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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 [38] had the largest ratio of [.764705999999999997]

# 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 12 11 1.15 17 0.647
2 A 11 10 0.86 18 0.556
3 A 12 11 1.13 17 0.647
4 A 14 13 0.89 18 0.722
5 A 10 9 1.27 26 0.346
6 A 10 9 1.27 26 0.346
7 A 4 4 1.05 27 0.148
8 A 10 9 1.27 27 0.333
9 A 8 7 1.21 18 0.389
10 A 10 9 1.06 18 0.500
11 A 10 9 1.06 18 0.500
12 A 8 7 1.21 16 0.438
13 A 8 7 1.14 13 0.538
14 A 8 7 1.20 18 0.389
15 A 5 5 1.19 18 0.278
16 A 4 4 1.14 18 0.222
17 A 4 4 1.00 18 0.222
18 A 4 4 1.15 18 0.222
19 A 4 4 1.09 18 0.222
20 A 10 9 1.00 20 0.450
21 A 10 9 1.16 20 0.450
22 A 11 10 1.10 20 0.500
23 A 10 9 1.17 18 0.500
24 A 8 7 0.97 15 0.467
25 A 9 8 0.98 20 0.400
26 A 4 4 1.00 20 0.200
27 A 4 4 1.20 20 0.200
28 A 4 4 0.99 20 0.200
29 A 4 4 1.15 20 0.200
30 A 4 4 1.08 20 0.200
31 A 8 7 1.40 25 0.280
32 A 9 8 1.09 26 0.308
33 A 9 8 1.04 33 0.242
34 A 3 3 1.00 17 0.176
35 A 3 3 1.00 22 0.136
36 A 12 11 0.96 17 0.647
37 A 4 4 1.02 22 0.182
38 A 14 13 1.12 17 0.765
39 A 13 12 0.77 22 0.545
40 A 13 12 1.15 17 0.706
41 A 6 6 0.85 22 0.273
42 A 2 2 1.00 21 0.095
43 A 2 2 1.00 21 0.095
44 A 3 3 1.00 19 0.158
45 A 2 2 1.00 21 0.095
46 A 2 2 1.00 21 0.095
47 A 3 3 1.00 20 0.150
48 A 2 2 1.00 21 0.095
49 A 2 2 1.00 21 0.095
50 A 4 4 0.99 19 0.211
51 A 2 2 1.00 21 0.095
52 A 2 2 1.00 21 0.095
53 A 2 2 1.00 21 0.095
54 A 2 2 1.00 21 0.095
55 A 5 5 1.05 19 0.263
56 A 2 2 1.00 21 0.095
57 A 2 2 1.00 21 0.095
58 A 2 2 1.00 23 0.087
59 N/A 1 0 1.00 21 0.000
60 A 2 2 1.00 21 0.095
61 A 2 2 1.00 21 0.095
62 A 2 2 1.00 19 0.105
63 A 2 2 1.00 21 0.095
64 A 2 2 1.00 21 0.095
65 A 2 2 1.00 21 0.095
66 A 2 2 1.00 22 0.091
67 A 2 2 1.00 24 0.083
68 A 2 2 1.00 24 0.083
69 A 2 2 1.00 26 0.077
70 A 2 2 1.00 26 0.077
71 A 2 2 1.00 24 0.083
72 A 2 2 1.00 26 0.077
73 A 2 2 1.00 26 0.077
74 A 2 2 1.00 26 0.077
75 A 2 2 1.00 26 0.077
76 A 2 2 1.00 26 0.077
77 A 4 4 0.86 24 0.167
78 A 2 2 1.00 26 0.077
79 A 2 2 1.00 26 0.077
80 A 2 2 1.00 26 0.077
81 A 2 2 1.00 26 0.077
82 A 6 6 1.01 24 0.250
83 A 2 2 1.00 26 0.077
84 A 2 2 1.00 26 0.077
85 A 2 2 1.00 26 0.077
86 A 2 2 1.00 26 0.077
87 A 2 2 1.00 26 0.077
88 A 2 2 1.00 26 0.077
89 A 2 2 1.00 26 0.077
90 N/A 1 0 1.00 26 0.000
91 A 2 2 1.00 26 0.077
92 A 2 2 1.00 26 0.077
93 A 2 2 1.00 24 0.083
94 N/A 1 0 1.00 26 0.000
95 N/A 1 0 1.00 26 0.000
96 N/A 1 0 1.00 26 0.000

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