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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 [80] had the largest ratio of [.846153999999999962]

# 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 4 3 0.83 13 0.231
2 A 4 3 0.89 13 0.231
3 A 4 3 1.00 13 0.231
4 A 4 3 1.00 13 0.231
5 A 4 3 0.83 13 0.231
6 A 4 3 0.83 13 0.231
7 A 4 3 1.00 11 0.273
8 A 4 3 1.00 11 0.273
9 A 4 3 1.00 11 0.273
10 A 4 3 1.00 11 0.273
11 A 4 3 1.00 13 0.231
12 A 4 3 0.83 13 0.231
13 A 4 3 0.89 13 0.231
14 A 4 3 1.00 13 0.231
15 A 4 3 1.00 13 0.231
16 A 4 3 0.83 13 0.231
17 A 4 3 0.83 13 0.231
18 A 3 2 1.00 13 0.154
19 A 3 2 1.00 13 0.154
20 A 3 2 1.00 13 0.154
21 A 3 2 1.00 13 0.154
22 A 3 2 1.00 13 0.154
23 A 3 2 1.00 13 0.154
24 A 4 3 0.83 13 0.231
25 A 4 3 0.89 13 0.231
26 A 4 3 1.00 13 0.231
27 A 4 3 1.00 13 0.231
28 A 4 3 0.83 13 0.231
29 A 4 3 0.83 13 0.231
30 A 4 3 0.83 13 0.231
31 A 4 3 0.89 13 0.231
32 A 4 3 1.00 13 0.231
33 A 4 3 1.00 13 0.231
34 A 4 3 0.83 13 0.231
35 A 4 3 0.83 13 0.231
36 A 4 3 1.00 15 0.200
37 A 4 3 0.84 15 0.200
38 A 4 3 1.00 15 0.200
39 A 4 3 0.79 15 0.200
40 A 4 3 0.94 19 0.158
41 A 5 4 0.96 21 0.190
42 A 5 4 1.02 21 0.190
43 A 3 2 1.00 13 0.154
44 A 3 2 1.00 13 0.154
45 A 3 2 1.00 13 0.154
46 A 5 4 0.91 21 0.190
47 A 4 3 1.24 21 0.143
48 A 5 4 0.94 21 0.190
49 A 4 3 1.24 21 0.143
50 A 3 2 1.00 19 0.105
51 A 4 3 1.00 21 0.143
52 A 4 3 0.94 19 0.158
53 A 4 3 0.90 21 0.143
54 A 4 3 0.89 21 0.143
55 A 4 3 0.86 22 0.136
56 A 4 3 0.82 24 0.125
57 A 4 3 0.80 24 0.125
58 A 11 10 1.01 21 0.476
59 A 11 10 1.02 21 0.476
60 A 3 2 1.00 21 0.095
61 A 10 9 0.97 19 0.474
62 A 10 9 0.94 13 0.692
63 A 6 5 1.03 21 0.238
64 A 11 10 1.01 21 0.476
65 A 11 10 0.97 21 0.476
66 A 5 4 0.91 21 0.190
67 A 11 10 0.99 21 0.476
68 A 11 10 0.96 21 0.476
69 A 3 2 1.00 21 0.095
70 A 11 10 0.99 19 0.526
71 A 11 10 0.96 13 0.769
72 A 5 4 0.92 21 0.190
73 A 12 11 1.01 21 0.524
74 A 12 11 0.99 21 0.524
75 A 5 4 0.89 21 0.190
76 A 12 11 1.00 21 0.524
77 A 12 11 0.98 21 0.524
78 A 3 2 1.00 21 0.095
79 A 12 11 1.02 19 0.579
80 A 12 11 0.99 13 0.846
81 A 5 4 0.90 21 0.190
82 A 13 12 1.03 21 0.571
83 A 13 12 1.02 21 0.571
84 A 5 4 0.91 21 0.190
85 A 11 10 0.95 24 0.417
86 A 11 10 0.96 24 0.417
87 A 3 2 1.00 24 0.083
88 A 10 9 0.96 22 0.409
89 A 6 5 0.95 24 0.208
90 A 11 10 0.95 24 0.417
91 A 11 10 0.92 24 0.417
92 A 5 4 0.83 24 0.167
93 A 11 10 0.95 24 0.417
94 A 11 10 0.92 24 0.417
95 A 3 2 1.00 24 0.083
96 A 11 10 0.98 22 0.455
97 A 5 4 0.84 24 0.167
98 A 12 11 0.95 24 0.458
99 A 12 11 0.94 24 0.458
100 A 5 4 0.80 24 0.167
101 A 12 11 0.95 24 0.458
102 A 12 11 0.93 24 0.458
103 A 3 2 1.00 24 0.083
104 A 12 11 1.00 22 0.500
105 A 5 4 0.82 24 0.167
106 A 13 12 0.96 24 0.500
107 A 13 12 0.96 24 0.500
108 A 5 4 0.82 24 0.167
109 A 3 2 1.00 21 0.095
110 A 4 3 1.26 19 0.158
111 A 3 2 1.00 21 0.095
112 A 3 2 1.00 21 0.095
113 A 3 2 1.00 21 0.095
114 A 3 2 1.00 21 0.095
115 A 3 2 1.00 21 0.095
116 A 5 4 0.97 17 0.235
117 A 14 13 0.94 17 0.765
118 A 12 11 0.95 15 0.733
119 A 10 9 0.94 13 0.692
120 A 5 4 1.08 17 0.235
121 A 4 3 1.01 17 0.176
122 A 5 4 0.98 17 0.235
123 A 5 4 0.97 19 0.211
124 A 4 3 0.98 19 0.158
125 A 5 4 0.99 17 0.235
126 A 3 2 1.00 15 0.133
127 A 11 10 1.06 19 0.526
128 A 17 16 1.05 19 0.842
129 A 6 5 1.11 27 0.185
130 A 6 5 1.13 28 0.179
131 A 6 5 0.62 49 0.102
132 A 6 5 1.11 50 0.100

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