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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 [37] had the largest ratio of [1.12500000000000000]

# 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 7 7 0.90 16 0.438
2 A 7 7 1.00 16 0.438
3 A 4 4 1.00 16 0.250
4 C 7 6 1.26 16 0.375
5 C 8 7 1.17 16 0.438
6 A 6 5 1.00 15 0.333
7 A 6 5 1.00 15 0.333
8 A 6 5 1.00 15 0.333
9 A 5 4 1.00 13 0.308
10 A 7 6 1.00 13 0.462
11 A 8 7 1.26 15 0.467
12 A 9 8 1.33 15 0.533
13 A 11 10 1.34 15 0.667
14 A 8 7 1.29 15 0.467
15 A 7 6 1.05 15 0.400
16 A 4 3 1.00 10 0.300
17 A 5 4 1.00 15 0.267
18 A 6 5 1.00 15 0.333
19 A 11 10 1.02 13 0.769
20 A 5 4 1.00 15 0.267
21 A 9 8 1.36 15 0.533
22 A 5 4 1.00 15 0.267
23 A 7 6 1.29 15 0.400
24 A 5 4 1.00 15 0.267
25 A 6 5 1.00 15 0.333
26 A 4 3 1.00 13 0.231
27 A 4 3 1.00 10 0.300
28 A 6 5 1.00 13 0.385
29 A 5 4 1.00 15 0.267
30 A 8 7 1.20 15 0.467
31 A 5 4 1.00 15 0.267
32 A 10 9 1.26 15 0.600
33 A 8 7 1.00 10 0.700
34 A 10 9 1.12 10 0.900
35 A 4 3 1.00 8 0.375
36 A 7 6 1.00 8 0.750
37 A 10 9 1.10 8 1.125
38 A 8 7 1.00 10 0.700
39 C 6 5 1.91 10 0.500
40 C 8 7 1.63 10 0.700
41 A 4 4 1.00 12 0.333
42 A 2 2 1.00 10 0.200
43 A 7 7 1.00 12 0.583
44 A 7 7 1.00 10 0.700
45 A 4 4 1.00 12 0.333
46 A 11 11 1.01 12 0.917
47 A 8 8 1.05 10 0.800
48 A 9 9 1.00 12 0.750
49 A 9 9 1.00 10 0.900
50 A 12 12 1.03 12 1.000
51 A 4 4 1.00 12 0.333
52 A 2 2 1.00 10 0.200
53 A 7 7 1.00 12 0.583
54 A 7 7 1.00 10 0.700
55 A 4 4 1.00 12 0.333
56 A 3 3 1.00 10 0.300
57 A 3 3 1.00 11 0.273
58 A 3 3 1.00 8 0.375
59 A 3 3 1.00 10 0.300
60 A 10 9 1.50 10 0.900
61 A 5 4 1.54 11 0.364
62 A 9 8 1.11 8 1.000
63 A 5 4 1.00 10 0.400
64 A 3 3 1.00 10 0.300
65 A 6 5 1.00 10 0.500
66 A 6 5 1.05 10 0.500
67 A 3 3 1.00 11 0.273
68 A 6 5 1.00 11 0.455
69 A 6 5 1.00 11 0.455
70 A 3 3 1.00 8 0.375
71 A 6 5 1.00 8 0.625
72 A 6 5 1.00 8 0.625
73 A 3 3 1.00 10 0.300
74 A 12 11 1.00 10 1.100
75 A 12 11 1.00 10 1.100
76 A 7 6 1.27 11 0.545
77 A 7 6 1.15 15 0.400
78 A 6 5 1.00 15 0.333
79 A 6 5 1.00 13 0.385
80 A 10 9 1.00 15 0.600
81 A 6 5 1.00 15 0.333
82 A 7 6 1.00 15 0.400
83 A 8 7 1.00 15 0.467
84 A 7 6 1.00 15 0.400
85 A 8 7 0.96 15 0.467

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