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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 [10] had the largest ratio of [34]

# 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 2 2 1.00 31 0.065
10 A 2 2 1.00 34 0.059
11 A 3 3 1.00 22 0.136
12 A 6 5 1.00 18 0.278
13 A 3 3 1.00 26 0.115
14 A 16 12 1.00 27 0.444
15 A 2 1 1.00 23 0.043
16 A 2 1 1.00 23 0.043
17 A 2 1 1.00 23 0.043
18 A 2 1 1.00 21 0.048
19 A 6 5 1.00 23 0.217
20 A 4 4 1.00 23 0.174
21 A 5 5 1.00 23 0.217
22 A 2 1 1.00 25 0.040
23 A 2 1 1.00 25 0.040
24 A 2 1 1.00 25 0.040
25 A 2 1 1.00 23 0.043
26 A 6 5 1.00 25 0.200
27 A 7 6 1.00 25 0.240
28 A 5 4 1.00 25 0.160
29 A 6 5 1.00 25 0.200
30 A 2 1 1.00 25 0.040
31 A 2 1 1.00 25 0.040
32 A 2 1 1.00 25 0.040
33 A 2 1 1.00 23 0.043
34 A 6 5 1.00 25 0.200
35 A 7 6 1.00 25 0.240
36 A 8 6 1.00 25 0.240
37 A 6 5 1.00 25 0.200
38 A 6 5 1.00 25 0.200
39 A 6 5 1.00 25 0.200
40 A 6 5 1.00 23 0.217
41 A 9 5 1.00 25 0.200
42 A 10 6 1.00 25 0.240
43 A 11 7 1.00 25 0.280
44 A 7 6 1.00 25 0.240
45 A 7 6 1.00 25 0.240
46 A 7 6 1.00 25 0.240
47 A 4 4 1.00 23 0.174
48 A 10 6 1.00 25 0.240
49 A 11 7 1.00 25 0.280
50 A 12 7 1.00 25 0.280
51 A 8 6 1.00 25 0.240
52 A 8 6 1.00 25 0.240
53 A 5 4 1.00 25 0.160
54 A 5 5 1.00 23 0.217
55 A 11 7 1.00 25 0.280
56 A 12 7 1.00 25 0.280
57 A 13 7 1.00 25 0.280
58 A 11 5 1.00 27 0.185
59 A 9 5 1.00 27 0.185
60 A 7 5 1.00 27 0.185
61 A 5 5 1.00 25 0.200
62 A 8 7 1.00 27 0.259
63 A 6 5 1.00 27 0.185
64 A 7 6 1.00 27 0.222
65 A 12 5 1.00 27 0.185
66 A 10 5 1.00 27 0.185
67 A 8 5 1.00 27 0.185
68 A 6 5 1.00 25 0.200
69 A 9 8 1.00 27 0.296
70 A 10 9 1.00 27 0.333
71 A 7 6 1.00 27 0.222
72 A 13 5 1.00 27 0.185
73 A 11 5 1.00 27 0.185
74 A 9 5 1.00 27 0.185
75 A 7 5 1.00 25 0.200
76 A 10 9 1.00 27 0.333
77 A 11 9 1.00 27 0.333
78 A 11 10 1.00 27 0.370
79 A 10 4 1.00 27 0.148
80 A 8 4 1.00 27 0.148
81 A 6 4 1.00 27 0.148
82 A 4 4 1.00 25 0.160
83 A 5 4 1.00 27 0.148
84 A 6 5 1.00 27 0.185
85 A 7 6 1.00 27 0.222
86 A 9 5 1.00 27 0.185
87 A 7 5 1.00 27 0.185
88 A 5 5 1.00 27 0.185
89 A 4 4 1.00 25 0.160
90 A 6 5 1.00 27 0.185
91 A 7 6 1.00 27 0.222
92 A 8 6 1.00 27 0.222
93 A 8 5 1.00 27 0.185
94 A 6 5 1.00 27 0.185
95 A 5 4 1.00 27 0.148
96 A 3 3 1.00 25 0.120
97 A 7 6 1.00 27 0.222
98 A 8 6 1.00 27 0.222
99 A 9 6 1.00 27 0.222
100 A 7 5 1.00 27 0.185
101 A 5 5 1.00 25 0.200
102 A 8 5 1.00 27 0.185
103 A 6 4 1.00 27 0.148
104 A 8 5 1.00 27 0.185
105 A 6 5 1.00 25 0.200
106 A 9 6 1.00 27 0.222
107 A 10 7 1.00 27 0.259
108 A 7 5 1.00 27 0.185
109 A 8 4 1.00 27 0.148
110 A 6 4 1.00 27 0.148
111 A 4 4 1.00 25 0.160
112 A 5 3 1.00 27 0.111
113 A 6 4 1.00 27 0.148
114 A 7 5 1.00 27 0.185
115 A 5 5 1.00 27 0.185
116 A 4 4 1.00 25 0.160
117 A 6 4 1.00 27 0.148
118 A 6 5 1.00 27 0.185
119 A 5 4 1.00 27 0.148
120 A 3 3 1.00 25 0.120
121 A 5 4 1.00 27 0.148
122 A 3 3 1.00 29 0.103
123 A 3 3 1.00 29 0.103

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