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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 [5] had the largest ratio of [.380952000000000013]

# 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 6 5 0.75 21 0.238
2 A 5 4 0.93 21 0.190
3 A 7 6 0.67 21 0.286
4 A 5 4 1.05 19 0.211
5 A 9 8 1.22 21 0.381
6 F 0 0 N/A 0.000 N/A
7 F 0 0 N/A 0.000 N/A
8 F 0 0 N/A 0.000 N/A
9 F 0 0 N/A 0.000 N/A
10 F 0 0 N/A 0.000 N/A
11 F 0 0 N/A 0.000 N/A
12 F 0 0 N/A 0.000 N/A
13 F 0 0 N/A 0.000 N/A
14 F 0 0 N/A 0.000 N/A
15 F 0 0 N/A 0.000 N/A
16 F 0 0 N/A 0.000 N/A
17 F 0 0 N/A 0.000 N/A
18 A 6 5 0.75 21 0.238
19 A 5 4 0.93 21 0.190
20 A 7 6 0.67 21 0.286
21 A 5 4 1.05 19 0.211
22 A 9 8 1.27 21 0.381
23 F 0 0 N/A 0.000 N/A
24 F 0 0 N/A 0.000 N/A
25 F 0 0 N/A 0.000 N/A
26 F 0 0 N/A 0.000 N/A
27 F 0 0 N/A 0.000 N/A
28 F 0 0 N/A 0.000 N/A
29 F 0 0 N/A 0.000 N/A
30 F 0 0 N/A 0.000 N/A
31 F 0 0 N/A 0.000 N/A
32 F 0 0 N/A 0.000 N/A
33 F 0 0 N/A 0.000 N/A
34 F 0 0 N/A 0.000 N/A
35 F 0 0 N/A 0.000 N/A
36 F 0 0 N/A 0.000 N/A
37 A 6 5 0.92 30 0.167
38 A 5 4 0.92 30 0.133
39 A 7 6 0.94 30 0.200
40 A 5 4 0.95 28 0.143
41 A 6 5 0.80 30 0.167
42 A 5 4 0.90 30 0.133
43 A 6 5 0.95 30 0.167
44 F 0 0 N/A 0.000 N/A
45 F 0 0 N/A 0.000 N/A
46 F 0 0 N/A 0.000 N/A
47 F 0 0 N/A 0.000 N/A
48 F 0 0 N/A 0.000 N/A
49 C 5 4 1.56 30 0.133
50 C 5 4 1.84 30 0.133
51 C 5 4 1.80 30 0.133
52 C 2 2 2.53 28 0.071
53 C 5 4 1.15 30 0.133
54 C 6 5 1.32 30 0.167
55 C 7 6 1.56 30 0.200
56 C 5 5 1.86 30 0.167
57 C 4 4 1.63 30 0.133
58 A 3 2 1.00 27 0.074
59 C 2 2 2.23 30 0.067
60 C 3 3 4.29 30 0.100
61 C 4 4 3.20 30 0.133
62 C 5 5 2.89 30 0.167
63 C 6 6 2.73 30 0.200
64 F 0 0 N/A 0.000 N/A
65 F 0 0 N/A 0.000 N/A
66 F 0 0 N/A 0.000 N/A
67 F 0 0 N/A 0.000 N/A
68 F 0 0 N/A 0.000 N/A
69 F 0 0 N/A 0.000 N/A
70 F 0 0 N/A 0.000 N/A
71 F 0 0 N/A 0.000 N/A
72 F 0 0 N/A 0.000 N/A
73 A 6 5 0.90 30 0.167
74 A 5 4 0.94 30 0.133
75 A 6 5 0.98 30 0.167
76 A 4 3 1.00 28 0.107
77 A 8 7 1.15 30 0.233
78 F 0 0 N/A 0.000 N/A
79 F 0 0 N/A 0.000 N/A
80 F 0 0 N/A 0.000 N/A
81 F 0 0 N/A 0.000 N/A
82 F 0 0 N/A 0.000 N/A
83 F 0 0 N/A 0.000 N/A
84 A 1 1 1.00 30 0.033
85 F 0 0 N/A 0.000 N/A
86 F 0 0 N/A 0.000 N/A
87 F 0 0 N/A 0.000 N/A
88 F 0 0 N/A 0.000 N/A
89 C 5 5 1.32 32 0.156
90 C 4 4 1.69 30 0.133
91 A 3 2 1.00 27 0.074
92 C 4 3 0.35 32 0.094
93 C 5 5 1.23 34 0.147
94 C 4 4 1.51 32 0.125
95 A 3 2 1.00 29 0.069
96 C 4 3 0.33 34 0.088
97 C 2 2 1.17 34 0.059
98 C 2 2 1.18 36 0.056

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