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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 [67] had the largest ratio of [22]

# 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 12 0.250
2 A 4 4 1.00 12 0.333
3 A 2 2 1.00 10 0.200
4 A 3 3 1.00 8 0.375
5 A 3 3 1.00 12 0.250
6 A 4 4 1.00 12 0.333
7 A 5 5 1.00 12 0.417
8 A 3 3 1.00 14 0.214
9 A 6 5 1.00 14 0.357
10 A 3 3 1.00 12 0.250
11 A 5 4 1.00 10 0.400
12 A 5 4 1.00 14 0.286
13 A 6 6 1.00 14 0.429
14 A 7 6 1.00 14 0.429
15 A 4 4 1.00 14 0.286
16 A 10 5 1.00 14 0.357
17 A 3 2 1.00 12 0.167
18 A 8 4 1.00 10 0.400
19 A 8 4 1.00 14 0.286
20 A 9 5 1.00 14 0.357
21 A 12 6 1.00 14 0.429
22 A 3 2 1.00 12 0.167
23 A 4 3 1.00 14 0.214
24 A 4 3 1.00 14 0.214
25 A 3 2 1.00 14 0.143
26 A 3 2 1.00 14 0.143
27 A 4 3 1.00 14 0.214
28 A 4 3 1.00 14 0.214
29 A 7 5 1.00 16 0.312
30 A 7 5 1.00 16 0.312
31 A 6 4 1.00 16 0.250
32 A 6 4 1.00 16 0.250
33 A 7 5 1.00 16 0.312
34 A 7 6 1.00 16 0.375
35 A 5 5 1.00 8 0.625
36 A 3 3 1.00 12 0.250
37 A 2 2 1.00 12 0.167
38 A 3 3 1.00 12 0.250
39 A 4 3 1.00 12 0.250
40 A 5 5 1.00 8 0.625
41 A 3 3 1.00 12 0.250
42 A 4 4 1.00 12 0.333
43 A 2 2 1.00 12 0.167
44 A 5 5 1.00 12 0.417
45 A 3 3 1.00 14 0.214
46 A 2 2 1.00 12 0.167
47 A 3 3 1.00 6 0.500
48 A 3 3 1.00 8 0.375
49 A 13 7 1.00 16 0.438
50 A 10 7 1.00 16 0.438
51 A 7 7 1.00 16 0.438
52 A 8 7 1.00 16 0.438
53 A 11 7 1.00 16 0.438
54 A 14 7 1.00 16 0.438
55 A 15 10 1.00 18 0.556
56 A 12 9 1.00 18 0.500
57 A 9 8 1.00 18 0.444
58 A 10 9 1.00 18 0.500
59 A 12 10 1.00 18 0.556
60 A 16 9 1.00 18 0.500
61 A 7 5 1.00 8 0.625
62 A 2 2 1.00 12 0.167
63 A 0 0 0.00 0 0.000
64 A 0 0 0.00 0 0.000
65 A 3 3 1.00 20 0.150
66 A 0 0 0.00 0 0.000
67 A 5 5 1.00 22 0.227
68 A 0 0 0.00 0 0.000
69 A 3 3 1.00 12 0.250
70 A 5 4 1.00 14 0.286
71 A 8 4 1.00 14 0.286
72 A 8 4 1.00 14 0.286
73 A 3 2 1.00 8 0.250
74 A 5 3 1.00 10 0.300
75 A 8 3 1.00 10 0.300
76 A 3 2 1.00 12 0.167
77 A 5 3 1.00 14 0.214
78 A 8 3 1.00 14 0.214
79 A 5 5 1.00 16 0.312
80 A 7 6 1.00 18 0.333
81 A 12 6 1.00 18 0.333
82 A 6 5 1.00 16 0.312
83 A 8 6 1.00 18 0.333
84 A 14 6 1.00 18 0.333
85 A 7 6 1.00 12 0.500
86 A 5 4 1.00 10 0.400
87 A 1 1 1.00 8 0.125
88 A 0 0 0.00 0 0.000
89 A 0 0 0.00 0 0.000
90 A 14 3 1.00 18 0.167
91 A 8 3 1.00 16 0.188
92 A 3 3 1.00 14 0.214
93 A 8 4 1.00 18 0.222
94 A 10 6 1.00 18 0.333
95 A 20 4 1.00 18 0.222
96 A 11 4 1.00 16 0.250
97 A 4 3 1.00 14 0.214
98 A 11 4 1.00 18 0.222
99 A 13 6 1.00 18 0.333

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