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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 [8] had the largest ratio of [31]

# 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 2 1 1.00 29 0.034
2 A 2 1 1.00 29 0.034
3 A 2 1 1.00 27 0.037
4 A 2 1 1.00 20 0.050
5 A 3 2 1.00 29 0.069
6 A 3 3 1.00 29 0.103
7 A 3 3 1.00 29 0.103
8 A 2 1 1.00 31 0.032
9 A 2 1 1.00 31 0.032
10 A 2 1 1.00 29 0.034
11 A 2 1 1.00 22 0.045
12 A 3 2 1.00 31 0.065
13 A 4 3 1.00 31 0.097
14 A 4 3 1.00 31 0.097
15 A 2 1 1.00 31 0.032
16 A 2 1 1.00 31 0.032
17 A 2 1 1.00 29 0.034
18 A 2 1 1.00 22 0.045
19 A 3 2 1.00 31 0.065
20 A 4 3 1.00 31 0.097
21 A 5 3 1.00 31 0.097
22 A 3 2 1.00 31 0.065
23 A 3 2 1.00 31 0.065
24 A 3 2 1.00 31 0.065
25 A 3 2 1.00 29 0.069
26 A 2 2 1.00 22 0.091
27 A 4 2 1.00 31 0.065
28 A 5 3 1.00 31 0.097
29 A 6 3 1.00 31 0.097
30 A 4 3 1.00 31 0.097
31 A 4 3 1.00 31 0.097
32 A 3 3 1.00 29 0.103
33 A 2 2 1.00 22 0.091
34 A 5 3 1.00 31 0.097
35 A 6 3 1.00 31 0.097
36 A 7 3 1.00 31 0.097
37 A 5 3 1.00 31 0.097
38 A 4 3 1.00 31 0.097
39 A 3 3 1.00 29 0.103
40 A 2 2 1.00 22 0.091
41 A 6 3 1.00 31 0.097
42 A 7 3 1.00 31 0.097
43 A 8 3 1.00 31 0.097
44 A 6 4 0.99 31 0.129
45 A 5 4 0.94 31 0.129
46 A 4 4 0.94 29 0.138
47 A 6 5 1.00 31 0.161
48 A 7 6 1.00 31 0.194
49 A 8 6 1.00 31 0.194
50 A 5 5 1.00 29 0.172
51 A 5 5 1.00 29 0.172

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