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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 [11] had the largest ratio of [.4444]

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 4 4 1.00 29 0.138
2 A 2 2 1.00 31 0.065
3 A 2 2 1.00 27 0.074
4 A 4 4 1.00 27 0.148
5 A 5 5 1.00 27 0.185
6 A 6 5 1.00 27 0.185
7 A 4 4 1.00 31 0.129
8 A 2 2 1.00 23 0.087
9 A 3 3 1.00 22 0.136
10 A 6 5 1.00 18 0.278
11 A 16 12 1.00 27 0.444
12 A 2 1 1.00 23 0.043
13 A 2 1 1.00 23 0.043
14 A 2 1 1.00 23 0.043
15 A 2 1 1.00 21 0.048
16 A 6 5 1.00 23 0.217
17 A 4 4 1.00 23 0.174
18 A 5 5 1.00 23 0.217
19 A 2 1 1.00 25 0.040
20 A 2 1 1.00 25 0.040
21 A 2 1 1.00 25 0.040
22 A 2 1 1.00 23 0.043
23 A 6 5 1.00 25 0.200
24 A 7 6 1.00 25 0.240
25 A 5 4 1.00 25 0.160
26 A 6 5 1.00 25 0.200
27 A 2 1 1.00 25 0.040
28 A 2 1 1.00 25 0.040
29 A 2 1 1.00 25 0.040
30 A 2 1 1.00 23 0.043
31 A 6 5 1.00 25 0.200
32 A 7 6 1.00 25 0.240
33 A 8 6 1.00 25 0.240
34 A 6 5 1.00 25 0.200
35 A 6 5 1.00 25 0.200
36 A 6 5 1.00 25 0.200
37 A 6 5 1.00 23 0.217
38 A 9 5 1.00 25 0.200
39 A 10 6 1.00 25 0.240
40 A 11 7 1.00 25 0.280
41 A 7 6 1.00 25 0.240
42 A 7 6 1.00 25 0.240
43 A 7 6 1.00 25 0.240
44 A 4 4 1.00 23 0.174
45 A 10 6 1.00 25 0.240
46 A 11 7 1.00 25 0.280
47 A 12 7 1.00 25 0.280
48 A 8 6 1.00 25 0.240
49 A 8 6 1.00 25 0.240
50 A 5 4 1.00 25 0.160
51 A 5 5 1.00 23 0.217
52 A 11 7 1.00 25 0.280
53 A 12 7 1.00 25 0.280
54 A 13 7 1.00 25 0.280
55 A 11 5 1.00 27 0.185
56 A 9 5 1.00 27 0.185
57 A 7 5 1.00 27 0.185
58 A 5 5 1.00 25 0.200
59 A 8 7 1.00 27 0.259
60 A 6 5 1.00 27 0.185
61 A 7 6 1.00 27 0.222
62 A 12 5 1.00 27 0.185
63 A 10 5 1.00 27 0.185
64 A 8 5 1.00 27 0.185
65 A 6 5 1.00 25 0.200
66 A 9 8 1.00 27 0.296
67 A 10 9 1.00 27 0.333
68 A 7 6 1.00 27 0.222
69 A 13 5 1.00 27 0.185
70 A 11 5 1.00 27 0.185
71 A 9 5 1.00 27 0.185
72 A 7 5 1.00 25 0.200
73 A 10 9 1.00 27 0.333
74 A 11 9 1.00 27 0.333
75 A 11 10 1.00 27 0.370
76 A 10 4 1.00 27 0.148
77 A 8 4 1.00 27 0.148
78 A 6 4 1.00 27 0.148
79 A 4 4 1.00 25 0.160
80 A 5 4 1.00 27 0.148
81 A 6 5 1.00 27 0.185
82 A 7 6 1.00 27 0.222
83 A 9 5 1.00 27 0.185
84 A 7 5 1.00 27 0.185
85 A 5 5 1.00 27 0.185
86 A 4 4 1.00 25 0.160
87 A 6 5 1.00 27 0.185
88 A 7 6 1.00 27 0.222
89 A 8 6 1.00 27 0.222
90 A 8 5 1.00 27 0.185
91 A 6 5 1.00 27 0.185
92 A 5 4 1.00 27 0.148
93 A 3 3 1.00 25 0.120
94 A 7 6 1.00 27 0.222
95 A 8 6 1.00 27 0.222
96 A 9 6 1.00 27 0.222
97 A 7 5 1.00 27 0.185
98 A 5 5 1.00 25 0.200
99 A 8 5 1.00 27 0.185
100 A 6 4 1.00 27 0.148
101 A 8 5 1.00 27 0.185
102 A 6 5 1.00 25 0.200
103 A 9 6 1.00 27 0.222
104 A 10 7 1.00 27 0.259
105 A 7 5 1.00 27 0.185
106 A 8 4 1.00 27 0.148
107 A 6 4 1.00 27 0.148
108 A 4 4 1.00 25 0.160
109 A 5 3 1.00 27 0.111
110 A 6 4 1.00 27 0.148
111 A 7 5 1.00 27 0.185
112 A 5 5 1.00 27 0.185
113 A 4 4 1.00 25 0.160
114 A 6 4 1.00 27 0.148
115 A 6 5 1.00 27 0.185
116 A 5 4 1.00 27 0.148
117 A 3 3 1.00 25 0.120
118 A 5 4 1.00 27 0.148

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