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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 [49] had the largest ratio of [19]

# 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 11 4 1.00 15 0.267
2 A 9 4 1.00 15 0.267
3 A 7 4 1.00 13 0.308
4 A 2 2 1.00 12 0.167
5 A 6 5 1.00 15 0.333
6 A 9 5 1.00 15 0.333
7 A 11 5 1.00 15 0.333
8 A 13 5 1.00 15 0.333
9 A 15 5 1.00 15 0.333
10 A 14 4 1.00 17 0.235
11 A 11 4 1.00 15 0.267
12 A 3 2 1.00 14 0.143
13 A 8 7 1.00 17 0.412
14 A 10 6 1.00 17 0.353
15 A 14 5 1.00 17 0.294
16 A 17 5 1.00 17 0.294
17 A 20 5 1.00 17 0.294
18 A 15 7 1.00 17 0.412
19 A 11 7 1.00 17 0.412
20 A 8 7 1.00 17 0.412
21 A 6 5 1.00 15 0.333
22 A 3 3 1.00 14 0.214
23 A 8 4 1.00 17 0.235
24 A 12 5 1.00 17 0.294
25 A 17 5 1.00 17 0.294
26 A 15 8 1.00 17 0.471
27 A 12 8 1.00 17 0.471
28 A 10 6 1.00 17 0.353
29 A 9 5 1.00 15 0.333
30 A 4 4 1.00 14 0.286
31 A 12 5 1.00 17 0.294
32 A 16 5 1.00 17 0.294
33 A 15 6 1.00 17 0.353
34 A 14 5 1.00 17 0.294
35 A 11 5 1.00 15 0.333
36 A 5 4 1.00 14 0.286
37 A 17 5 1.00 17 0.294
38 A 21 5 1.00 17 0.294
39 A 26 5 1.00 17 0.294
40 A 12 3 1.00 17 0.176
41 A 10 3 1.00 17 0.176
42 A 8 3 1.00 15 0.200
43 A 6 3 1.00 14 0.214
44 A 7 6 1.00 17 0.353
45 A 7 6 1.00 17 0.353
46 A 10 5 1.00 17 0.294
47 A 12 5 1.00 17 0.294
48 A 14 5 1.00 17 0.294
49 A 17 3 1.00 19 0.158
50 A 14 3 1.00 17 0.176
51 A 11 3 1.00 16 0.188
52 A 11 6 1.00 19 0.316
53 A 10 7 1.00 19 0.368
54 A 12 7 1.00 19 0.368
55 A 13 6 1.00 19 0.316
56 A 17 5 1.00 19 0.263
57 A 14 7 1.00 19 0.368
58 A 12 6 1.00 19 0.316
59 A 11 6 1.00 19 0.316
60 A 8 4 1.00 17 0.235
61 A 8 4 1.00 16 0.250
62 A 13 4 1.00 19 0.210
63 A 14 6 1.00 19 0.316
64 A 18 5 1.00 19 0.263
65 A 24 9 1.00 19 0.474
66 A 20 8 1.00 19 0.421
67 A 17 6 1.00 19 0.316
68 A 9 5 1.00 17 0.294
69 A 18 5 1.00 16 0.312
70 A 22 6 1.00 19 0.316
71 A 32 6 1.00 19 0.316
72 A 27 8 1.00 19 0.421
73 A 28 7 1.00 19 0.368
74 A 19 6 1.00 17 0.353
75 A 28 5 1.00 16 0.312
76 A 41 7 1.00 19 0.368
77 A 60 6 1.00 19 0.316
78 A 46 7 1.00 19 0.368
79 A 13 4 1.00 17 0.235
80 A 11 4 1.00 17 0.235
81 A 9 4 1.00 15 0.267
82 A 7 4 1.00 14 0.286
83 A 8 6 1.00 17 0.353
84 A 8 7 1.00 17 0.412
85 A 8 6 1.00 17 0.353
86 A 11 5 1.00 17 0.294
87 A 17 4 1.00 17 0.235
88 A 14 4 1.00 16 0.250
89 A 14 7 1.00 19 0.368
90 A 13 8 1.00 19 0.421
91 A 12 8 1.00 19 0.421
92 A 14 7 1.00 19 0.368
93 A 15 7 1.00 19 0.368
94 A 15 6 1.00 19 0.316
95 A 14 6 1.00 19 0.316
96 A 11 4 1.00 19 0.210
97 A 11 4 1.00 17 0.235
98 A 11 4 1.00 16 0.250
99 A 16 4 1.00 19 0.210
100 A 17 5 1.00 19 0.263
101 A 18 6 1.00 19 0.316
102 A 23 6 1.00 19 0.316
103 A 12 5 1.00 19 0.263
104 A 34 7 1.00 17 0.412
105 A 36 8 1.00 16 0.500
106 A 41 8 1.00 19 0.421
107 A 47 7 1.00 19 0.368
108 A 51 8 1.00 19 0.421
109 A 71 10 1.00 19 0.526
110 A 37 9 1.00 19 0.474
111 A 89 9 1.00 17 0.529
112 A 99 10 1.00 16 0.625
113 A 110 9 1.00 19 0.474

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