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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 [15] had the largest ratio of [.750000000000000000]

# 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 16 0.125
2 N/A 2 0 1.00 16 0.000
3 A 2 2 1.00 16 0.125
4 N/A 2 0 1.00 16 0.000
5 A 2 2 1.00 14 0.143
6 N/A 2 0 1.00 16 0.000
7 N/A 2 0 1.00 16 0.000
8 A 5 4 1.00 18 0.222
9 N/A 1 0 1.00 18 0.000
10 A 5 4 0.99 18 0.222
11 N/A 1 0 1.00 18 0.000
12 A 8 7 0.98 16 0.438
13 N/A 1 0 1.00 18 0.000
14 N/A 1 0 1.00 18 0.000
15 A 10 9 1.16 12 0.750
16 A 5 4 1.00 18 0.222
17 N/A 1 0 1.00 18 0.000
18 A 5 4 0.98 18 0.222
19 N/A 1 0 1.00 18 0.000
20 A 8 7 1.17 16 0.438
21 N/A 1 0 1.00 18 0.000
22 N/A 2 0 1.00 16 0.000
23 A 5 4 1.00 18 0.222
24 N/A 1 0 1.00 18 0.000
25 A 5 4 0.99 18 0.222
26 N/A 1 0 1.00 18 0.000
27 A 13 12 1.28 16 0.750
28 N/A 1 0 1.00 18 0.000
29 N/A 1 0 1.00 18 0.000
30 N/A 1 0 1.00 18 0.000
31 A 2 2 1.00 18 0.111
32 A 2 2 1.00 18 0.111
33 A 2 2 1.00 16 0.125
34 N/A 2 0 1.00 18 0.000
35 N/A 2 0 1.00 18 0.000
36 A 5 4 1.01 20 0.200
37 A 5 4 1.01 20 0.200
38 A 5 4 1.01 18 0.222
39 N/A 1 0 1.00 20 0.000
40 N/A 1 0 1.00 20 0.000
41 A 5 4 1.00 20 0.200
42 A 5 4 1.00 20 0.200
43 A 5 4 1.00 18 0.222
44 N/A 1 0 1.00 20 0.000
45 N/A 2 0 1.00 18 0.000
46 A 5 4 1.00 20 0.200
47 A 5 4 1.00 20 0.200
48 A 5 4 1.00 18 0.222
49 N/A 1 0 1.00 20 0.000
50 N/A 1 0 1.00 20 0.000
51 A 2 2 1.00 20 0.100
52 A 2 2 1.00 20 0.100
53 A 2 2 1.00 20 0.100
54 N/A 2 0 1.00 20 0.000
55 N/A 2 0 1.00 20 0.000
56 A 5 4 1.00 22 0.182
57 A 5 4 1.01 22 0.182
58 A 8 7 1.02 22 0.318
59 N/A 1 0 1.00 22 0.000
60 N/A 1 0 1.00 22 0.000
61 A 6 5 1.25 14 0.357
62 A 5 4 1.00 22 0.182
63 A 5 4 1.00 22 0.182
64 A 8 7 1.15 22 0.318
65 N/A 1 0 1.00 22 0.000
66 N/A 1 0 1.00 22 0.000
67 A 5 4 1.00 22 0.182
68 A 5 4 1.00 22 0.182
69 A 13 12 1.28 22 0.545
70 N/A 1 0 1.00 22 0.000
71 N/A 1 0 1.00 22 0.000
72 N/A 2 0 1.00 20 0.000
73 A 2 2 1.00 20 0.100
74 A 2 2 1.00 22 0.091
75 A 2 2 1.00 22 0.091
76 A 9 8 0.71 22 0.364
77 A 6 5 0.66 24 0.208
78 A 6 5 0.66 24 0.208
79 A 9 8 1.02 22 0.364
80 A 6 5 0.84 24 0.208
81 A 6 5 0.84 24 0.208
82 A 14 13 1.07 22 0.591
83 A 6 5 0.80 24 0.208
84 A 6 5 0.81 24 0.208

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