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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 [114] had the largest ratio of [.423076999999999981]

# 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 20 0.100
5 A 2 2 1.00 22 0.091
6 A 2 2 1.00 22 0.091
7 A 2 2 1.00 22 0.091
8 A 2 2 1.00 22 0.091
9 A 2 2 1.00 22 0.091
10 A 2 2 1.00 22 0.091
11 A 2 2 1.00 24 0.083
12 A 2 2 1.00 24 0.083
13 A 2 2 1.00 22 0.091
14 A 2 2 1.00 24 0.083
15 A 2 2 1.00 24 0.083
16 A 2 2 1.00 24 0.083
17 A 2 2 1.00 24 0.083
18 A 2 2 1.00 24 0.083
19 A 2 2 1.00 24 0.083
20 A 2 2 1.00 24 0.083
21 A 2 2 1.00 24 0.083
22 A 2 2 1.00 24 0.083
23 A 2 2 1.00 24 0.083
24 A 2 2 1.00 24 0.083
25 A 2 2 1.00 22 0.091
26 A 2 2 1.00 24 0.083
27 A 2 2 1.00 24 0.083
28 A 2 2 1.00 24 0.083
29 A 2 2 1.00 24 0.083
30 A 2 2 1.00 24 0.083
31 A 2 2 1.00 24 0.083
32 A 2 2 1.00 24 0.083
33 A 2 2 1.00 22 0.091
34 A 2 2 1.00 24 0.083
35 A 2 2 1.00 24 0.083
36 A 2 2 1.00 24 0.083
37 A 2 2 1.00 24 0.083
38 A 2 2 1.00 24 0.083
39 A 2 2 1.00 24 0.083
40 A 2 2 1.00 24 0.083
41 A 2 2 1.00 22 0.091
42 A 2 2 1.00 24 0.083
43 A 2 2 1.00 24 0.083
44 A 2 2 1.00 24 0.083
45 A 2 2 1.00 24 0.083
46 A 2 2 1.00 24 0.083
47 A 2 2 1.00 24 0.083
48 A 2 2 1.00 24 0.083
49 A 2 2 1.00 22 0.091
50 A 2 2 1.00 24 0.083
51 A 2 2 1.00 24 0.083
52 A 2 2 1.00 24 0.083
53 A 2 2 1.00 24 0.083
54 A 2 2 1.00 24 0.083
55 A 2 2 1.00 24 0.083
56 A 2 2 1.00 24 0.083
57 A 2 2 1.00 24 0.083
58 A 2 2 1.00 24 0.083
59 A 2 2 1.00 24 0.083
60 A 2 2 1.00 26 0.077
61 A 2 2 1.00 26 0.077
62 A 2 2 1.00 26 0.077
63 A 2 2 1.00 26 0.077
64 A 2 2 1.00 26 0.077
65 A 2 2 1.00 26 0.077
66 A 2 2 1.00 26 0.077
67 A 2 2 1.00 26 0.077
68 A 9 8 1.11 26 0.308
69 A 8 7 1.11 26 0.269
70 A 7 6 1.11 26 0.231
71 A 6 5 1.07 26 0.192
72 A 5 4 1.02 26 0.154
73 A 6 5 1.21 26 0.192
74 A 7 6 1.27 26 0.231
75 A 8 7 1.26 26 0.269
76 A 9 8 1.25 26 0.308
77 A 11 10 1.06 26 0.385
78 A 10 9 1.08 26 0.346
79 A 9 8 1.09 26 0.308
80 A 7 6 1.07 26 0.231
81 A 8 7 0.99 26 0.269
82 A 8 7 1.14 26 0.269
83 A 9 8 1.17 26 0.308
84 A 10 9 1.17 26 0.346
85 A 11 10 1.15 26 0.385
86 F 0 0 N/A 0.000 N/A
87 F 0 0 N/A 0.000 N/A
88 A 9 8 0.96 26 0.308
89 F 0 0 N/A 0.000 N/A
90 A 10 9 0.99 26 0.346
91 A 9 8 1.07 26 0.308
92 A 10 9 1.08 26 0.346
93 F 0 0 N/A 0.000 N/A
94 A 7 6 0.68 26 0.231
95 A 5 4 0.64 24 0.167
96 A 8 7 1.06 26 0.269
97 A 7 6 0.98 26 0.231
98 A 8 7 1.17 26 0.269
99 A 5 4 0.76 26 0.154
100 A 7 6 0.75 26 0.231
101 A 10 9 0.75 26 0.346
102 A 8 7 0.55 26 0.269
103 A 6 5 0.55 24 0.208
104 A 10 9 1.01 26 0.346
105 A 9 8 0.92 26 0.308
106 A 9 8 0.84 26 0.308
107 A 10 9 0.96 26 0.346
108 A 10 9 1.15 26 0.346
109 A 6 5 0.53 26 0.192
110 A 9 8 0.54 26 0.308
111 A 11 10 0.53 26 0.385
112 A 9 8 0.48 26 0.308
113 A 7 6 0.50 24 0.250
114 A 12 11 1.00 26 0.423
115 A 11 10 0.92 26 0.385
116 A 11 10 0.83 26 0.385
117 A 12 11 0.78 26 0.423
118 A 11 10 0.85 26 0.385
119 F 0 0 N/A 0.000 N/A
120 A 6 5 0.98 26 0.192
121 A 4 3 0.85 24 0.125
122 A 6 5 1.18 26 0.192
123 A 4 3 1.17 26 0.115
124 A 6 5 1.16 26 0.192
125 A 8 7 1.16 26 0.269
126 A 6 5 1.22 26 0.192
127 A 6 5 1.21 26 0.192
128 A 4 3 0.92 24 0.125
129 A 5 4 1.08 26 0.154
130 A 6 5 1.10 26 0.192
131 A 8 7 1.05 26 0.269
132 A 8 7 1.20 26 0.269
133 A 6 5 0.98 26 0.192
134 A 2 2 0.51 26 0.077
135 A 2 2 0.71 24 0.083
136 A 7 6 1.06 26 0.231
137 A 8 7 1.07 26 0.269
138 A 10 10 0.96 29 0.345
139 A 8 8 0.94 29 0.276
140 A 8 8 0.89 29 0.276
141 A 8 8 1.02 29 0.276
142 A 10 10 1.00 29 0.345
143 A 10 10 0.94 29 0.345
144 A 10 10 0.86 29 0.345
145 A 10 10 0.82 29 0.345
146 A 10 10 0.92 29 0.345
147 A 12 12 1.04 29 0.414
148 A 10 10 1.04 29 0.345
149 A 8 8 1.02 29 0.276
150 A 6 6 1.00 29 0.207
151 A 8 8 1.04 29 0.276
152 A 10 10 1.03 29 0.345
153 A 12 12 1.05 29 0.414
154 A 12 12 1.01 29 0.414
155 A 10 10 1.01 29 0.345
156 A 8 8 1.01 29 0.276
157 A 8 8 0.96 29 0.276
158 A 8 8 1.00 29 0.276
159 A 10 10 1.00 29 0.345
160 A 12 12 1.01 29 0.414
161 A 10 10 0.98 29 0.345
162 A 10 10 0.93 29 0.345
163 A 10 10 0.96 29 0.345
164 A 10 10 0.92 29 0.345
165 A 10 10 0.96 29 0.345
166 A 12 12 0.98 29 0.414
167 A 2 2 1.00 24 0.083
168 A 2 2 1.00 24 0.083
169 A 2 2 1.00 22 0.091
170 A 2 2 0.99 24 0.083
171 A 4 4 1.09 24 0.167
172 A 4 4 1.03 24 0.167

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