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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 [46] had the largest ratio of [55]

# 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 3 1.00 29 0.103
2 A 10 3 1.00 29 0.103
3 A 8 3 1.00 27 0.111
4 A 6 3 1.00 20 0.150
5 A 5 4 1.00 29 0.138
6 A 3 3 1.00 29 0.103
7 A 3 3 1.00 29 0.103
8 A 14 3 1.00 31 0.097
9 A 12 3 1.00 31 0.097
10 A 10 3 1.00 29 0.103
11 A 8 3 1.00 22 0.136
12 A 7 4 1.00 31 0.129
13 A 6 5 1.00 31 0.161
14 A 4 3 1.00 31 0.097
15 A 16 3 1.00 31 0.097
16 A 14 3 1.00 31 0.097
17 A 12 3 1.00 29 0.103
18 A 10 3 1.00 22 0.136
19 A 9 4 1.00 31 0.129
20 A 8 5 0.99 31 0.161
21 A 11 4 1.00 31 0.129
22 A 9 4 1.00 31 0.129
23 A 7 4 1.00 31 0.129
24 A 5 4 1.00 29 0.138
25 A 2 2 1.00 22 0.091
26 A 4 2 1.00 31 0.065
27 A 5 3 1.00 31 0.097
28 A 6 3 1.00 31 0.097
29 A 8 5 0.99 31 0.161
30 A 6 5 1.00 31 0.161
31 A 3 3 1.00 29 0.103
32 A 2 2 1.00 22 0.091
33 A 5 3 1.00 31 0.097
34 A 6 3 1.00 31 0.097
35 A 7 3 1.00 31 0.097
36 A 4 3 1.00 31 0.097
37 A 3 3 1.00 29 0.103
38 A 2 2 1.00 22 0.091
39 A 6 3 1.00 31 0.097
40 A 7 3 1.00 31 0.097
41 A 7 3 1.00 31 0.097
42 A 4 4 0.94 29 0.138
43 A 6 5 1.00 31 0.161
44 A 7 6 1.00 31 0.194
45 A 4 4 1.00 47 0.085
46 A 4 4 1.20 55 0.073

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