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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 [25] had the largest ratio of [.3913]

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 22 0.045
2 A 2 1 1.00 22 0.045
3 A 2 1 1.00 22 0.045
4 A 2 1 1.00 22 0.045
5 A 2 1 1.00 20 0.050
6 A 8 8 1.00 22 0.364
7 A 8 8 1.00 22 0.364
8 A 8 8 1.00 22 0.364
9 A 7 6 1.00 25 0.240
10 A 6 6 1.00 25 0.240
11 A 5 5 1.00 25 0.200
12 A 7 6 1.00 25 0.240
13 A 7 6 1.00 25 0.240
14 A 14 8 1.00 25 0.320
15 A 14 8 1.00 25 0.320
16 A 13 7 1.00 23 0.304
17 A 13 7 1.00 22 0.318
18 A 14 8 1.00 25 0.320
19 A 14 8 1.00 25 0.320
20 A 7 6 1.00 23 0.261
21 A 4 4 1.00 23 0.174
22 A 5 5 1.00 23 0.217
23 A 7 6 1.00 23 0.261
24 A 5 4 1.00 23 0.174
25 A 15 9 1.00 23 0.391
26 A 15 9 1.00 23 0.391
27 A 14 8 1.00 23 0.348
28 A 13 7 1.00 21 0.333
29 A 13 7 1.00 20 0.350
30 A 14 8 1.00 23 0.348
31 A 15 9 1.00 23 0.391
32 A 5 5 1.00 21 0.238
33 A 7 6 1.00 21 0.286
34 A 8 7 1.00 18 0.389
35 A 8 5 1.00 25 0.200
36 A 5 5 1.00 25 0.200
37 A 7 4 1.00 25 0.160
38 A 4 3 1.00 23 0.130
39 A 7 4 1.00 22 0.182
40 A 7 6 1.00 25 0.240
41 A 8 5 1.00 25 0.200
42 A 5 4 1.00 25 0.160
43 A 8 5 1.00 25 0.200
44 A 20 7 1.00 23 0.304
45 A 5 5 1.00 23 0.217
46 A 21 7 1.00 23 0.304
47 A 4 3 1.00 21 0.143
48 A 19 6 1.00 20 0.300
49 A 7 6 1.00 23 0.261
50 A 20 7 1.00 23 0.304
51 A 11 8 1.00 23 0.348
52 A 21 9 1.00 23 0.391
53 A 7 6 1.00 25 0.240
54 A 7 6 1.00 25 0.240
55 A 7 6 1.00 23 0.261
56 A 7 6 1.00 22 0.273
57 A 7 6 1.00 25 0.240
58 A 7 7 1.00 25 0.280
59 A 7 6 1.01 25 0.240
60 A 7 6 1.00 25 0.240
61 A 7 6 1.00 25 0.240
62 A 7 6 1.00 25 0.240
63 A 7 6 1.00 25 0.240
64 A 7 6 1.00 23 0.261
65 A 7 6 1.00 22 0.273
66 A 7 6 1.00 25 0.240
67 A 8 7 1.00 25 0.280
68 A 7 6 1.00 25 0.240
69 A 7 6 1.00 25 0.240
70 A 7 6 1.00 25 0.240
71 A 1 1 1.00 19 0.053
72 A 2 2 1.00 24 0.083
73 A 2 2 1.00 26 0.077
74 A 2 2 1.00 30 0.067
75 A 1 1 1.00 21 0.048
76 A 2 2 1.00 26 0.077
77 A 2 2 1.00 28 0.071
78 A 2 2 1.00 32 0.062
79 A 1 1 1.00 18 0.056
80 A 3 3 1.00 23 0.130
81 A 3 3 1.00 25 0.120
82 A 3 3 1.00 29 0.103
83 A 1 1 1.00 19 0.053
84 A 2 2 1.00 24 0.083
85 A 2 2 1.00 26 0.077
86 A 2 2 1.00 30 0.067
87 A 1 1 1.00 19 0.053
88 A 2 2 1.00 24 0.083
89 A 2 2 1.00 26 0.077
90 A 2 2 1.00 30 0.067
91 A 1 1 1.00 21 0.048
92 A 2 2 1.00 26 0.077
93 A 2 2 1.00 28 0.071
94 A 2 2 1.00 32 0.062
95 A 1 1 1.00 21 0.048
96 A 2 2 1.00 26 0.077
97 A 2 2 1.00 28 0.071
98 A 2 2 1.00 32 0.062
99 A 1 1 1.00 18 0.056
100 A 4 3 0.94 23 0.130
101 A 4 3 0.94 25 0.120
102 A 4 3 1.00 29 0.103
103 A 1 1 1.00 18 0.056
104 A 3 3 1.00 23 0.130
105 A 3 3 1.00 25 0.120
106 A 3 3 1.00 29 0.103
107 A 1 1 1.00 19 0.053
108 A 2 2 1.00 24 0.083
109 A 2 2 1.00 26 0.077
110 A 2 2 1.00 30 0.067
111 A 1 1 1.00 21 0.048
112 A 2 2 1.00 26 0.077
113 A 2 2 1.00 28 0.071
114 A 2 2 1.00 32 0.062
115 A 1 1 1.00 18 0.056
116 A 1 1 1.00 23 0.043
117 A 1 1 1.00 25 0.040
118 A 2 2 1.00 29 0.069
119 A 3 3 1.00 59 0.051

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