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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 [46] 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 1.00 16 0.438
2 A 8 7 0.84 16 0.438
3 A 5 5 0.90 16 0.312
4 A 6 6 1.00 16 0.375
5 A 3 3 1.00 16 0.188
6 A 6 6 1.00 14 0.429
7 A 8 8 0.91 14 0.571
8 A 6 5 0.84 16 0.312
9 A 10 10 1.00 16 0.625
10 A 6 5 1.00 15 0.333
11 A 6 5 1.00 15 0.333
12 A 6 5 1.00 15 0.333
13 A 5 4 1.00 13 0.308
14 A 7 6 1.00 13 0.462
15 A 8 7 1.24 15 0.467
16 A 9 8 1.33 15 0.533
17 A 8 7 1.30 15 0.467
18 A 7 6 1.23 15 0.400
19 A 6 5 1.02 15 0.333
20 A 4 3 1.00 10 0.300
21 A 5 4 1.00 15 0.267
22 A 5 4 1.00 15 0.267
23 A 5 4 1.00 15 0.267
24 A 11 10 1.02 13 0.769
25 A 6 5 1.00 10 0.500
26 A 6 5 1.00 10 0.500
27 A 6 5 1.00 10 0.500
28 A 5 4 1.00 15 0.267
29 A 5 4 1.00 15 0.267
30 A 5 4 1.00 15 0.267
31 A 4 3 1.00 13 0.231
32 A 6 5 1.00 13 0.385
33 A 7 6 1.24 15 0.400
34 A 8 7 1.30 15 0.467
35 A 8 7 1.33 15 0.467
36 A 7 6 1.23 15 0.400
37 A 6 5 1.00 15 0.333
38 A 4 3 1.00 10 0.300
39 A 5 4 1.00 15 0.267
40 A 5 4 1.00 15 0.267
41 A 5 4 1.00 15 0.267
42 A 8 7 1.00 10 0.700
43 A 10 9 1.12 10 0.900
44 A 4 3 0.47 8 0.375
45 A 7 6 0.64 8 0.750
46 A 10 9 0.79 8 1.125
47 A 6 6 1.00 12 0.500
48 A 6 6 1.00 10 0.600
49 A 8 8 1.00 12 0.667
50 A 8 8 1.00 10 0.800
51 A 6 6 1.00 12 0.500
52 A 6 6 1.00 10 0.600
53 A 8 8 1.00 12 0.667
54 A 8 8 1.00 10 0.800
55 A 2 2 1.00 10 0.200
56 A 4 4 1.00 12 0.333
57 A 4 4 1.00 12 0.333
58 A 8 8 1.07 10 0.800
59 A 12 12 1.03 12 1.000
60 A 11 11 1.01 12 0.917
61 A 2 2 1.00 10 0.200
62 A 4 4 1.00 12 0.333
63 A 4 4 1.00 12 0.333
64 A 5 5 1.00 10 0.500
65 A 7 7 1.00 12 0.583
66 A 7 7 1.00 12 0.583
67 A 4 3 1.00 13 0.231
68 A 4 3 1.00 21 0.143
69 A 4 3 1.00 15 0.200
70 A 10 9 1.11 10 0.900
71 A 5 4 1.54 11 0.364
72 A 9 8 0.68 8 1.000
73 A 5 4 0.56 10 0.400
74 A 3 3 1.00 10 0.300
75 A 6 5 1.00 10 0.500
76 A 6 5 1.05 10 0.500
77 A 3 3 1.00 11 0.273
78 A 6 5 1.00 11 0.455
79 A 6 5 1.00 11 0.455
80 A 3 3 1.00 8 0.375
81 A 6 5 1.00 8 0.625
82 A 6 5 1.00 8 0.625
83 A 3 3 1.00 10 0.300
84 A 10 9 1.00 10 0.900
85 A 10 9 0.78 10 0.900
86 A 7 6 1.12 11 0.545
87 A 7 6 1.12 15 0.400
88 A 10 9 1.30 15 0.600
89 A 6 5 1.00 15 0.333
90 A 6 5 1.00 13 0.385
91 A 9 8 1.00 15 0.533
92 A 6 5 1.00 15 0.333
93 A 8 7 1.00 15 0.467
94 A 7 6 1.00 15 0.400
95 A 8 7 1.00 15 0.467
96 A 7 6 1.00 15 0.400
97 A 8 7 0.98 15 0.467
98 A 7 6 1.00 15 0.400

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