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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi only. 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 also given. The larger this ratio is, the harder the integral is to solve. In this test file, problem number [30] had the largest ratio of [.761905000000000054]

# 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 7 7 1.72 32 0.219
2 A 7 7 0.82 33 0.212
3 A 7 7 0.82 33 0.212
4 B 7 7 2.05 34 0.206
5 A 8 8 1.26 38 0.211
6 A 7 7 1.42 38 0.184
7 A 6 6 1.72 38 0.158
8 B 6 6 2.07 38 0.158
9 A 7 7 1.84 38 0.184
10 A 10 10 0.97 40 0.250
11 A 8 8 0.91 40 0.200
12 A 6 6 0.82 40 0.150
13 A 6 6 0.87 40 0.150
14 A 8 8 0.94 40 0.200
15 B 6 6 2.01 52 0.115
16 A 5 5 1.27 27 0.185
17 B 11 11 3.22 48 0.229
18 A 2 2 1.00 14 0.143
19 A 2 2 1.00 22 0.091
20 A 4 4 0.98 27 0.148
21 A 4 4 0.96 32 0.125
22 C 2 2 18.42 26 0.077
23 A 1 1 1.00 41 0.024
24 A 1 1 1.00 94 0.011
25 A 8 7 1.08 23 0.304
26 A 10 9 1.06 23 0.391
27 A 12 11 1.05 23 0.478
28 A 12 11 1.46 21 0.524
29 A 14 13 1.20 21 0.619
30 A 17 16 1.17 21 0.762
31 A 2 2 1.00 25 0.080
32 A 2 2 1.00 23 0.087
33 A 8 7 1.00 25 0.280
34 A 11 10 0.97 25 0.400
35 A 14 13 0.97 25 0.520
36 A 8 7 1.00 25 0.280
37 A 8 7 1.00 22 0.318
38 A 4 3 1.00 18 0.167
39 A 9 8 0.98 23 0.348
40 A 12 11 1.56 23 0.478
41 A 7 6 1.03 38 0.158
42 A 11 10 1.03 38 0.263
43 A 13 12 0.96 38 0.316
44 A 7 6 1.10 36 0.167
45 A 14 13 1.18 36 0.361
46 A 17 16 1.14 36 0.444
47 A 2 2 1.00 40 0.050
48 A 2 2 1.00 38 0.053
49 A 7 6 1.00 40 0.150
50 A 11 10 0.98 40 0.250
51 A 14 13 1.00 40 0.325
52 A 7 6 1.00 55 0.109
53 A 12 11 1.02 55 0.200
54 A 14 13 1.02 55 0.236
55 A 12 11 1.02 50 0.220
56 A 17 16 1.05 50 0.320
57 A 2 2 1.00 63 0.032
58 A 2 2 1.00 63 0.032
59 A 2 2 1.00 61 0.033
60 A 2 2 1.00 63 0.032
61 A 9 8 1.00 63 0.127
62 A 12 11 0.97 63 0.175
63 A 15 14 0.97 63 0.222
64 A 2 2 1.00 26 0.077
65 A 3 3 1.00 31 0.097
66 A 3 3 1.00 36 0.083
67 A 3 3 1.09 41 0.073
68 A 3 3 1.00 46 0.065
69 A 3 3 1.00 51 0.059
70 A 3 3 1.00 21 0.143
71 A 3 3 1.00 26 0.115
72 A 3 3 1.00 31 0.097
73 A 3 3 1.00 36 0.083
74 A 3 3 1.00 41 0.073
75 A 3 3 1.00 46 0.065
76 A 3 3 1.00 16 0.188
77 A 3 3 1.00 21 0.143
78 A 3 3 1.00 26 0.115
79 A 3 3 1.00 31 0.097
80 A 3 3 1.00 36 0.083
81 A 3 3 1.00 41 0.073
82 A 3 3 1.00 26 0.115
83 A 3 3 1.00 31 0.097
84 A 3 3 1.00 36 0.083
85 A 3 3 1.00 41 0.073
86 A 3 3 1.00 46 0.065
87 A 3 3 1.00 51 0.059
88 A 3 3 1.00 21 0.143
89 A 7 7 1.06 26 0.269
90 A 7 7 1.05 31 0.226
91 A 3 3 0.97 36 0.083
92 A 3 3 0.96 41 0.073
93 A 3 3 0.96 46 0.065
94 A 3 3 1.00 16 0.188
95 A 3 3 1.00 21 0.143
96 A 3 3 1.00 26 0.115
97 A 3 3 1.00 31 0.097
98 A 3 3 1.00 36 0.083
99 A 3 3 1.00 41 0.073
100 A 15 14 0.96 32 0.438
101 A 12 11 0.99 32 0.344
102 A 10 9 1.01 32 0.281
103 A 9 8 0.97 32 0.250
104 A 13 12 0.96 32 0.375
105 A 1 1 1.00 28 0.036
106 A 6 5 1.00 31 0.161
107 A 6 5 1.00 33 0.152
108 A 5 4 1.00 36 0.111

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