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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 [4] had the largest ratio of [.458332999999999990]

# 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 F 0 0 N/A 0.000 N/A
2 A 14 13 1.04 33 0.394
3 A 14 13 1.11 31 0.419
4 A 12 11 1.11 24 0.458
5 F 0 0 N/A 0.000 N/A
6 F 0 0 N/A 0.000 N/A
7 F 0 0 N/A 0.000 N/A
8 A 5 4 0.97 33 0.121
9 A 5 4 0.97 33 0.121
10 A 5 4 0.98 33 0.121
11 A 10 9 0.99 33 0.273
12 A 7 6 0.99 31 0.194
13 A 6 5 0.99 24 0.208
14 A 5 4 0.99 31 0.129
15 A 5 4 0.98 33 0.121
16 A 5 4 0.97 33 0.121
17 A 5 4 0.97 33 0.121
18 A 5 4 0.98 33 0.121
19 A 5 4 0.99 33 0.121
20 A 8 7 1.13 33 0.212
21 A 10 9 1.13 31 0.290
22 A 5 4 0.99 31 0.129
23 A 5 4 0.98 33 0.121
24 A 5 4 0.98 33 0.121
25 A 13 12 1.03 35 0.343
26 A 11 10 1.01 35 0.286
27 A 11 10 0.97 33 0.303
28 A 12 11 0.95 33 0.333
29 A 6 5 0.94 35 0.143
30 A 13 12 1.02 35 0.343
31 A 11 10 1.05 26 0.385
32 A 13 12 1.04 35 0.343
33 A 17 16 1.13 35 0.457
34 A 11 10 0.99 35 0.286
35 A 9 8 0.96 35 0.229
36 A 6 5 1.00 33 0.152
37 A 6 5 0.97 33 0.152
38 A 6 5 0.94 35 0.143
39 A 8 7 1.02 35 0.200
40 A 7 6 1.03 35 0.171
41 A 7 6 1.02 26 0.231
42 A 12 11 1.03 35 0.314
43 A 12 11 1.00 35 0.314
44 A 8 7 1.00 35 0.200
45 A 8 7 0.99 35 0.200
46 A 8 7 1.00 33 0.212
47 A 6 5 0.97 33 0.152
48 A 6 5 0.95 35 0.143
49 A 14 13 1.03 35 0.371

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