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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 [16]

# 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 3 3 1.00 16 0.188
2 A 2 2 1.00 16 0.125
3 A 2 2 1.00 16 0.125
4 A 3 2 1.00 16 0.125
5 A 3 2 1.00 16 0.125
6 A 4 3 1.00 15 0.200
7 A 4 3 1.00 15 0.200
8 A 3 3 1.00 15 0.200
9 A 2 2 1.00 13 0.154
10 A 4 4 1.00 13 0.308
11 A 5 5 1.00 15 0.333
12 A 6 6 1.00 15 0.400
13 A 6 6 1.00 15 0.400
14 A 5 5 1.00 15 0.333
15 A 4 4 1.00 15 0.267
16 A 2 2 1.00 10 0.200
17 A 4 3 1.00 15 0.200
18 A 4 3 1.00 15 0.200
19 A 7 7 1.00 13 0.538
20 A 4 3 1.00 15 0.200
21 A 6 6 1.00 15 0.400
22 A 4 3 1.00 15 0.200
23 A 5 5 1.00 15 0.333
24 A 3 3 1.00 15 0.200
25 A 3 3 1.00 15 0.200
26 A 2 2 1.00 13 0.154
27 A 2 2 1.00 10 0.200
28 A 4 4 1.00 13 0.308
29 A 3 3 1.00 15 0.200
30 A 5 5 1.00 15 0.333
31 A 4 3 1.00 15 0.200
32 A 6 6 1.00 15 0.400
33 A 4 4 1.00 10 0.400
34 A 5 5 1.00 10 0.500
35 A 2 2 1.00 8 0.250
36 A 4 4 1.00 8 0.500
37 A 5 5 1.00 8 0.625
38 A 3 3 1.00 10 0.300
39 A 3 2 1.00 10 0.200
40 A 3 2 1.00 10 0.200
41 A 2 2 1.00 12 0.167
42 A 1 1 1.00 10 0.100
43 A 3 3 1.00 12 0.250
44 A 3 3 1.00 10 0.300
45 A 2 2 1.00 12 0.167
46 A 6 6 1.00 12 0.500
47 A 4 4 1.00 10 0.400
48 A 4 4 1.00 12 0.333
49 A 4 4 1.00 10 0.400
50 A 6 6 1.00 12 0.500
51 A 2 2 1.00 12 0.167
52 A 1 1 1.00 10 0.100
53 A 3 3 1.00 12 0.250
54 A 3 3 1.00 10 0.300
55 A 2 2 1.00 12 0.167
56 A 8 3 1.00 10 0.300
57 A 8 3 1.00 11 0.273
58 A 7 5 1.00 8 0.625
59 A 7 5 1.00 10 0.500
60 A 10 6 1.34 10 0.600
61 A 4 3 1.00 11 0.273
62 A 10 6 1.00 8 0.750
63 A 3 3 1.00 10 0.300
64 A 12 3 1.00 10 0.300
65 A 7 3 1.00 10 0.300
66 A 9 3 1.00 10 0.300
67 A 12 3 1.00 11 0.273
68 A 7 3 1.00 11 0.273
69 A 9 3 1.00 11 0.273
70 A 11 5 1.00 8 0.625
71 A 7 3 1.00 8 0.375
72 A 9 3 1.00 8 0.375
73 A 11 5 1.00 10 0.500
74 A 8 6 1.00 10 0.600
75 A 10 6 1.00 10 0.600
76 A 4 4 1.00 11 0.364
77 A 4 4 1.00 15 0.267
78 A 3 3 1.00 15 0.200
79 A 3 3 1.00 13 0.231
80 A 4 4 1.00 15 0.267
81 A 11 10 1.00 15 0.667
82 A 4 4 1.00 15 0.267
83 A 5 5 1.00 15 0.333
84 A 4 4 1.00 15 0.267
85 A 5 5 1.00 15 0.333

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