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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 [23] had the largest ratio of [1.39999999999999991]

# 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 1.16 10 0.800
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 9 8 1.11 10 0.800
7 A 6 5 0.95 10 0.500
8 A 7 6 1.06 10 0.600
9 A 8 7 1.12 10 0.700
10 A 6 5 1.11 10 0.500
11 A 4 4 1.21 8 0.500
12 A 3 3 1.00 6 0.500
13 A 8 7 1.14 10 0.700
14 A 6 5 1.00 10 0.500
15 A 3 3 1.00 10 0.300
16 A 7 6 1.02 10 0.600
17 A 9 8 1.16 10 0.800
18 A 10 9 1.05 10 0.900
19 A 9 8 1.01 10 0.800
20 A 6 5 1.00 10 0.500
21 A 10 9 1.00 8 1.125
22 A 6 5 0.95 6 0.833
23 A 15 14 1.32 10 1.400
24 A 8 7 1.04 10 0.700
25 A 13 12 1.18 10 1.200
26 A 14 13 1.23 10 1.300
27 A 7 6 0.94 12 0.500
28 A 6 5 0.94 12 0.417
29 A 7 6 0.95 10 0.600
30 A 8 7 0.95 8 0.875
31 A 16 15 1.28 12 1.250
32 A 6 5 1.02 12 0.417
33 A 6 5 0.90 12 0.417
34 A 7 6 0.91 10 0.600
35 A 9 8 0.97 8 1.000
36 A 16 15 1.23 12 1.250
37 A 6 5 1.01 12 0.417
38 A 3 2 0.93 14 0.143
39 A 3 2 0.93 16 0.125
40 A 3 2 0.93 16 0.125
41 A 7 6 0.92 14 0.429
42 A 9 8 1.18 10 0.800
43 A 5 4 0.98 10 0.400
44 A 5 4 0.98 8 0.500
45 A 4 3 0.98 6 0.500
46 A 5 4 1.00 10 0.400
47 A 4 3 1.10 10 0.300
48 A 6 5 1.02 10 0.500
49 A 5 4 0.94 10 0.400
50 A 10 9 0.99 19 0.474

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