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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 [3] had the largest ratio of [.526316000000000006]

# 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 F 0 0 N/A 0.000 N/A
3 A 21 20 1.66 38 0.526
4 A 12 11 1.06 38 0.289
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 F 0 0 N/A 0.000 N/A
9 F 0 0 N/A 0.000 N/A
10 B 19 18 2.26 38 0.474
11 A 13 12 1.62 38 0.316
12 F 0 0 N/A 0.000 N/A
13 F 0 0 N/A 0.000 N/A
14 F 0 0 N/A 0.000 N/A
15 A 7 6 1.24 41 0.146
16 A 7 6 1.31 34 0.176
17 A 8 7 0.82 43 0.163
18 A 8 7 0.96 41 0.171
19 A 10 9 0.82 43 0.209
20 A 3 3 0.77 43 0.070
21 A 3 3 0.90 43 0.070
22 A 3 3 0.88 43 0.070
23 A 3 3 1.01 43 0.070
24 A 3 3 1.07 40 0.075
25 A 3 3 1.33 43 0.070
26 A 9 8 1.42 41 0.195
27 A 10 9 1.32 46 0.196
28 A 16 15 1.63 46 0.326
29 A 20 19 1.57 46 0.413
30 A 12 11 1.33 51 0.216
31 A 17 16 1.48 51 0.314
32 A 2 2 1.48 39 0.051
33 A 6 5 1.05 38 0.132
34 A 2 2 1.45 47 0.043
35 A 6 5 1.05 63 0.079
36 A 3 3 1.28 78 0.038
37 A 3 3 1.45 78 0.038
38 A 10 9 1.09 34 0.265
39 A 13 12 1.05 39 0.308
40 A 15 14 1.06 44 0.318
41 B 9 8 2.52 33 0.242
42 B 11 10 2.18 38 0.263
43 B 12 11 2.07 43 0.256
44 F 0 0 N/A 0.000 N/A
45 F 0 0 N/A 0.000 N/A
46 F 0 0 N/A 0.000 N/A
47 F 0 0 N/A 0.000 N/A
48 F 0 0 N/A 0.000 N/A
49 F 0 0 N/A 0.000 N/A
50 F 0 0 N/A 0.000 N/A

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