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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 [13] had the largest ratio of [.800000000000000044]

# 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 10 9 1.20 18 0.500
2 A 10 9 0.89 20 0.450
3 A 9 8 0.88 20 0.400
4 A 8 7 0.92 18 0.389
5 A 8 7 1.01 17 0.412
6 A 8 7 1.07 20 0.350
7 A 8 7 1.04 20 0.350
8 A 5 4 1.00 20 0.200
9 A 5 4 1.00 20 0.200
10 A 5 4 1.00 20 0.200
11 A 5 4 1.00 20 0.200
12 A 5 4 1.00 20 0.200
13 A 17 16 1.06 20 0.800
14 A 15 14 1.05 20 0.700
15 A 13 12 1.04 20 0.600
16 A 11 10 1.02 20 0.500
17 A 9 8 0.99 20 0.400
18 A 13 12 1.05 20 0.600
19 A 12 11 1.00 18 0.611
20 A 13 12 0.98 17 0.706
21 A 11 10 1.04 20 0.500
22 A 11 10 1.06 20 0.500
23 A 8 7 1.04 20 0.350
24 A 9 8 1.05 20 0.400
25 A 12 11 1.10 20 0.550
26 A 14 13 1.10 20 0.650
27 A 15 14 1.12 20 0.700
28 A 2 2 0.96 36 0.056
29 A 2 2 0.97 38 0.053
30 A 2 2 0.75 58 0.034
31 A 2 2 0.98 30 0.067
32 A 2 2 0.97 36 0.056
33 A 1 1 1.00 46 0.022
34 A 11 10 1.00 24 0.417
35 A 1 1 1.00 48 0.021
36 A 1 1 1.00 45 0.022
37 A 1 1 1.00 69 0.014
38 A 1 1 1.00 86 0.012

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