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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 [97] had the largest ratio of [25]

# 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 8 7 1.00 10 0.700
2 A 7 6 1.00 10 0.600
3 A 6 6 1.00 8 0.750
4 A 4 4 1.00 6 0.667
5 A 14 8 1.00 10 0.800
6 A 5 5 1.00 10 0.500
7 A 7 7 1.00 10 0.700
8 A 8 8 1.00 10 0.800
9 A 17 9 1.00 12 0.750
10 A 11 8 1.00 10 0.800
11 A 8 6 1.00 8 0.750
12 A 17 9 1.00 12 0.750
13 A 12 8 1.00 12 0.667
14 A 23 11 1.00 12 0.917
15 A 16 12 1.00 10 1.200
16 A 10 7 1.00 8 0.875
17 A 20 10 1.00 12 0.833
18 A 14 9 1.00 12 0.750
19 A 32 13 1.00 12 1.083
20 A 4 3 1.00 10 0.300
21 A 4 3 1.00 10 0.300
22 A 4 3 1.00 8 0.375
23 A 3 3 1.00 6 0.500
24 A 7 6 1.00 10 0.600
25 A 5 5 1.00 10 0.500
26 A 6 5 1.00 10 0.500
27 A 7 5 1.00 10 0.500
28 A 3 3 1.00 4 0.750
29 A 7 6 1.00 10 0.600
30 A 7 6 1.00 10 0.600
31 A 7 7 1.00 10 0.700
32 A 5 5 1.30 10 0.500
33 A 5 5 1.00 10 0.500
34 A 3 3 1.37 10 0.300
35 A 4 4 1.00 8 0.500
36 A 3 3 1.62 6 0.500
37 A 5 5 1.33 10 0.500
38 B 6 6 2.83 10 0.600
39 C 5 5 1.53 10 0.500
40 A 8 6 1.00 10 0.600
41 A 7 5 1.00 10 0.500
42 A 10 6 1.00 10 0.600
43 A 9 5 1.00 10 0.500
44 A 12 6 1.00 10 0.600
45 A 6 6 1.00 12 0.500
46 A 5 5 1.00 12 0.417
47 A 4 4 1.22 12 0.333
48 A 7 7 1.00 12 0.583
49 A 5 5 1.00 12 0.417
50 A 4 4 1.00 12 0.333
51 A 6 6 1.00 10 0.600
52 A 8 8 1.00 8 1.000
53 A 5 5 1.16 12 0.417
54 A 5 5 1.00 12 0.417
55 A 7 7 1.00 12 0.583
56 A 4 4 1.00 12 0.333
57 A 4 4 1.00 12 0.333
58 A 4 4 1.00 10 0.400
59 A 5 5 1.00 12 0.417
60 A 4 4 1.00 12 0.333
61 A 4 4 1.00 10 0.400
62 A 4 4 1.00 8 0.500
63 A 6 6 1.22 12 0.500
64 A 4 4 1.00 12 0.333
65 A 9 6 1.00 12 0.500
66 A 8 6 1.00 12 0.500
67 A 7 6 1.00 12 0.500
68 A 8 5 1.00 10 0.500
69 A 7 5 1.00 8 0.625
70 A 5 3 1.00 12 0.250
71 A 4 2 1.00 12 0.167
72 A 5 3 1.00 12 0.250
73 A 4 2 1.00 12 0.167
74 A 5 3 1.00 12 0.250
75 A 4 2 1.00 12 0.167
76 A 8 5 1.00 12 0.417
77 A 7 5 1.00 12 0.417
78 A 6 5 1.00 12 0.417
79 A 5 4 1.00 10 0.400
80 A 6 4 1.00 8 0.500
81 A 5 3 1.00 12 0.250
82 A 5 3 1.00 12 0.250
83 A 4 2 1.00 12 0.167
84 A 5 3 1.00 12 0.250
85 A 4 2 1.00 12 0.167
86 A 5 3 1.00 12 0.250
87 A 4 2 1.00 12 0.167
88 A 5 4 1.00 24 0.167
89 A 8 7 1.00 22 0.318
90 A 7 7 1.00 22 0.318
91 A 4 4 1.00 22 0.182
92 A 5 5 1.00 20 0.250
93 A 8 8 1.00 19 0.421
94 A 5 5 1.00 22 0.227
95 A 9 8 1.00 22 0.364
96 A 8 7 1.00 22 0.318
97 B 7 5 2.17 25 0.200
98 A 8 8 1.00 19 0.421
99 A 5 5 1.00 12 0.417
100 A 5 5 1.00 14 0.357

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