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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 [7] had the largest ratio of [.258064999999999989]

# 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 6 6 0.99 31 0.194
2 A 4 4 1.01 31 0.129
3 A 2 2 1.07 29 0.069
4 A 6 5 1.01 31 0.161
5 A 6 5 1.03 31 0.161
6 A 6 5 1.20 31 0.161
7 A 9 8 0.89 31 0.258
8 A 7 6 0.91 31 0.194
9 A 5 4 0.92 28 0.143
10 A 5 4 0.93 31 0.129
11 A 6 5 1.01 31 0.161
12 A 5 5 0.94 29 0.172
13 A 4 4 0.95 29 0.138
14 A 3 3 0.94 29 0.103
15 A 2 2 1.00 27 0.074
16 A 2 2 1.00 26 0.077
17 A 4 3 1.00 29 0.103
18 A 2 2 1.00 29 0.069
19 A 4 3 1.00 29 0.103
20 A 2 2 1.00 29 0.069
21 A 6 5 0.95 29 0.172
22 A 8 7 0.90 31 0.226
23 A 4 4 0.93 31 0.129
24 A 6 5 0.91 31 0.161
25 A 2 2 1.00 29 0.069
26 A 4 3 1.00 28 0.107
27 A 4 3 1.00 31 0.097
28 A 4 3 1.00 31 0.097
29 A 4 3 1.00 31 0.097
30 A 2 2 1.00 31 0.065
31 A 6 5 0.93 31 0.161
32 A 8 7 0.83 31 0.226
33 A 4 4 0.84 31 0.129
34 A 7 6 1.11 31 0.194
35 A 2 2 0.96 29 0.069
36 A 4 3 1.00 28 0.107
37 A 4 3 1.00 31 0.097
38 A 2 2 0.99 31 0.065
39 A 6 5 0.90 31 0.161
40 A 4 4 0.89 31 0.129
41 A 8 7 0.88 31 0.226
42 A 4 3 1.00 31 0.097
43 A 1 1 1.00 57 0.018

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