4 4 1.18 22 0.182
154 A 3 3 1.20 22 0.136
155 A 3 3 1.14 24 0.125
156 A 2 2 1.00 24 0.083
157 A 2 2 1.00 22 0.091
158 A 2 2 1.00 24 0.083
159 A 4 4 1.16 24 0.167
160 A 5 5 1.24 24 0.208
161 A 5 5 1.13 24 0.208
162 A 7 6 1.00 26 0.231
163 A 4 3 1.00 24 0.125
164 A 3 2 1.00 19 0.105
165 N/A 1 0 1.00 26 0.000
166 A 7 6 1.02 26 0.231
167 A 4 3 1.00 24 0.125
168 A 3 2 1.00 19 0.105
169 N/A 1 0 1.00 26 0.000
170 A 2 2 0.99 36 0.056
171 A 1 1 0.01 36 0.028
172 A 4 4 1.06 22 0.182
173 A 7 6 1.00 24 0.250
174 A 4 3 1.00 22 0.136
175 A 3 2 1.00 17 0.118
176 N/A 1 0 1.00 24 0.000
177 F 0 0 N/A 0.000 N/A
178 F 0 0 N/A 0.000 N/A
179 A 5 4 1.00 26 0.154
180 A 3 2 1.00 21 0.095
181 N/A 1 0 1.00 26 0.000
182 N/A 1 0 1.00 28 0.000

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