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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 [110] had the largest ratio of [.323529000000000011]

# 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 28 0.071
2 A 2 2 1.00 28 0.071
3 A 2 2 1.00 26 0.077
4 A 2 2 1.00 21 0.095
5 A 2 2 1.00 28 0.071
6 A 2 2 1.00 28 0.071
7 A 2 2 1.00 28 0.071
8 A 2 2 1.00 28 0.071
9 A 2 2 1.00 28 0.071
10 A 2 2 1.00 28 0.071
11 A 2 2 1.00 28 0.071
12 A 2 2 1.00 28 0.071
13 A 2 2 1.00 30 0.067
14 A 2 2 1.00 30 0.067
15 A 2 2 1.00 28 0.071
16 A 2 2 1.00 23 0.087
17 A 2 2 1.00 30 0.067
18 A 2 2 1.00 30 0.067
19 A 2 2 1.00 30 0.067
20 A 2 2 1.00 30 0.067
21 A 2 2 1.00 30 0.067
22 A 2 2 1.00 30 0.067
23 A 2 2 1.00 30 0.067
24 A 2 2 1.00 30 0.067
25 A 2 2 1.00 30 0.067
26 A 2 2 1.00 30 0.067
27 A 2 2 1.00 30 0.067
28 A 2 2 1.00 28 0.071
29 A 2 2 1.00 23 0.087
30 A 2 2 1.00 30 0.067
31 A 2 2 1.00 30 0.067
32 A 2 2 1.00 30 0.067
33 A 2 2 1.00 30 0.067
34 A 2 2 1.00 30 0.067
35 A 2 2 1.00 30 0.067
36 A 2 2 1.00 28 0.071
37 A 2 2 1.00 23 0.087
38 A 2 2 1.00 30 0.067
39 A 2 2 1.00 30 0.067
40 A 2 2 1.00 30 0.067
41 A 2 2 1.00 30 0.067
42 A 2 2 1.00 30 0.067
43 A 2 2 1.00 28 0.071
44 A 2 2 1.00 23 0.087
45 A 2 2 1.00 30 0.067
46 A 2 2 1.00 30 0.067
47 A 2 2 1.00 30 0.067
48 A 2 2 1.00 30 0.067
49 A 2 2 1.00 30 0.067
50 A 2 2 1.00 28 0.071
51 A 2 2 1.00 23 0.087
52 A 2 2 1.00 30 0.067
53 A 2 2 1.00 30 0.067
54 A 2 2 1.00 30 0.067
55 A 2 2 1.00 32 0.062
56 A 2 2 1.00 32 0.062
57 A 2 2 1.00 30 0.067
58 A 2 2 1.00 25 0.080
59 A 2 2 1.00 32 0.062
60 A 6 5 1.30 32 0.156
61 A 8 7 1.17 32 0.219
62 A 8 7 1.18 32 0.219
63 A 2 2 1.00 32 0.062
64 A 2 2 1.00 32 0.062
65 A 2 2 1.00 30 0.067
66 A 2 2 1.00 25 0.080
67 A 2 2 1.00 32 0.062
68 A 6 5 1.28 32 0.156
69 A 9 8 1.31 32 0.250
70 A 10 9 1.22 32 0.281
71 A 2 2 1.00 32 0.062
72 A 2 2 1.00 32 0.062
73 A 2 2 1.00 30 0.067
74 A 2 2 1.00 25 0.080
75 A 2 2 1.00 32 0.062
76 A 6 5 1.23 32 0.156
77 A 8 7 1.28 32 0.219
78 A 8 7 1.33 32 0.219
79 A 2 2 1.00 32 0.062
80 A 2 2 1.00 32 0.062
81 A 2 2 1.00 30 0.067
82 A 2 2 1.00 25 0.080
83 A 2 2 1.00 32 0.062
84 A 6 5 1.12 32 0.156
85 A 10 9 1.20 32 0.281
86 A 8 7 1.15 32 0.219
87 A 2 2 1.00 32 0.062
88 A 2 2 1.00 32 0.062
89 A 2 2 1.00 30 0.067
90 A 2 2 1.00 25 0.080
91 A 2 2 1.11 32 0.062
92 A 6 5 1.24 32 0.156
93 A 9 8 1.23 32 0.250
94 A 2 2 1.00 32 0.062
95 A 2 2 1.00 32 0.062
96 A 2 2 1.00 30 0.067
