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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 [1] had the largest ratio of [25]

# 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 15 12 1.00 25 0.480
2 A 3 2 1.00 12 0.167
3 A 4 3 1.00 14 0.214
4 A 4 3 1.00 14 0.214
5 A 3 3 1.00 14 0.214
6 A 5 5 1.00 14 0.357
7 A 6 6 1.00 14 0.429
8 A 4 4 1.00 10 0.400
9 A 3 3 1.00 10 0.300
10 A 3 3 1.00 10 0.300
11 A 5 5 1.00 12 0.417
12 A 4 4 1.00 12 0.333
13 A 3 3 1.00 12 0.250
14 A 4 3 1.00 17 0.176
15 A 5 5 1.00 17 0.294
16 A 3 3 1.00 15 0.200
17 A 5 5 1.00 15 0.333
18 A 5 4 1.00 17 0.235
19 A 6 6 1.00 17 0.353
20 A 5 5 1.00 15 0.333
21 A 7 5 1.00 15 0.333
22 A 7 7 1.00 17 0.412
23 A 6 6 1.00 12 0.500
24 A 5 5 1.00 17 0.294
25 A 6 6 1.00 17 0.353
26 A 7 6 1.00 17 0.353
27 A 8 8 1.00 17 0.471
28 A 6 5 1.00 15 0.333
29 A 8 6 1.00 15 0.400
30 A 7 7 1.00 17 0.412
31 A 8 8 1.00 16 0.500
32 A 7 7 1.00 16 0.438
33 A 6 6 1.00 16 0.375
34 A 3 3 1.00 16 0.188
35 A 4 4 1.00 16 0.250
36 A 6 6 1.00 16 0.375
37 A 7 6 1.00 16 0.375
38 A 6 6 1.00 12 0.500
39 A 5 5 1.00 12 0.417
40 A 3 3 1.00 12 0.250
41 A 7 6 1.00 10 0.600
42 A 6 5 1.00 10 0.500
43 A 3 3 1.00 10 0.300
44 A 5 5 1.00 17 0.294
45 A 6 6 1.00 17 0.353
46 A 4 4 1.00 15 0.267
47 A 7 5 1.00 15 0.333
48 A 5 5 1.00 17 0.294
49 A 5 5 1.00 17 0.294
50 A 4 4 1.00 17 0.235
51 A 5 5 1.00 15 0.333
52 A 8 6 1.00 15 0.400
53 A 6 6 1.00 17 0.353
54 A 6 6 1.00 17 0.353
55 A 6 6 1.00 17 0.353
56 A 6 5 1.00 15 0.333
57 A 9 7 1.00 15 0.467
58 A 7 7 1.00 17 0.412
59 A 7 6 1.00 8 0.750
60 A 8 7 1.00 15 0.467
61 A 9 8 1.00 15 0.533
62 A 4 4 1.00 15 0.267
63 A 6 6 1.00 15 0.400
64 A 7 7 1.00 15 0.467

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