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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 [56] had the largest ratio of [.699999999999999956]

# 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 5 5 1.11 26 0.192
2 A 4 4 0.88 26 0.154
3 A 3 3 1.00 26 0.115
4 A 5 4 1.32 26 0.154
5 A 6 5 1.07 26 0.192
6 A 7 6 1.02 26 0.231
7 A 3 3 1.00 20 0.150
8 A 3 3 1.00 18 0.167
9 A 1 1 1.00 16 0.062
10 A 3 3 1.00 20 0.150
11 A 2 2 1.00 20 0.100
12 A 3 3 1.00 20 0.150
13 A 3 3 1.00 20 0.150
14 A 3 3 1.00 20 0.150
15 A 3 3 1.00 20 0.150
16 A 3 3 1.00 20 0.150
17 A 3 3 1.00 22 0.136
18 A 3 3 1.00 20 0.150
19 A 3 3 1.00 18 0.167
20 A 3 3 1.00 22 0.136
21 A 3 3 1.00 22 0.136
22 A 3 3 1.00 22 0.136
23 A 3 3 1.00 22 0.136
24 A 3 3 1.00 22 0.136
25 A 3 3 1.00 22 0.136
26 A 3 3 1.00 22 0.136
27 A 6 5 1.00 22 0.227
28 A 4 3 1.00 22 0.136
29 A 8 7 1.02 20 0.350
30 A 5 5 1.05 18 0.278
31 A 5 5 1.09 22 0.227
32 A 5 5 1.02 22 0.227
33 A 5 5 1.11 22 0.227
34 A 4 4 1.10 22 0.182
35 A 5 4 1.00 22 0.182
36 A 5 4 1.00 22 0.182
37 A 5 4 1.00 22 0.182
38 A 5 5 1.29 22 0.227
39 A 5 5 1.17 22 0.227
40 A 5 5 1.05 20 0.250
41 A 5 5 1.03 18 0.278
42 A 5 5 0.97 22 0.227
43 A 2 2 1.00 9 0.222
44 A 3 3 1.00 14 0.214
45 A 4 4 1.00 16 0.250
46 A 12 11 1.21 24 0.458
47 A 10 9 1.23 22 0.409
48 A 6 5 0.96 20 0.250
49 A 5 4 1.31 24 0.167
50 A 8 7 0.81 24 0.292
51 A 8 7 0.82 24 0.292
52 A 6 5 1.03 24 0.208
53 A 8 7 1.07 24 0.292
54 A 10 9 1.09 24 0.375
55 A 16 15 1.16 22 0.682
56 A 15 14 1.18 20 0.700
57 A 12 11 1.19 24 0.458
58 A 7 6 1.24 24 0.250
59 A 6 5 1.25 24 0.208
60 A 10 9 0.90 24 0.375
61 A 10 9 0.86 24 0.375
62 A 10 9 0.86 24 0.375
63 A 12 11 1.01 24 0.458
64 A 9 8 1.08 24 0.333
65 A 12 11 1.10 24 0.458
66 A 8 7 1.30 24 0.292
67 A 5 4 1.37 24 0.167
68 A 4 3 1.65 22 0.136
69 A 3 2 1.00 20 0.100
70 A 4 3 1.00 24 0.125
71 A 7 6 1.05 24 0.250
72 A 12 11 1.15 24 0.458
73 A 10 9 1.23 24 0.375
74 A 7 6 1.33 24 0.250
75 A 1 1 1.00 24 0.042
76 A 1 1 1.00 24 0.042
77 A 4 3 1.00 24 0.125
78 A 7 6 1.09 22 0.273
79 A 9 8 1.04 20 0.400
80 A 11 10 1.03 24 0.417
81 A 13 12 1.01 24 0.500
82 A 4 4 0.91 28 0.143
83 A 4 4 0.93 28 0.143
84 A 2 2 1.00 26 0.077
85 A 4 4 1.02 28 0.143
86 A 5 5 1.02 28 0.179
87 A 3 2 1.00 18 0.111
88 A 4 3 1.00 18 0.167
89 A 5 4 1.00 22 0.182
90 A 5 4 1.00 24 0.167

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