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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [38] had the largest ratio of [.5882]

Table 2.1:Rubi specific breakdown of results for each integral
# 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 12 8 1.00 17 0.471
2 A 13 7 1.00 18 0.389
3 A 19 6 1.00 17 0.353
4 A 13 10 1.00 18 0.556
5 A 19 6 1.00 26 0.231
6 A 19 6 1.00 26 0.231
7 A 7 4 1.00 27 0.148
8 A 19 6 1.00 27 0.222
9 A 19 6 1.00 18 0.333
10 A 19 7 1.00 18 0.389
11 A 10 7 1.00 18 0.389
12 A 19 6 1.00 16 0.375
13 A 19 6 1.00 13 0.462
14 A 19 6 1.00 18 0.333
15 A 5 5 1.00 18 0.278
16 A 7 4 1.00 18 0.222
17 A 7 4 1.00 18 0.222
18 A 7 4 1.00 18 0.222
19 A 7 4 1.00 18 0.222
20 A 19 6 1.00 20 0.300
21 A 19 7 1.00 20 0.350
22 A 11 8 1.00 20 0.400
23 A 19 6 1.00 18 0.333
24 A 19 6 1.00 15 0.400
25 A 19 6 1.00 20 0.300
26 A 5 5 1.00 20 0.250
27 A 7 4 1.00 20 0.200
28 A 7 4 1.00 20 0.200
29 A 7 4 1.00 20 0.200
30 A 7 4 1.00 20 0.200
31 A 9 6 1.00 25 0.240
32 A 9 6 1.00 26 0.231
33 A 9 6 1.00 33 0.182
34 A 5 5 1.00 17 0.294
35 A 6 6 1.00 22 0.273
36 A 11 8 1.00 17 0.471
37 A 5 4 1.00 22 0.182
38 A 14 10 1.00 17 0.588
39 A 15 9 1.00 22 0.409
40 A 21 8 1.00 17 0.471
41 A 9 6 1.00 22 0.273
42 A 2 1 1.00 22 0.045
43 A 2 1 1.00 24 0.042
44 A 2 1 1.00 24 0.042

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