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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 [36] had the largest ratio of [.928571000000000035]

# 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 2 2 1.00 15 0.133
2 A 2 2 1.00 15 0.133
3 A 2 2 1.00 13 0.154
4 A 6 6 1.00 12 0.500
5 A 2 2 1.00 15 0.133
6 A 2 2 1.00 15 0.133
7 A 2 2 1.00 15 0.133
8 A 2 2 1.00 15 0.133
9 A 2 2 1.00 15 0.133
10 A 2 2 1.00 17 0.118
11 A 2 2 1.00 15 0.133
12 C 8 8 1.20 14 0.571
13 A 2 2 1.00 17 0.118
14 A 2 2 1.00 17 0.118
15 A 2 2 1.00 17 0.118
16 A 2 2 1.00 17 0.118
17 A 2 2 1.00 17 0.118
18 A 2 2 1.00 17 0.118
19 A 2 2 1.00 17 0.118
20 A 2 2 1.00 17 0.118
21 A 2 2 1.00 15 0.133
22 A 7 7 1.00 14 0.500
23 A 2 2 1.00 17 0.118
24 A 2 2 1.00 17 0.118
25 A 2 2 1.00 17 0.118
26 A 2 2 1.00 17 0.118
27 A 2 2 1.00 17 0.118
28 A 2 2 1.00 17 0.118
29 A 2 2 1.00 15 0.133
30 C 11 11 1.18 14 0.786
31 A 2 2 1.00 17 0.118
32 A 2 2 1.00 17 0.118
33 A 2 2 1.00 17 0.118
34 A 2 2 1.00 17 0.118
35 A 2 2 1.00 15 0.133
36 C 13 13 1.07 14 0.929
37 A 2 2 1.00 17 0.118
38 A 2 2 1.00 17 0.118
39 A 2 2 1.00 17 0.118
40 A 2 2 1.00 17 0.118
41 A 2 2 1.00 17 0.118
42 A 2 2 1.00 15 0.133
43 A 2 2 1.00 14 0.143
44 A 2 2 1.00 17 0.118
45 A 2 2 1.00 17 0.118
46 A 2 2 1.00 17 0.118
47 A 2 2 1.00 17 0.118
48 A 2 2 1.00 17 0.118
49 A 2 2 1.00 19 0.105
50 A 2 2 1.00 17 0.118
51 A 2 2 1.00 16 0.125
52 A 2 2 1.00 19 0.105
53 A 2 2 1.00 19 0.105
54 A 2 2 1.00 19 0.105
55 A 2 2 1.00 19 0.105
56 A 2 2 1.00 19 0.105
57 A 2 2 1.00 19 0.105
58 A 2 2 1.00 19 0.105
59 A 2 2 1.00 19 0.105
60 A 2 2 1.00 17 0.118
61 A 2 2 1.00 16 0.125
62 A 2 2 1.00 19 0.105
63 A 2 2 1.00 19 0.105
64 A 2 2 1.00 19 0.105
65 A 5 5 1.06 19 0.263
66 A 5 5 1.02 19 0.263
67 A 5 5 1.03 19 0.263
68 A 3 3 1.02 17 0.176
69 A 2 2 1.00 16 0.125
70 A 2 2 1.00 19 0.105
71 A 2 2 1.00 19 0.105
72 A 9 9 1.50 19 0.474
73 A 6 6 1.02 19 0.316
74 A 3 3 0.99 17 0.176
75 A 2 2 1.00 16 0.125
76 A 2 2 1.00 19 0.105
77 A 2 2 1.00 19 0.105
78 A 2 2 1.00 19 0.105
79 A 2 2 1.00 17 0.118
80 A 2 2 1.00 17 0.118
81 A 2 2 1.00 15 0.133
82 A 2 2 1.00 14 0.143
83 A 2 2 1.00 17 0.118
84 A 2 2 1.00 17 0.118
85 A 2 2 1.00 17 0.118
86 A 2 2 1.00 17 0.118
87 A 2 2 1.00 17 0.118
88 A 2 2 1.00 16 0.125
89 A 2 2 1.00 19 0.105
90 A 2 2 1.00 19 0.105
91 A 2 2 1.00 19 0.105
92 A 2 2 1.00 19 0.105
93 A 2 2 1.00 19 0.105
94 A 2 2 1.00 19 0.105
95 A 2 2 1.00 19 0.105
96 A 2 2 1.00 19 0.105
97 A 2 2 1.00 17 0.118
98 A 2 2 1.00 16 0.125
99 A 2 2 1.00 19 0.105
100 A 2 2 1.00 19 0.105
101 A 2 2 1.00 19 0.105
102 A 5 5 1.02 19 0.263
103 A 3 3 1.01 19 0.158
104 A 5 5 1.04 17 0.294
105 A 5 5 1.13 16 0.312
106 A 5 5 1.21 19 0.263
107 A 9 9 1.46 19 0.474
108 A 9 9 1.03 19 0.474
109 B 7 7 2.06 19 0.368
110 A 6 6 1.10 19 0.316
111 A 7 7 1.58 17 0.412

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