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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 [50] had the largest ratio of [1.28570999999999991]

# 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 8 1.07 14 0.571
2 A 6 6 1.04 14 0.429
3 A 4 4 1.00 14 0.286
4 A 2 2 1.00 14 0.143
5 A 4 3 1.00 14 0.214
6 A 6 5 1.00 14 0.357
7 A 8 7 1.05 14 0.500
8 A 4 4 1.00 14 0.286
9 A 4 4 1.00 14 0.286
10 A 4 4 1.00 14 0.286
11 A 4 4 1.00 14 0.286
12 A 4 4 1.00 14 0.286
13 A 4 4 1.00 14 0.286
14 A 4 4 1.00 12 0.333
15 A 4 4 1.00 13 0.308
16 A 2 2 1.00 12 0.167
17 A 2 2 1.00 12 0.167
18 A 2 2 1.00 12 0.167
19 A 5 5 1.09 12 0.417
20 A 8 8 1.12 12 0.667
21 A 11 11 1.14 12 0.917
22 A 2 2 1.00 12 0.167
23 A 5 5 1.09 12 0.417
24 A 8 8 1.12 12 0.667
25 A 11 11 1.14 12 0.917
26 A 2 2 1.00 12 0.167
27 A 5 5 1.09 12 0.417
28 A 7 7 1.12 12 0.583
29 A 11 11 1.14 12 0.917
30 A 2 2 1.00 12 0.167
31 A 5 5 1.09 12 0.417
32 A 7 7 1.12 12 0.583
33 A 11 11 1.14 12 0.917
34 A 5 4 0.67 12 0.333
35 A 8 7 0.80 12 0.583
36 A 11 10 0.88 12 0.833
37 A 14 13 0.94 12 1.083
38 A 5 4 0.68 12 0.333
39 A 8 7 0.80 12 0.583
40 A 11 10 0.89 12 0.833
41 A 14 13 0.94 12 1.083
42 A 5 4 0.68 12 0.333
43 A 8 7 0.80 12 0.583
44 A 10 9 0.89 12 0.750
45 A 14 13 0.94 12 1.083
46 A 5 4 0.67 12 0.333
47 A 8 7 0.80 12 0.583
48 A 10 9 0.88 12 0.750
49 A 14 13 0.94 12 1.083
50 A 18 18 1.04 14 1.286
51 A 15 15 1.03 14 1.071
52 A 12 12 1.01 14 0.857
53 A 4 4 1.00 14 0.286
54 A 4 4 1.00 14 0.286
55 A 7 7 1.00 14 0.500
56 A 15 15 1.04 14 1.071
57 A 18 18 1.09 14 1.286
58 A 5 4 1.00 14 0.286
59 A 5 4 1.00 14 0.286
60 A 5 4 1.00 14 0.286
61 A 5 4 1.00 14 0.286
62 A 5 4 1.00 14 0.286
63 A 5 4 1.00 14 0.286
64 A 5 4 1.00 12 0.333
65 A 4 3 1.00 12 0.250
66 A 4 3 1.00 12 0.250
67 A 4 3 1.00 12 0.250
68 A 4 3 1.00 12 0.250
69 A 4 3 1.00 12 0.250
70 A 4 3 1.00 12 0.250
71 A 5 4 1.00 12 0.333
72 A 6 5 1.00 12 0.417

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