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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 [55] had the largest ratio of [87]

# 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 24 0.042
2 A 2 1 1.00 24 0.042
3 A 2 1 1.00 24 0.042
4 A 2 1 1.00 22 0.045
5 A 3 3 1.00 24 0.125
6 A 3 3 1.00 24 0.125
7 A 3 3 1.00 24 0.125
8 A 4 4 1.00 24 0.167
9 A 2 1 1.00 26 0.038
10 A 2 1 1.00 26 0.038
11 A 2 1 1.00 24 0.042
12 A 4 3 1.00 26 0.115
13 A 4 4 1.00 26 0.154
14 A 4 3 1.00 26 0.115
15 A 4 3 1.00 26 0.115
16 A 2 1 1.00 26 0.038
17 A 2 1 1.00 26 0.038
18 A 2 1 1.00 24 0.042
19 A 5 3 1.00 26 0.115
20 A 5 4 1.00 26 0.154
21 A 5 4 1.00 26 0.154
22 A 5 3 1.00 26 0.115
23 A 7 5 1.00 30 0.167
24 A 6 5 1.00 30 0.167
25 A 5 5 1.00 30 0.167
26 A 5 5 1.00 30 0.167
27 A 4 4 1.00 30 0.133
28 A 5 5 1.00 30 0.167
29 A 7 5 1.00 30 0.167
30 A 6 5 1.00 30 0.167
31 A 6 6 1.00 30 0.200
32 A 6 5 1.00 30 0.167
33 A 5 4 1.00 30 0.133
34 A 6 5 1.00 30 0.167
35 A 7 5 1.00 30 0.167
36 A 6 5 1.00 30 0.167
37 A 5 5 1.00 30 0.167
38 A 4 4 1.00 30 0.133
39 A 3 3 1.00 30 0.100
40 A 4 4 1.00 30 0.133
41 A 5 4 1.00 30 0.133
42 A 7 6 1.00 30 0.200
43 A 6 6 1.00 30 0.200
44 A 5 5 1.00 30 0.167
45 A 3 3 1.00 30 0.100
46 A 4 4 1.00 30 0.133
47 A 5 4 1.00 30 0.133
48 A 3 3 1.00 30 0.100
49 A 8 7 1.00 31 0.226
50 A 8 7 1.00 31 0.226
51 A 8 7 1.00 32 0.219
52 A 4 4 1.00 30 0.133
53 A 5 5 1.00 30 0.167
54 A 6 5 1.00 30 0.167
55 A 2 2 1.00 87 0.023
56 A 5 5 1.00 81 0.062
57 A 6 6 1.00 28 0.214
58 A 14 8 1.00 30 0.267
59 A 9 7 1.00 30 0.233
60 A 5 5 1.00 28 0.179
61 A 2 2 1.00 21 0.095
62 A 5 3 1.00 30 0.100
63 A 7 5 1.00 30 0.167
64 A 14 9 1.28 32 0.281
65 A 7 7 1.00 32 0.219
66 A 6 6 1.00 32 0.188
67 A 1 1 1.00 32 0.031
68 A 3 3 1.00 32 0.094
69 A 6 6 1.00 32 0.188
70 A 9 8 1.00 32 0.250
71 A 14 9 1.19 32 0.281
72 A 7 7 1.00 32 0.219
73 A 6 6 1.00 32 0.188
74 A 3 3 1.00 32 0.094
75 A 6 6 1.00 32 0.188
76 A 9 8 1.00 32 0.250
77 A 12 8 1.00 32 0.250
78 A 6 6 1.00 32 0.188
79 A 1 1 1.00 32 0.031
80 A 3 2 1.00 32 0.062
81 A 5 5 1.00 32 0.156
82 A 8 7 1.00 32 0.219
83 A 14 9 1.00 32 0.281
84 A 3 3 1.00 32 0.094
85 A 3 3 1.00 32 0.094
86 A 5 5 1.00 32 0.156
87 A 8 7 1.00 32 0.219
88 A 11 6 1.00 32 0.188
89 A 7 7 0.99 28 0.250
90 A 6 6 1.00 28 0.214
91 A 1 1 1.00 28 0.036
92 A 3 3 1.00 28 0.107
93 A 6 6 1.00 28 0.214
94 A 6 6 1.00 32 0.188
95 A 1 1 1.00 32 0.031
96 A 1 1 1.00 32 0.031
97 A 3 3 1.00 30 0.100
98 A 4 4 1.00 28 0.143
99 A 11 9 1.00 33 0.273
100 A 8 7 1.00 32 0.219
101 A 11 9 1.00 33 0.273
102 A 8 7 1.00 32 0.219
103 A 0 0 0.00 0 0.000
104 A 7 7 1.00 34 0.206
105 A 2 2 1.00 34 0.059
106 A 2 2 1.00 34 0.059
107 A 0 0 0.00 0 0.000
108 A 8 8 1.00 34 0.235
109 A 5 5 1.00 34 0.147
110 A 0 0 0.00 0 0.000
111 A 7 7 1.00 34 0.206
112 A 0 0 0.00 0 0.000
113 A 2 2 1.00 34 0.059
114 A 2 2 1.00 34 0.059
115 A 0 0 0.00 0 0.000

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