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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 [11] had the largest ratio of [29]

# 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 8 7 1.00 5 1.400
2 A 2 2 1.00 15 0.133
3 F 0 0 N/A 0. N/A
4 B 32 13 3.42 14 0.929
5 C 5 4 6.42 19 0.210
6 A 7 7 1.00 13 0.538
7 A 4 4 1.00 13 0.308
8 A 9 7 1.00 14 0.500
9 A 7 7 1.00 12 0.583
10 A 5 5 1.41 19 0.263
11 A 7 8 1.00 29 0.276
12 C 40 15 1.91 14 1.071
13 C 32 16 1.88 27 0.593
14 A 9 11 1.13 18 0.611
15 A 3 4 1.00 24 0.167
16 A 3 4 1.00 12 0.333
17 A 3 4 1.00 22 0.182
18 A 4 4 1.00 15 0.267
19 A 4 4 1.00 13 0.308
20 A 2 3 1.00 23 0.130
21 A 5 6 1.00 17 0.353
22 A 7 8 1.34 15 0.533
23 A 4 9 1.00 25 0.360
24 A 5 5 1.00 27 0.185
25 A 2 3 1.00 23 0.130
26 A 18 11 1.00 27 0.407
27 A 3 3 1.00 17 0.176
28 A 2 2 1.00 13 0.154
29 A 7 6 1.00 17 0.353
30 A 5 5 1.00 15 0.333
31 A 4 4 1.00 15 0.267
32 A 2 2 1.00 17 0.118
33 A 5 5 1.00 13 0.385
34 A 3 3 1.00 15 0.200
35 A 2 2 1.00 13 0.154
36 A 5 5 1.00 13 0.385
37 A 2 2 1.00 11 0.182
38 A 2 2 1.00 24 0.083
39 A 2 2 1.00 24 0.083
40 A 4 5 1.00 10 0.500
41 A 6 7 1.00 12 0.583
42 B 5 5 2.11 13 0.385
43 A 4 4 1.00 13 0.308
44 A 4 4 1.28 15 0.267
45 F 0 0 N/A 0. N/A
46 A 13 10 1.00 12 0.833
47 A 12 8 1.00 12 0.667
48 A 6 6 1.19 18 0.333
49 A 4 4 1.00 14 0.286
50 A 6 6 1.00 14 0.429

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