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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 [48] had the largest ratio of [.705882000000000009]

# 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 3 3 0.99 11 0.273
2 A 3 3 1.00 15 0.200
3 A 2 2 1.00 22 0.091
4 B 2 2 2.08 17 0.118
5 A 2 2 1.95 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 20 0.100
9 A 2 2 1.00 22 0.091
10 A 14 13 1.10 22 0.591
11 A 16 15 1.12 22 0.682
12 A 2 2 1.00 23 0.087
13 A 2 2 1.00 23 0.087
14 A 2 2 1.00 21 0.095
15 A 2 2 1.00 23 0.087
16 A 12 11 0.86 23 0.478
17 A 14 13 0.88 23 0.565
18 A 2 2 1.00 22 0.091
19 A 2 2 1.00 22 0.091
20 A 2 2 1.00 20 0.100
21 A 13 12 1.08 22 0.545
22 A 13 12 1.08 22 0.545
23 A 13 12 1.07 22 0.545
24 A 2 2 1.00 23 0.087
25 A 2 2 1.00 23 0.087
26 A 2 2 1.00 21 0.095
27 A 13 12 0.97 23 0.522
28 A 12 11 0.96 23 0.478
29 A 12 11 0.97 23 0.478
30 A 2 2 1.00 35 0.057
31 A 2 2 1.00 35 0.057
32 A 2 2 1.00 22 0.091
33 A 4 3 1.00 25 0.120
34 A 3 3 1.00 15 0.200
35 A 3 3 1.00 15 0.200
36 A 3 3 1.00 20 0.150
37 A 3 3 1.00 20 0.150
38 A 10 9 1.10 17 0.529
39 A 3 3 1.00 25 0.120
40 A 3 3 1.00 35 0.086
41 A 3 3 1.00 35 0.086
42 A 3 3 1.11 22 0.136
43 A 3 3 1.00 25 0.120
44 A 3 3 1.00 15 0.200
45 A 3 3 1.00 15 0.200
46 A 3 3 1.00 20 0.150
47 A 3 3 1.00 20 0.150
48 A 13 12 1.22 17 0.706
49 A 3 3 1.00 25 0.120
50 C 2 2 5.78 28 0.071
51 C 2 2 4.19 28 0.071
52 C 6 6 2.50 27 0.222
53 A 3 3 1.00 17 0.176
54 A 4 4 0.99 19 0.211
55 A 4 4 1.00 19 0.211
56 A 3 3 1.13 17 0.176
57 A 1 1 1.00 9 0.111
58 A 3 3 1.00 19 0.158
59 A 3 3 1.00 19 0.158
60 A 3 3 1.00 19 0.158
61 A 2 2 1.00 26 0.077
62 A 2 2 1.20 26 0.077
63 A 2 2 1.12 26 0.077
64 A 2 2 1.00 35 0.057
65 A 4 4 1.02 35 0.114
66 A 6 6 1.01 35 0.171
67 A 2 2 1.00 9 0.222
68 A 3 3 1.00 17 0.176
69 A 4 4 1.03 24 0.167
70 A 2 2 0.62 31 0.065

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