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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 [70] had the largest ratio of [.750000000000000000]

# 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 5 4 0.81 12 0.333
2 A 5 4 0.80 14 0.286
3 N/A 1 0 1.00 40 0.000
4 A 7 6 1.00 40 0.150
5 A 6 5 1.01 40 0.125
6 A 4 3 0.95 38 0.079
7 N/A 1 0 1.00 40 0.000
8 N/A 1 0 1.00 40 0.000
9 A 3 2 1.00 7 0.286
10 A 7 6 1.29 15 0.400
11 A 6 5 1.30 13 0.385
12 A 5 4 1.40 11 0.364
13 N/A 1 0 1.00 15 0.000
14 A 8 7 1.29 21 0.333
15 A 7 6 1.26 19 0.316
16 A 6 5 1.26 17 0.294
17 N/A 1 0 1.00 21 0.000
18 A 9 8 1.28 22 0.364
19 A 8 7 1.26 20 0.350
20 A 7 6 1.26 18 0.333
21 N/A 1 0 1.00 22 0.000
22 A 3 2 1.00 7 0.286
23 A 7 6 1.29 15 0.400
24 A 6 5 1.30 13 0.385
25 A 5 4 1.40 11 0.364
26 N/A 1 0 1.00 15 0.000
27 A 9 8 1.29 21 0.381
28 A 8 7 1.26 19 0.368
29 A 7 6 1.26 17 0.353
30 N/A 1 0 1.00 21 0.000
31 A 8 7 1.28 22 0.318
32 A 7 6 1.26 20 0.300
33 A 6 5 1.26 18 0.278
34 N/A 1 0 1.00 22 0.000
35 A 9 8 1.09 15 0.533
36 A 8 7 1.10 15 0.467
37 A 7 6 1.10 13 0.462
38 A 6 5 1.08 7 0.714
39 N/A 1 0 1.00 15 0.000
40 A 7 6 1.24 15 0.400
41 A 6 5 1.28 13 0.385
42 A 5 4 1.36 11 0.364
43 N/A 1 0 1.00 15 0.000
44 A 9 8 1.18 19 0.421
45 A 8 7 1.17 17 0.412
46 A 7 6 1.18 15 0.400
47 N/A 1 0 1.00 19 0.000
48 A 8 7 1.17 22 0.318
49 A 7 6 1.17 20 0.300
50 A 6 5 1.16 18 0.278
51 N/A 1 0 1.00 22 0.000
52 A 9 8 1.09 15 0.533
53 A 8 7 1.10 15 0.467
54 A 7 6 1.10 13 0.462
55 A 6 5 1.08 7 0.714
56 N/A 1 0 1.00 15 0.000
57 A 7 6 1.25 15 0.400
58 A 6 5 1.28 13 0.385
59 A 5 4 1.36 11 0.364
60 N/A 1 0 1.00 15 0.000
61 A 9 8 1.18 19 0.421
62 A 8 7 1.18 17 0.412
63 A 7 6 1.18 15 0.400
64 N/A 1 0 1.00 19 0.000
65 A 8 7 1.17 22 0.318
66 A 7 6 1.16 20 0.300
67 A 6 5 1.16 18 0.278
68 N/A 1 0 1.00 22 0.000
69 A 2 2 1.00 24 0.083
70 A 4 3 1.00 4 0.750
71 A 5 4 0.89 6 0.667
72 A 6 5 1.02 8 0.625
73 A 4 3 0.96 8 0.375
74 A 5 4 0.94 10 0.400
75 A 6 5 1.05 12 0.417
76 A 9 8 0.90 12 0.667
77 A 7 7 1.94 14 0.500
78 A 7 7 1.98 16 0.438
79 A 7 6 1.22 10 0.600
80 A 1 1 1.00 19 0.053
81 A 6 5 0.94 20 0.250
82 A 8 7 1.01 20 0.350
83 A 13 12 1.30 20 0.600
84 A 13 12 1.31 20 0.600
85 A 9 8 1.01 20 0.400
86 A 7 6 0.96 20 0.300

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