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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 [26] had the largest ratio of [1.80000000000000004]

# 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 11 10 1.16 10 1.000
2 A 4 4 1.02 10 0.400
3 A 4 4 1.06 10 0.400
4 A 4 4 1.08 8 0.500
5 A 2 2 1.00 6 0.333
6 A 11 10 1.11 10 1.000
7 A 6 5 1.03 10 0.500
8 A 7 6 1.06 10 0.600
9 A 6 5 1.11 10 0.500
10 A 4 4 1.21 8 0.500
11 A 3 3 1.00 6 0.500
12 A 10 9 1.14 10 0.900
13 A 6 5 1.00 10 0.500
14 A 3 3 1.00 10 0.300
15 A 7 6 1.02 10 0.600
16 A 11 10 1.17 10 1.000
17 A 10 9 1.05 10 0.900
18 A 9 8 1.02 10 0.800
19 A 6 5 1.01 10 0.500
20 A 10 9 0.99 8 1.125
21 A 6 5 0.94 6 0.833
22 A 17 16 1.27 10 1.600
23 A 9 8 1.10 10 0.800
24 A 14 13 1.25 10 1.300
25 A 15 14 1.27 10 1.400
26 A 19 18 1.28 10 1.800
27 A 7 6 0.93 12 0.500
28 A 6 5 0.94 12 0.417
29 A 7 6 0.94 10 0.600
30 A 8 7 0.90 8 0.875
31 A 18 17 1.22 12 1.417
32 A 6 5 1.02 12 0.417
33 A 6 5 0.91 12 0.417
34 A 7 6 0.91 10 0.600
35 A 9 8 0.94 8 1.000
36 A 18 17 1.18 12 1.417
37 A 6 5 1.01 12 0.417
38 A 7 6 0.92 12 0.500
39 A 7 6 0.92 14 0.429
40 A 11 10 1.19 10 1.000
41 A 5 4 0.99 10 0.400
42 A 5 4 0.99 8 0.500
43 A 4 3 0.99 6 0.500
44 A 5 4 1.00 10 0.400
45 A 4 3 1.13 10 0.300
46 A 6 5 1.02 10 0.500
47 A 5 4 0.95 10 0.400
48 A 5 4 0.91 10 0.400
49 A 12 11 1.12 19 0.579

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