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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 [32] had the largest ratio of [40]

# 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 4 4 1.00 12 0.333
2 A 4 4 1.00 14 0.286
3 A 6 4 1.00 25 0.160
4 A 5 4 1.00 25 0.160
5 A 4 4 1.00 23 0.174
6 A 8 8 1.00 25 0.320
7 A 2 2 1.00 25 0.080
8 A 3 3 1.00 25 0.120
9 A 4 3 1.00 25 0.120
10 A 5 3 1.00 25 0.120
11 A 4 3 1.00 25 0.120
12 A 4 3 1.00 25 0.120
13 A 4 3 1.00 25 0.120
14 A 2 2 1.00 21 0.095
15 A 4 4 1.00 25 0.160
16 A 5 5 1.00 25 0.200
17 A 6 5 1.00 25 0.200
18 A 6 4 1.00 27 0.148
19 A 5 4 1.00 27 0.148
20 A 4 4 1.00 27 0.148
21 A 3 3 1.00 27 0.111
22 A 4 4 1.00 27 0.148
23 A 5 4 1.00 27 0.148
24 A 6 4 1.00 27 0.148
25 A 7 6 1.00 27 0.222
26 A 6 6 1.00 27 0.222
27 A 5 5 1.00 27 0.185
28 A 6 6 1.00 27 0.222
29 A 7 6 1.00 27 0.222
30 A 8 7 1.00 11 0.636
31 A 0 0 0.00 0 0.000
32 A 9 7 1.00 40 0.175
33 A 7 6 1.00 40 0.150
34 A 4 4 1.00 38 0.105
35 A 0 0 0.00 0 0.000
36 A 0 0 0.00 0 0.000
37 A 2 2 1.00 11 0.182
38 A 2 2 1.00 11 0.182
39 A 2 2 1.00 9 0.222
40 A 2 2 1.00 7 0.286
41 A 2 2 1.00 11 0.182
42 A 2 2 1.00 11 0.182
43 A 2 2 1.00 11 0.182
44 A 2 2 1.00 9 0.222
45 A 2 2 1.00 7 0.286
46 A 2 2 1.00 11 0.182
47 A 2 2 1.00 7 0.286
48 A 11 6 1.00 15 0.400
49 A 9 5 1.00 13 0.385
50 A 7 4 1.00 11 0.364
51 A 0 0 0.00 0 0.000
52 A 7 7 1.00 21 0.333
53 A 6 6 1.00 19 0.316
54 A 5 5 1.00 17 0.294
55 A 0 0 0.00 0 0.000
56 A 7 7 1.00 21 0.333
57 A 6 6 1.00 19 0.316
58 A 5 5 1.00 17 0.294
59 A 0 0 0.00 0 0.000
60 A 2 2 1.00 7 0.286
61 A 11 6 1.00 15 0.400
62 A 9 5 1.00 13 0.385
63 A 7 4 1.00 11 0.364
64 A 0 0 0.00 0 0.000
65 A 7 7 1.00 21 0.333
66 A 6 6 1.00 19 0.316
67 A 5 5 1.00 17 0.294
68 A 0 0 0.00 0 0.000
69 A 7 7 1.00 21 0.333
70 A 6 6 1.00 19 0.316
71 A 5 5 1.00 17 0.294
72 A 0 0 0.00 0 0.000
73 A 6 4 1.00 3 1.333
74 A 8 5 1.00 5 1.000
75 A 10 6 1.00 7 0.857
76 A 12 6 1.00 15 0.400
77 A 10 6 1.00 15 0.400
78 A 8 5 1.00 13 0.385
79 A 6 4 1.00 7 0.571
80 A 0 0 0.00 0 0.000
81 A 11 6 1.00 15 0.400
82 A 9 5 1.00 13 0.385
83 A 7 4 1.00 11 0.364
84 A 0 0 0.00 0 0.000
85 A 7 7 1.00 19 0.368
86 A 6 6 1.00 17 0.353
87 A 5 5 1.00 15 0.333
88 A 0 0 0.00 0 0.000
89 A 7 7 1.00 22 0.318
90 A 6 6 1.00 20 0.300
91 A 5 5 1.00 18 0.278
92 A 0 0 0.00 0 0.000
93 A 12 6 1.00 15 0.400
94 A 10 6 1.00 15 0.400
95 A 8 5 1.00 13 0.385
96 A 6 4 1.00 7 0.571
97 A 0 0 0.00 0 0.000
98 A 11 6 1.00 15 0.400
99 A 9 5 1.00 13 0.385
100 A 7 4 1.00 11 0.364
101 A 0 0 0.00 0 0.000
102 A 7 7 1.00 19 0.368
103 A 6 6 1.00 17 0.353
104 A 5 5 1.00 15 0.333
105 A 0 0 0.00 0 0.000
106 A 7 7 1.00 22 0.318
107 A 6 6 1.00 20 0.300
108 A 5 5 1.00 18 0.278
109 A 0 0 0.00 0 0.000
110 A 4 3 1.00 4 0.750
111 A 7 4 1.00 6 0.667
112 A 9 5 1.00 8 0.625
113 A 4 3 1.00 8 0.375
114 A 7 4 1.00 10 0.400
115 A 9 5 1.00 12 0.417
116 A 6 6 1.00 12 0.500
117 A 9 5 1.08 14 0.357
118 A 11 6 1.04 16 0.375
119 A 5 6 1.00 10 0.600
120 A 5 4 1.00 8 0.500
121 A 9 8 1.00 14 0.571
122 A 4 4 1.00 8 0.500
123 A 1 1 1.00 14 0.071
124 A 1 1 1.00 19 0.053
125 A 5 3 1.00 26 0.115
126 A 9 6 1.00 21 0.286
127 A 8 6 1.00 21 0.286
128 A 7 6 1.00 19 0.316
129 A 6 6 1.00 18 0.333
130 A 6 5 1.00 21 0.238
131 A 6 6 1.00 21 0.286
132 A 7 6 1.00 21 0.286
133 A 8 6 1.00 21 0.286
134 A 2 2 1.00 39 0.051
135 A 2 2 1.00 39 0.051
136 A 2 2 1.00 37 0.054
137 A 2 2 1.00 39 0.051
138 A 2 2 1.00 39 0.051
139 A 2 2 1.00 39 0.051
140 A 2 2 1.00 40 0.050
141 A 2 2 1.00 40 0.050
142 A 2 2 1.00 38 0.053
143 A 2 2 1.00 40 0.050
144 A 2 2 1.00 40 0.050
145 A 2 2 1.00 40 0.050
146 A 9 7 1.00 24 0.292
147 A 5 5 1.00 20 0.250
148 A 8 7 1.00 20 0.350
149 A 13 10 1.00 20 0.500
150 A 13 10 1.00 20 0.500
151 A 8 7 1.00 20 0.350
152 A 5 5 1.00 20 0.250
153 A 13 9 1.00 24 0.375

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