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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 [71] had the largest ratio of [48]

# 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 3 2 1.00 4 0.500
2 A 3 2 1.00 11 0.182
3 A 2 1 1.00 11 0.091
4 A 1 1 1.00 2 0.500
5 A 1 1 1.00 7 0.143
6 A 2 2 1.00 7 0.286
7 A 1 1 1.00 11 0.091
8 A 1 1 1.00 6 0.167
9 A 2 2 1.00 7 0.286
10 A 2 2 1.00 4 0.500
11 A 1 1 1.00 6 0.167
12 A 3 2 1.00 6 0.333
13 A 4 2 1.00 16 0.125
14 A 5 3 1.00 7 0.429
15 A 3 1 1.00 14 0.071
16 A 2 2 1.00 5 0.400
17 A 1 1 1.00 7 0.143
18 A 1 1 1.00 11 0.091
19 A 2 2 1.00 11 0.182
20 A 1 1 1.00 5 0.200
21 A 1 1 1.00 6 0.167
22 A 2 2 1.00 9 0.222
23 A 3 3 1.00 14 0.214
24 A 2 1 1.00 9 0.111
25 A 3 3 1.00 7 0.429
26 A 2 2 1.00 15 0.133
27 A 2 2 1.00 17 0.118
28 A 3 3 1.00 13 0.231
29 A 1 1 1.00 5 0.200
30 A 3 3 1.00 8 0.375
31 A 7 7 1.00 11 0.636
32 A 3 2 1.00 12 0.167
33 A 3 3 1.00 6 0.500
34 A 2 1 1.00 9 0.111
35 A 4 3 1.00 13 0.231
36 A 4 4 1.00 15 0.267
37 A 3 2 1.00 15 0.133
38 A 6 3 1.00 13 0.231
39 A 3 2 1.00 15 0.133
40 A 5 5 1.00 29 0.172
41 A 2 2 1.00 4 0.500
42 A 6 6 1.16 19 0.316
43 A 1 1 1.00 6 0.167
44 A 2 2 1.00 5 0.400
45 A 1 1 1.00 10 0.100
46 A 5 3 1.00 13 0.231
47 A 1 1 1.00 5 0.200
48 A 1 1 1.00 7 0.143
49 A 6 6 1.00 9 0.667
50 A 10 6 1.55 7 0.857
51 A 1 1 1.00 27 0.037
52 A 1 1 1.00 4 0.250
53 A 4 3 1.00 6 0.500
54 A 2 2 1.00 10 0.200
55 A 7 4 1.00 9 0.444
56 A 2 1 1.00 12 0.083
57 A 1 1 1.00 4 0.250
58 A 6 4 1.00 7 0.571
59 A 4 3 1.00 11 0.273
60 A 6 3 1.00 9 0.333
61 A 2 2 1.00 4 0.500
62 A 3 3 1.00 6 0.500
63 A 2 2 1.00 4 0.500
64 A 2 2 1.00 6 0.333
65 A 2 1 1.00 9 0.111
66 A 2 1 1.00 12 0.083
67 A 2 2 1.00 20 0.100
68 A 2 2 1.00 10 0.200
69 A 6 6 1.00 30 0.200
70 A 5 5 1.00 39 0.128
71 A 6 5 1.00 48 0.104
72 A 4 4 1.00 31 0.129
73 A 3 2 1.00 15 0.133
74 A 3 2 1.00 4 0.500
75 A 3 2 1.00 11 0.182
76 A 5 3 1.00 13 0.231
77 A 10 6 1.00 33 0.182
78 A 1 1 1.00 7 0.143
79 A 5 5 1.00 8 0.625
80 A 2 2 1.00 9 0.222
81 A 3 3 1.00 11 0.273
82 A 3 3 1.00 8 0.375
83 A 3 2 1.00 15 0.133
84 A 2 2 1.00 16 0.125
85 A 1 1 1.00 6 0.167
86 A 1 1 1.00 3 0.333
87 A 4 2 1.00 17 0.118
88 A 2 2 1.00 4 0.500
89 A 2 1 1.00 11 0.091
90 A 3 3 1.00 14 0.214
91 A 2 2 1.00 7 0.286
92 A 2 2 1.00 11 0.182
93 A 3 2 1.00 13 0.154
94 A 1 1 1.00 8 0.125
95 A 2 2 1.00 7 0.286
96 A 1 1 1.00 4 0.250
97 A 2 2 1.00 5 0.400
98 A 3 3 1.00 17 0.176
99 A 3 3 1.00 16 0.188
100 A 3 2 1.00 15 0.133
101 A 3 3 1.00 15 0.200
102 A 3 3 1.00 8 0.375
103 A 1 1 1.00 20 0.050
104 A 1 1 1.00 25 0.040
105 A 1 1 1.00 26 0.038
106 A 1 1 1.00 31 0.032
107 A 1 1 1.00 24 0.042
108 A 1 1 1.00 29 0.034
109 A 1 1 1.00 18 0.056
110 A 1 1 1.00 23 0.043
111 A 1 1 1.00 24 0.042
112 A 1 1 1.00 29 0.034
113 A 1 1 1.00 27 0.037

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