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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 [33] had the largest ratio of [33]

# 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 12 8 1.00 17 0.471
2 A 13 7 1.00 18 0.389
3 A 19 6 1.00 17 0.353
4 A 13 10 1.00 18 0.556
5 A 19 6 1.00 26 0.231
6 A 19 6 1.00 26 0.231
7 A 7 4 1.00 27 0.148
8 A 19 6 1.00 27 0.222
9 A 19 6 1.00 18 0.333
10 A 19 7 1.00 18 0.389
11 A 10 7 1.00 18 0.389
12 A 19 6 1.00 16 0.375
13 A 19 6 1.00 13 0.462
14 A 19 6 1.00 18 0.333
15 A 5 5 1.00 18 0.278
16 A 7 4 1.00 18 0.222
17 A 7 4 1.00 18 0.222
18 A 7 4 1.00 18 0.222
19 A 7 4 1.00 18 0.222
20 A 19 6 1.00 20 0.300
21 A 19 7 1.00 20 0.350
22 A 11 8 1.00 20 0.400
23 A 19 6 1.00 18 0.333
24 A 19 6 1.00 15 0.400
25 A 19 6 1.00 20 0.300
26 A 5 5 1.00 20 0.250
27 A 7 4 1.00 20 0.200
28 A 7 4 1.00 20 0.200
29 A 7 4 1.00 20 0.200
30 A 7 4 1.00 20 0.200
31 A 9 6 1.00 25 0.240
32 A 9 6 1.00 26 0.231
33 A 9 6 1.00 33 0.182
34 A 5 5 1.00 17 0.294
35 A 6 6 1.00 22 0.273
36 A 11 8 1.00 17 0.471
37 A 5 4 1.00 22 0.182
38 A 14 10 1.00 17 0.588
39 A 15 9 1.00 22 0.409
40 A 21 8 1.00 17 0.471
41 A 9 6 1.00 22 0.273
42 A 5 4 1.00 21 0.190
43 A 5 4 1.00 21 0.190
44 A 3 3 1.00 19 0.158
45 A 6 4 1.00 21 0.190
46 A 7 4 1.00 21 0.190
47 A 3 3 1.00 20 0.150
48 A 9 5 1.00 21 0.238
49 A 7 5 1.00 21 0.238
50 A 4 4 1.00 19 0.210
51 A 10 5 1.00 21 0.238
52 A 11 5 1.00 21 0.238
53 A 11 5 1.00 21 0.238
54 A 8 5 1.00 21 0.238
55 A 5 4 1.00 19 0.210
56 A 15 5 1.00 21 0.238
57 A 16 5 1.00 21 0.238
58 A 6 5 1.00 23 0.217
59 A 0 0 0.00 0 0.000
60 A 10 5 1.00 21 0.238
61 A 8 5 1.00 21 0.238
62 A 6 5 1.00 19 0.263
63 A 6 5 1.00 21 0.238
64 A 8 5 1.00 21 0.238
65 A 10 5 1.00 21 0.238
66 A 2 1 1.00 22 0.045
67 A 2 1 1.00 24 0.042
68 A 2 1 1.00 24 0.042
69 A 5 3 1.00 26 0.115
70 A 5 3 1.00 26 0.115
71 A 3 2 1.00 24 0.083
72 A 6 3 1.00 26 0.115
73 A 7 3 1.00 26 0.115
74 A 8 3 1.00 26 0.115
75 A 9 4 1.00 26 0.154
76 A 9 5 1.00 26 0.192
77 A 4 3 0.91 24 0.125
78 A 10 4 1.00 26 0.154
79 A 11 4 1.00 26 0.154
80 A 11 4 1.00 26 0.154
81 A 11 5 1.00 26 0.192
82 A 5 3 1.00 24 0.125
83 A 15 4 1.00 26 0.154
84 A 16 4 1.00 26 0.154
85 A 6 5 1.00 26 0.192
86 A 6 5 1.00 26 0.192
87 A 6 5 1.00 26 0.192
88 A 6 5 1.00 26 0.192
89 A 6 5 1.00 26 0.192
90 A 0 0 0.00 0 0.000
91 A 10 5 1.00 26 0.192
92 A 8 5 1.00 26 0.192
93 A 6 5 1.00 24 0.208
94 A 0 0 0.00 0 0.000
95 A 0 0 0.00 0 0.000
96 A 0 0 0.00 0 0.000

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