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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 [48] had the largest ratio of [.750000000000000000]

# 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 17 0.059
2 A 5 5 1.21 17 0.294
3 A 4 4 1.18 17 0.235
4 A 3 3 1.13 17 0.176
5 A 2 2 1.00 15 0.133
6 A 1 1 1.00 9 0.111
7 A 1 1 1.00 17 0.059
8 A 2 2 1.00 17 0.118
9 A 3 3 0.97 17 0.176
10 A 4 4 0.99 17 0.235
11 A 5 5 1.01 17 0.294
12 A 6 6 1.21 48 0.125
13 A 5 5 1.18 37 0.135
14 A 4 4 1.13 26 0.154
15 A 3 3 1.00 28 0.107
16 A 4 4 0.97 39 0.103
17 A 5 5 0.99 50 0.100
18 A 6 6 1.01 61 0.098
19 A 2 2 1.00 19 0.105
20 A 2 2 1.00 50 0.040
21 A 2 2 1.00 39 0.051
22 A 2 2 1.00 28 0.071
23 A 1 1 1.00 17 0.059
24 A 1 1 1.00 19 0.053
25 A 2 2 1.00 30 0.067
26 A 2 2 1.00 41 0.049
27 A 1 1 1.00 7 0.143
28 A 1 1 1.00 7 0.143
29 A 1 1 1.00 7 0.143
30 A 7 6 1.21 13 0.462
31 A 6 5 1.17 13 0.385
32 A 5 4 1.11 13 0.308
33 A 4 3 1.00 13 0.231
34 A 3 2 1.00 13 0.154
35 A 4 3 1.00 13 0.231
36 A 5 4 1.01 13 0.308
37 A 6 5 1.02 13 0.385
38 A 7 6 1.02 13 0.462
39 A 7 6 1.15 19 0.316
40 A 6 5 1.13 19 0.263
41 A 5 4 1.09 19 0.211
42 A 4 3 1.00 19 0.158
43 A 3 2 1.00 19 0.105
44 A 4 3 1.00 19 0.158
45 A 5 4 1.03 19 0.211
46 A 6 5 1.04 19 0.263
47 A 7 6 1.04 19 0.316
48 A 10 9 1.24 12 0.750
49 A 1 1 1.00 19 0.053
50 A 2 2 1.00 21 0.095
51 A 2 2 1.00 15 0.133
52 A 2 2 1.00 20 0.100
53 A 2 2 1.00 25 0.080
54 A 2 2 1.00 30 0.067
55 A 2 2 1.00 21 0.095
56 A 2 2 1.00 21 0.095
57 A 2 2 1.00 21 0.095
58 A 2 2 1.00 19 0.105
59 A 4 4 1.08 18 0.222
60 A 2 2 1.00 21 0.095
61 A 2 2 1.00 21 0.095
62 A 2 2 1.00 21 0.095
63 A 2 2 1.00 21 0.095
64 A 2 2 1.00 22 0.091
65 A 2 2 1.00 22 0.091
66 A 2 2 1.00 22 0.091
67 A 2 2 1.00 20 0.100
68 A 4 4 1.12 19 0.211
69 A 2 2 1.00 22 0.091
70 A 2 2 1.00 22 0.091
71 A 2 2 1.00 22 0.091
72 A 2 2 1.00 22 0.091
73 A 2 2 1.00 22 0.091
74 A 2 2 1.00 25 0.080
75 A 2 2 1.00 25 0.080
76 A 2 2 1.00 23 0.087
77 A 5 5 1.09 18 0.278
78 A 2 2 1.00 25 0.080
79 A 2 2 1.00 25 0.080
80 A 2 2 1.00 25 0.080
81 A 2 2 1.00 25 0.080
82 A 2 2 1.00 25 0.080
83 A 1 1 1.00 39 0.026
84 A 1 1 1.00 38 0.026
85 A 1 1 1.00 36 0.028
86 A 1 1 1.00 35 0.029
87 A 1 1 1.00 35 0.029
88 A 1 1 1.00 38 0.026
89 A 1 1 1.00 38 0.026
90 A 5 5 1.20 15 0.333
91 A 4 4 1.17 15 0.267
92 A 3 3 1.11 15 0.200
93 A 2 2 1.00 13 0.154
94 A 1 1 1.00 11 0.091
95 A 2 2 1.44 15 0.133
96 A 3 3 1.25 15 0.200
97 A 4 4 1.18 15 0.267
98 A 5 5 1.17 15 0.333

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