97 A 2 2 1.00 25 0.080
98 A 2 2 1.00 32 0.062
99 A 6 5 1.27 32 0.156
100 A 9 8 1.26 32 0.250
101 A 11 10 0.64 34 0.294
102 A 10 9 0.71 34 0.265
103 A 9 8 0.83 34 0.235
104 A 9 8 1.02 34 0.235
105 A 9 8 1.04 34 0.235
106 A 9 8 1.20 34 0.235
107 A 9 8 1.12 34 0.235
108 A 6 6 1.06 34 0.176
109 A 7 7 0.90 34 0.206
110 A 12 11 0.59 34 0.324
111 A 11 10 0.64 34 0.294
112 A 10 9 0.71 34 0.265
113 A 10 9 0.84 34 0.265
114 A 10 9 1.03 34 0.265
115 A 10 9 1.06 34 0.265
116 A 10 9 1.16 34 0.265
117 A 10 9 1.12 34 0.265
118 A 6 6 1.06 34 0.176
119 A 7 7 0.90 34 0.206
120 A 12 11 0.59 34 0.324
121 A 11 10 0.64 34 0.294
122 A 11 10 0.73 34 0.294
123 A 11 10 0.87 34 0.294
124 A 11 10 1.05 34 0.294
125 A 11 10 0.95 34 0.294
126 A 11 10 1.11 34 0.294
127 A 11 10 1.12 34 0.294
128 A 6 6 1.06 34 0.176
129 A 7 7 0.90 34 0.206
130 A 8 8 0.80 34 0.235
131 A 10 9 0.71 34 0.265
132 A 9 8 0.83 34 0.235
133 A 8 7 1.05 34 0.206
134 A 8 7 1.13 34 0.206
135 A 8 7 1.09 34 0.206
136 A 8 7 1.11 34 0.206
137 A 6 6 1.06 34 0.176
138 A 11 10 0.74 34 0.294
139 A 10 9 0.85 34 0.265
140 A 9 8 1.04 34 0.235
141 A 8 7 1.12 34 0.206
142 A 8 7 1.20 34 0.206
143 A 8 7 1.20 34 0.206
144 A 6 6 1.12 34 0.176
145 A 11 10 0.88 34 0.294
146 A 10 9 1.05 34 0.265
147 A 9 8 1.05 34 0.235
148 A 8 7 1.11 34 0.206
149 A 8 7 1.37 34 0.206
150 A 6 6 1.19 34 0.176
151 A 7 7 1.01 34 0.206
152 A 11 10 1.16 39 0.256
153 A 2 2 1.00 32 0.062
154 A 2 2 1.00 32 0.062
155 A 2 2 1.00 30 0.067
156 A 2 2 1.00 25 0.080
157 A 2 2 1.00 32 0.062
158 A 4 4 1.17 32 0.125
159 A 11 10 0.83 32 0.312
160 A 2 2 1.00 32 0.062
161 A 2 2 1.00 32 0.062
162 A 2 2 1.00 30 0.067
163 A 2 2 1.00 25 0.080
164 A 2 2 1.00 32 0.062
165 A 4 4 1.07 32 0.125
166 A 10 9 0.80 32 0.281
167 A 2 2 1.00 32 0.062
168 A 2 2 1.00 32 0.062
169 A 2 2 1.00 30 0.067
170 A 2 2 1.00 25 0.080
171 A 2 2 1.19 32 0.062
172 A 4 4 1.20 32 0.125
173 A 10 9 0.91 32 0.281
174 A 2 2 1.00 30 0.067
175 A 2 2 1.00 30 0.067
176 A 2 2 1.00 28 0.071
177 A 2 2 1.00 23 0.087
178 A 2 2 1.00 30 0.067
179 A 3 3 1.17 30 0.100
180 A 7 7 1.33 30 0.233
181 A 6 6 1.52 30 0.200
182 A 7 7 0.97 32 0.219
183 A 7 7 0.97 32 0.219
184 A 7 7 0.97 32 0.219
185 A 7 7 1.02 32 0.219
186 A 7 7 1.08 32 0.219
187 A 7 7 1.42 32 0.219
188 A 7 7 1.41 32 0.219
189 A 7 7 1.42 32 0.219
190 A 3 3 1.05 20 0.150
191 A 5 5 1.00 25 0.200
192 A 6 6 1.17 30 0.200

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