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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 [47] had the largest ratio of [.6875]

Table 2.1:Rubi specific breakdown of results for each integral
# 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 2 1 1.00 18 0.056
2 A 2 1 1.00 23 0.043
3 A 2 1 1.00 28 0.036
4 A 2 1 1.00 33 0.030
5 A 2 1 1.00 38 0.026
6 A 2 1 1.00 20 0.050
7 A 2 1 1.00 25 0.040
8 A 2 1 1.00 30 0.033
9 A 2 1 1.00 35 0.029
10 A 10 7 1.00 18 0.389
11 A 9 7 1.00 23 0.304
12 A 8 6 1.00 28 0.214
13 A 10 7 1.00 33 0.212
14 A 12 8 1.00 38 0.210
15 A 15 8 1.00 16 0.500
16 A 14 8 1.00 21 0.381
17 A 15 7 1.00 26 0.269
18 A 17 8 1.00 31 0.258
19 A 19 9 1.00 36 0.250
20 A 9 7 1.00 20 0.350
21 A 8 7 1.00 25 0.280
22 A 9 8 1.00 30 0.267
23 A 11 9 1.00 35 0.257
24 A 13 10 1.00 40 0.250
25 A 13 10 1.00 55 0.182
26 A 12 9 1.00 18 0.500
27 A 11 9 1.00 23 0.391
28 A 10 8 1.00 28 0.286
29 A 10 8 1.00 33 0.242
30 A 11 9 1.00 38 0.237
31 A 17 10 1.00 16 0.625
32 A 16 10 1.00 21 0.476
33 A 15 9 1.00 26 0.346
34 A 15 9 1.00 31 0.290
35 A 16 10 1.00 36 0.278
36 A 11 9 1.00 20 0.450
37 A 10 9 1.00 25 0.360
38 A 9 8 1.00 30 0.267
39 A 9 8 1.00 35 0.229
40 A 10 9 1.00 40 0.225
41 A 13 11 1.00 55 0.200
42 A 14 10 1.00 18 0.556
43 A 13 9 1.00 23 0.391
44 A 12 9 1.00 28 0.321
45 A 12 10 1.00 33 0.303
46 A 13 11 1.00 38 0.290
47 A 19 11 1.00 16 0.688
48 A 18 10 1.00 21 0.476
49 A 17 10 1.00 26 0.385
50 A 17 11 1.00 31 0.355
51 A 18 12 1.00 36 0.333
52 A 13 10 1.00 20 0.500
53 A 12 9 1.00 25 0.360
54 A 11 9 1.00 30 0.300
55 A 11 10 1.00 35 0.286
56 A 12 11 1.00 40 0.275
57 A 11 9 0.99 55 0.164
58 A 11 10 1.00 50 0.200
59 A 13 10 1.00 50 0.200
60 A 2 1 1.00 63 0.016
61 A 2 1 1.00 63 0.016
62 A 2 1 1.00 61 0.016
63 A 2 1 1.00 63 0.016
64 A 9 8 1.00 63 0.127
65 A 11 10 1.00 63 0.159
66 A 13 10 1.00 63 0.159
67 A 2 2 1.00 26 0.077
68 A 3 2 1.00 31 0.065
69 A 3 2 1.00 36 0.056
70 A 3 2 1.00 41 0.049
71 A 3 2 1.00 46 0.043
72 A 3 2 1.00 51 0.039
73 A 4 3 1.00 21 0.143
74 A 4 3 1.00 26 0.115
75 A 6 4 1.00 31 0.129
76 A 6 4 1.00 36 0.111
77 A 6 4 1.00 41 0.098
78 A 6 4 1.00 46 0.087
79 A 3 2 1.00 16 0.125
80 A 3 2 1.00 21 0.095
81 A 3 2 1.00 26 0.077
82 A 3 2 1.00 31 0.065
83 A 3 2 1.00 36 0.056
84 A 3 2 1.00 41 0.049
85 A 3 2 1.00 26 0.077
86 A 3 2 1.00 31 0.065
87 A 3 2 1.00 36 0.056
88 A 3 2 1.00 41 0.049
89 A 3 2 1.00 46 0.043
90 A 3 2 1.00 51 0.039
91 A 9 5 1.00 21 0.238
92 A 9 5 1.00 26 0.192
93 A 9 5 1.00 31 0.161
94 A 3 2 1.00 36 0.056
95 A 3 2 1.00 41 0.049
96 A 3 2 1.00 46 0.043
97 A 3 2 1.00 16 0.125
98 A 3 2 1.00 21 0.095
99 A 3 2 1.00 26 0.077
100 A 3 2 1.00 31 0.065
101 A 3 2 1.00 36 0.056
102 A 3 2 1.00 41 0.049
103 A 1 1 1.00 28 0.036
104 A 5 5 1.00 31 0.161
105 A 5 5 1.00 33 0.152
106 A 4 4 1.00 36 0.111

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