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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 [32] had the largest ratio of [20]

# 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 6 6 1.00 14 0.429
2 A 5 5 1.00 14 0.357
3 A 4 4 1.00 12 0.333
4 A 0 0 0.00 0 0.000
5 A 0 0 0.00 0 0.000
6 A 7 7 1.00 16 0.438
7 A 6 6 1.00 16 0.375
8 A 3 2 1.00 14 0.143
9 A 0 0 0.00 0 0.000
10 A 0 0 0.00 0 0.000
11 A 13 10 1.00 16 0.625
12 A 9 7 1.00 16 0.438
13 A 7 7 1.00 14 0.500
14 A 0 0 0.00 0 0.000
15 A 0 0 0.00 0 0.000
16 A 44 18 1.00 18 1.000
17 A 43 17 1.00 18 0.944
18 A 37 12 1.00 18 0.667
19 A 37 12 1.00 18 0.667
20 A 43 17 1.00 18 0.944
21 A 0 0 0.00 0 0.000
22 A 0 0 0.00 0 0.000
23 A 0 0 0.00 0 0.000
24 A 0 0 0.00 0 0.000
25 A 0 0 0.00 0 0.000
26 A 0 0 0.00 0 0.000
27 A 0 0 0.00 0 0.000
28 A 0 0 0.00 0 0.000
29 A 0 0 0.00 0 0.000
30 A 0 0 0.00 0 0.000
31 A 0 0 0.00 0 0.000
32 A 5 3 1.00 20 0.150
33 A 4 3 1.00 20 0.150
34 A 3 3 1.00 18 0.167
35 A 7 4 1.00 20 0.200
36 A 7 4 1.00 20 0.200
37 A 8 5 1.00 20 0.250
38 A 10 3 1.00 20 0.150
39 A 8 3 1.00 20 0.150
40 A 7 3 1.00 18 0.167
41 A 21 5 1.00 20 0.250
42 A 24 7 1.00 20 0.350
43 A 14 3 1.00 20 0.150
44 A 11 3 1.00 20 0.150
45 A 11 3 1.00 18 0.167
46 A 53 7 1.00 20 0.350
47 A 60 9 1.00 20 0.450
48 A 0 0 0.00 0 0.000
49 A 0 0 0.00 0 0.000
50 A 2 2 1.00 20 0.100
51 A 4 2 1.00 20 0.100
52 A 5 2 1.00 20 0.100
53 A 8 7 1.00 18 0.389
54 A 7 6 1.00 18 0.333
55 A 6 5 1.00 16 0.312
56 A 0 0 0.00 0 0.000
57 A 0 0 0.00 0 0.000
58 A 15 9 1.00 20 0.450
59 A 13 10 1.00 20 0.500
60 A 9 7 1.00 18 0.389
61 A 0 0 0.00 0 0.000
62 A 0 0 0.00 0 0.000
63 A 28 11 1.00 20 0.550
64 A 22 11 1.00 20 0.550
65 A 16 9 1.00 18 0.500
66 A 0 0 0.00 0 0.000
67 A 0 0 0.00 0 0.000
68 A 6 6 1.00 20 0.300
69 A 5 5 1.00 20 0.250
70 A 4 4 1.00 18 0.222
71 A 0 0 0.00 0 0.000
72 A 0 0 0.00 0 0.000
73 A 28 10 1.00 20 0.500
74 A 24 11 1.00 20 0.550
75 A 5 5 1.00 18 0.278
76 A 0 0 0.00 0 0.000
77 A 0 0 0.00 0 0.000

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