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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 [83] had the largest ratio of [51]

# 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 1 1 1.00 10 0.100
2 C 5 2 3.47 37 0.054
3 A 9 6 1.00 15 0.400
4 A 3 3 1.00 19 0.158
5 A 8 7 1.00 17 0.412
6 A 6 6 1.00 17 0.353
7 A 3 3 1.00 17 0.176
8 A 4 2 1.00 23 0.087
9 A 18 12 1.66 27 0.444
10 B 25 13 2.46 39 0.333
11 A 7 3 1.00 45 0.067
12 A 7 4 1.00 32 0.125
13 A 5 3 1.00 32 0.094
14 A 2 2 1.00 27 0.074
15 A 2 2 1.00 29 0.069
16 A 2 1 1.00 30 0.033
17 A 3 2 1.00 13 0.154
18 A 3 2 1.00 15 0.133
19 A 2 2 1.00 23 0.087
20 A 2 2 1.00 25 0.080
21 A 3 2 1.00 11 0.182
22 A 2 2 1.00 18 0.111
23 A 6 6 1.00 20 0.300
24 A 6 5 1.00 31 0.161
25 A 2 2 1.00 29 0.069
26 A 2 2 1.00 35 0.057
27 A 5 5 1.00 32 0.156
28 A 6 6 1.00 21 0.286
29 A 359 30 1.00 14 2.143
30 A 2 2 1.00 23 0.087
31 A 3 2 1.00 13 0.154
32 A 2 2 1.00 33 0.061
33 A 5 5 1.00 15 0.333
34 A 5 5 1.00 15 0.333
35 A 1 1 1.00 11 0.091
36 A 5 5 1.00 15 0.333
37 A 1 1 1.00 17 0.059
38 A 3 3 1.00 18 0.167
39 A 2 2 1.60 16 0.125
40 A 5 5 1.62 17 0.294
41 A 5 5 1.77 13 0.385
42 A 5 5 1.84 16 0.312
43 F 0 0 N/A 0 N/A
44 F 0 0 N/A 0 N/A
45 F 0 0 N/A 0 N/A
46 A 19 14 1.16 32 0.438
47 A 19 9 1.00 20 0.450
48 A 29 9 1.00 20 0.450
49 A 49 9 1.00 20 0.450
50 A 14 6 1.00 23 0.261
51 A 24 6 1.00 23 0.261
52 C 9 8 3.09 48 0.167
53 A 7 7 1.00 24 0.292
54 A 7 7 1.00 24 0.292
55 A 1 1 1.00 18 0.056
56 A 2 2 1.00 13 0.154
57 A 6 6 1.00 15 0.400
58 A 25 15 1.00 17 0.882
59 A 19 12 1.46 22 0.546
60 A 12 11 1.00 17 0.647
61 A 9 8 1.00 21 0.381
62 A 1 1 1.00 38 0.026
63 A 1 1 1.00 33 0.030
64 A 2 2 1.00 38 0.053
65 A 1 1 1.00 19 0.053
66 A 4 4 1.00 19 0.210
67 A 4 4 1.00 24 0.167
68 A 1 1 1.00 24 0.042
69 A 7 7 1.00 24 0.292
70 A 7 7 1.00 24 0.292
71 A 3 3 1.00 26 0.115
72 A 3 3 1.00 22 0.136
73 A 1 1 1.00 22 0.045
74 A 1 1 1.00 23 0.043
75 A 8 8 1.00 18 0.444
76 A 8 7 1.00 23 0.304
77 A 1 1 1.00 21 0.048
78 A 1 1 1.00 19 0.053
79 A 1 1 1.00 19 0.053
80 A 1 1 1.00 19 0.053
81 A 4 4 1.00 34 0.118
82 C 5 5 529.00 40 0.125
83 C 7 7 3.91 51 0.137
84 A 2 2 1.00 29 0.069
85 A 2 2 1.00 18 0.111
86 A 1 1 1.00 25 0.040
87 A 1 1 1.00 25 0.040
88 A 1 1 1.00 25 0.040
89 A 1 1 1.00 25 0.040
90 A 2 2 1.00 40 0.050
91 A 2 2 1.00 40 0.050
92 A 1 1 1.00 18 0.056
93 A 3 3 1.00 15 0.200
94 A 1 1 1.00 21 0.048
95 A 8 7 1.00 23 0.304
96 A 5 5 1.00 24 0.208
97 A 1 1 1.00 19 0.053
98 A 8 8 1.00 20 0.400
99 A 5 5 1.00 22 0.227
100 B 16 12 2.84 25 0.480
101 B 17 13 2.84 24 0.542
102 B 16 12 3.00 23 0.522
103 A 5 4 1.00 20 0.200
104 A 5 4 1.00 25 0.160
105 A 3 3 1.00 19 0.158
106 A 2 2 1.00 11 0.182
107 A 6 6 1.00 15 0.400
108 A 13 12 1.00 19 0.632
109 A 13 12 1.00 22 0.546
110 A 14 12 1.26 27 0.444
111 A 5 5 1.00 17 0.294
112 A 6 6 1.00 27 0.222
113 A 3 3 1.00 19 0.158
114 A 10 10 1.00 20 0.500
115 A 17 6 1.69 24 0.250
116 A 14 8 1.00 19 0.421

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