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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 [14]

# 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 4 2 1.00 14 0.143
2 A 3 2 1.00 14 0.143
3 A 2 2 1.00 14 0.143
4 A 1 1 1.00 14 0.071
5 A 2 2 1.00 14 0.143
6 A 3 3 1.00 14 0.214
7 A 4 3 1.00 14 0.214
8 A 2 2 1.00 14 0.143
9 A 2 2 1.00 14 0.143
10 A 2 2 1.00 14 0.143
11 A 2 2 1.00 14 0.143
12 A 2 2 1.00 14 0.143
13 A 2 2 1.00 14 0.143
14 A 2 2 1.00 12 0.167
15 A 2 2 1.00 13 0.154
16 A 1 1 1.00 12 0.083
17 A 1 1 1.00 12 0.083
18 A 1 1 1.00 12 0.083
19 A 3 3 1.00 12 0.250
20 A 4 4 1.00 12 0.333
21 A 5 4 1.00 12 0.333
22 A 1 1 1.00 12 0.083
23 A 3 3 1.00 12 0.250
24 A 4 4 1.00 12 0.333
25 A 5 4 1.00 12 0.333
26 A 1 1 1.00 12 0.083
27 A 3 3 1.00 12 0.250
28 A 4 4 1.00 12 0.333
29 A 5 4 1.00 12 0.333
30 A 1 1 1.00 12 0.083
31 A 3 3 1.00 12 0.250
32 A 4 4 1.00 12 0.333
33 A 5 4 1.00 12 0.333
34 A 2 2 1.00 12 0.167
35 A 4 4 1.00 12 0.333
36 A 5 5 1.00 12 0.417
37 A 6 5 1.00 12 0.417
38 A 2 2 1.00 12 0.167
39 A 4 4 1.00 12 0.333
40 A 5 5 1.00 12 0.417
41 A 6 5 1.00 12 0.417
42 A 2 2 1.00 12 0.167
43 A 4 4 1.00 12 0.333
44 A 5 5 1.00 12 0.417
45 A 6 5 1.00 12 0.417
46 A 2 2 1.00 12 0.167
47 A 4 4 1.00 12 0.333
48 A 5 5 1.00 12 0.417
49 A 6 5 1.00 12 0.417
50 A 7 7 1.00 14 0.500
51 A 6 6 1.00 14 0.429
52 A 2 2 1.00 14 0.143
53 A 2 2 1.00 14 0.143
54 A 4 4 1.00 14 0.286
55 A 7 7 1.00 14 0.500
56 A 3 3 1.00 14 0.214
57 A 3 3 1.00 14 0.214
58 A 3 3 1.00 14 0.214
59 A 3 3 1.00 14 0.214
60 A 3 3 1.00 14 0.214
61 A 3 3 1.00 14 0.214
62 A 3 3 1.00 12 0.250

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