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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 [11] had the largest ratio of [1.75000000000000000]

# 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 9 8 1.48 10 0.800
2 A 8 7 1.46 10 0.700
3 A 7 6 1.30 8 0.750
4 N/A 3 0 1.00 10 0.000
5 N/A 3 0 1.00 10 0.000
6 A 12 11 1.39 12 0.917
7 A 11 10 1.30 12 0.833
8 A 7 7 1.06 10 0.700
9 N/A 2 0 1.00 12 0.000
10 N/A 2 0 1.00 12 0.000
11 A 22 21 1.34 12 1.750
12 A 18 17 1.29 12 1.417
13 A 13 12 1.18 10 1.200
14 N/A 3 0 1.00 12 0.000
15 N/A 3 0 1.00 12 0.000
16 A 9 9 1.09 23 0.391
17 A 7 7 1.07 23 0.304
18 A 5 5 1.07 21 0.238
19 A 8 8 0.94 23 0.348
20 A 8 8 1.00 23 0.348
21 A 10 10 0.99 23 0.435
22 A 3 3 1.00 23 0.130
23 A 3 3 1.00 23 0.130
24 A 3 3 1.00 21 0.143
25 A 3 3 1.00 23 0.130
26 A 3 3 1.00 23 0.130
27 A 3 3 1.00 23 0.130
28 A 3 3 1.00 23 0.130
29 A 3 3 1.00 21 0.143
30 A 3 3 1.00 23 0.130
31 A 3 3 1.00 23 0.130
32 N/A 2 0 1.00 23 0.000
33 N/A 2 0 1.00 21 0.000
34 A 3 3 1.00 23 0.130
35 A 3 3 1.00 23 0.130
36 A 3 3 1.00 23 0.130
37 A 3 3 1.00 18 0.167
38 A 3 3 1.00 18 0.167
39 A 3 3 1.00 16 0.188
40 N/A 2 0 1.00 18 0.000
41 N/A 2 0 1.00 18 0.000
42 A 3 3 1.00 20 0.150
43 A 3 3 1.00 20 0.150
44 A 3 3 0.99 18 0.167
45 N/A 2 0 1.00 20 0.000
46 N/A 2 0 1.00 20 0.000
47 A 3 3 1.00 20 0.150
48 A 3 3 0.98 20 0.150
49 A 3 3 0.99 18 0.167
50 N/A 2 0 1.00 20 0.000
51 N/A 2 0 1.00 20 0.000
52 A 9 8 1.01 20 0.400
53 A 8 7 1.03 20 0.350
54 A 7 6 1.05 18 0.333
55 N/A 2 0 1.00 20 0.000
56 N/A 2 0 1.00 20 0.000
57 A 3 3 1.00 20 0.150
58 A 3 3 1.00 20 0.150
59 A 10 9 1.07 18 0.500
60 N/A 2 0 1.00 20 0.000
61 N/A 2 0 1.00 20 0.000

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