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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 [22] had the largest ratio of [21]

# 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 5 4 1.00 13 0.308
2 A 9 7 1.00 13 0.538
3 A 5 4 1.00 13 0.308
4 A 8 6 1.00 11 0.546
5 A 8 7 1.00 11 0.636
6 A 3 2 1.00 13 0.154
7 A 8 7 1.00 13 0.538
8 A 4 3 1.00 13 0.231
9 A 9 8 1.00 13 0.615
10 A 4 3 1.00 13 0.231
11 A 8 5 1.00 19 0.263
12 A 6 4 1.00 19 0.210
13 A 8 5 1.00 19 0.263
14 A 5 4 1.00 19 0.210
15 A 6 5 1.00 17 0.294
16 A 4 2 1.00 17 0.118
17 A 3 1 1.00 19 0.053
18 A 7 6 1.00 19 0.316
19 A 3 1 1.00 19 0.053
20 A 9 6 1.00 19 0.316
21 A 3 1 1.00 19 0.053
22 A 8 6 1.00 21 0.286
23 A 11 7 1.00 21 0.333
24 A 6 6 1.00 21 0.286
25 A 9 7 1.00 19 0.368
26 A 6 4 1.00 19 0.210
27 A 3 2 1.00 21 0.095
28 A 10 7 1.00 21 0.333
29 A 3 2 1.00 21 0.095
30 A 13 9 1.00 21 0.429
31 A 3 2 1.00 21 0.095
32 A 16 8 1.00 21 0.381
33 A 7 6 1.00 21 0.286
34 A 13 8 1.00 19 0.421
35 A 8 5 1.00 19 0.263
36 A 3 2 1.00 21 0.095
37 A 12 7 1.00 21 0.333
38 A 3 2 1.00 21 0.095
39 A 17 9 1.00 21 0.429
40 A 3 2 1.00 21 0.095
41 A 19 8 1.00 21 0.381
42 A 7 6 1.00 21 0.286
43 A 16 9 1.00 19 0.474
44 A 10 5 1.00 19 0.263
45 A 3 2 1.00 21 0.095
46 A 14 9 1.00 21 0.429
47 A 3 2 1.00 21 0.095
48 A 21 9 1.00 21 0.429
49 A 3 2 1.00 21 0.095
50 A 25 9 1.00 21 0.429
51 A 13 9 1.00 21 0.429
52 A 8 6 1.00 21 0.286
53 A 10 9 1.00 21 0.429
54 A 7 6 1.00 21 0.286
55 A 6 6 1.00 19 0.316
56 A 6 5 1.00 19 0.263
57 A 3 2 1.00 21 0.095
58 A 15 11 1.00 21 0.524
59 A 3 2 1.00 21 0.095
60 A 3 2 1.00 21 0.095
61 A 9 6 1.00 21 0.286
62 A 8 6 1.00 21 0.286
63 A 7 6 1.00 21 0.286
64 A 3 2 1.00 21 0.095
65 A 3 2 1.00 21 0.095
66 A 3 2 1.00 21 0.095
67 A 9 6 1.00 21 0.286
68 A 8 6 1.00 21 0.286
69 A 7 6 1.00 21 0.286
70 A 3 2 1.00 21 0.095
71 A 3 2 1.00 21 0.095
72 A 3 2 1.00 21 0.095
73 A 8 6 1.00 21 0.286
74 A 7 6 1.00 21 0.286
75 A 3 2 1.00 21 0.095
76 A 3 2 1.00 21 0.095
77 A 3 2 1.00 21 0.095
78 A 6 5 1.00 9 0.556
79 A 8 5 1.00 21 0.238
80 A 6 5 1.00 21 0.238
81 A 5 4 1.00 19 0.210
82 A 14 6 1.00 21 0.286
83 A 0 0 0.00 0 0.000
84 A 7 4 1.00 21 0.190
85 A 6 4 1.00 21 0.190
86 A 2 2 1.00 21 0.095
87 A 4 4 1.00 21 0.190
88 A 0 0 0.00 0 0.000
89 A 0 0 0.00 0 0.000
90 A 0 0 0.00 0 0.000
91 A 0 0 0.00 0 0.000

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