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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 [131] had the largest ratio of [42]

# 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 1 1.00 26 0.038
2 A 2 1 1.00 24 0.042
3 A 2 1 1.00 23 0.043
4 A 2 1 1.00 26 0.038
5 A 2 1 1.00 26 0.038
6 A 2 1 1.00 26 0.038
7 A 2 1 1.00 26 0.038
8 A 2 1 1.00 26 0.038
9 A 2 1 1.00 26 0.038
10 A 2 1 1.00 26 0.038
11 A 2 1 1.00 28 0.036
12 A 2 1 1.00 26 0.038
13 A 2 1 1.00 25 0.040
14 A 2 1 1.00 28 0.036
15 A 2 1 1.00 28 0.036
16 A 2 1 1.00 28 0.036
17 A 2 1 1.00 28 0.036
18 A 2 1 1.00 28 0.036
19 A 2 1 1.00 28 0.036
20 A 2 1 1.00 28 0.036
21 A 13 11 1.00 28 0.393
22 A 12 11 1.00 28 0.393
23 A 11 10 1.00 28 0.357
24 A 10 9 1.00 26 0.346
25 A 8 7 1.00 25 0.280
26 A 12 10 1.00 28 0.357
27 A 13 12 1.00 28 0.429
28 A 13 11 1.00 28 0.393
29 A 11 10 1.00 28 0.357
30 A 10 9 1.00 28 0.321
31 A 10 9 1.00 28 0.321
32 A 10 9 1.00 26 0.346
33 A 10 9 1.00 25 0.360
34 A 14 12 1.00 28 0.429
35 A 15 13 1.00 28 0.464
36 A 15 13 1.00 28 0.464
37 A 2 1 1.00 30 0.033
38 A 2 1 1.00 30 0.033
39 A 2 1 1.00 28 0.036
40 A 8 5 1.00 30 0.167
41 A 10 6 0.98 30 0.200
42 A 10 9 1.00 28 0.321
43 A 11 10 1.00 30 0.333
44 A 11 10 1.00 31 0.323
45 A 11 10 1.00 34 0.294
46 A 11 10 1.00 34 0.294
47 A 7 6 1.00 30 0.200
48 A 7 6 1.00 30 0.200
49 A 7 6 1.00 30 0.200
50 A 7 6 1.00 28 0.214
51 A 7 6 1.00 30 0.200
52 A 7 6 1.00 30 0.200
53 A 7 6 1.00 30 0.200
54 A 7 6 1.00 30 0.200
55 A 5 3 1.00 30 0.100
56 A 5 3 1.00 30 0.100
57 A 5 3 1.00 27 0.111
58 A 5 3 1.00 30 0.100
59 A 5 3 1.00 30 0.100
60 A 5 3 1.00 30 0.100
61 A 8 7 1.00 30 0.233
62 A 7 7 1.00 30 0.233
63 A 6 6 1.00 30 0.200
64 A 5 5 1.00 28 0.179
65 A 8 7 1.00 30 0.233
66 A 8 7 1.00 30 0.233
67 A 8 7 1.00 30 0.233
68 A 6 4 1.00 30 0.133
69 A 6 4 1.00 30 0.133
70 A 4 3 1.00 30 0.100
71 A 4 3 1.00 27 0.111
72 A 6 4 1.00 30 0.133
73 A 6 4 1.00 30 0.133
74 A 7 5 1.00 31 0.161
75 A 7 5 1.00 31 0.161
76 A 7 5 1.00 31 0.161
77 A 7 5 1.00 31 0.161
78 A 5 4 1.00 29 0.138
79 A 4 3 1.00 31 0.097
80 A 4 3 1.00 31 0.097
81 A 4 3 1.00 31 0.097
82 A 6 4 1.00 31 0.129
83 A 6 4 1.00 31 0.129
84 A 6 4 1.00 31 0.129
85 A 6 4 1.00 31 0.129
86 A 4 3 1.00 28 0.107
87 A 5 3 1.00 31 0.097
88 A 5 3 1.00 31 0.097
89 A 5 3 1.00 31 0.097
90 A 5 3 1.00 31 0.097
91 A 7 5 1.00 31 0.161
92 A 7 5 1.00 31 0.161
93 A 7 5 1.00 31 0.161
94 A 5 4 1.00 31 0.129
95 A 5 4 1.00 31 0.129
96 A 5 4 1.00 28 0.143
97 A 6 3 1.00 31 0.097
98 A 6 3 1.00 31 0.097
99 A 6 3 1.00 31 0.097
100 A 8 7 1.00 31 0.226
101 A 8 7 1.00 31 0.226
102 A 8 7 1.00 31 0.226
103 A 8 7 1.00 31 0.226
104 A 6 6 1.00 29 0.207
105 A 8 7 1.00 31 0.226
106 A 8 7 1.00 31 0.226
107 A 8 7 1.00 31 0.226
108 A 8 7 1.00 31 0.226
109 A 12 7 1.00 31 0.226
110 A 12 7 1.00 31 0.226
111 A 12 7 1.00 31 0.226
112 A 12 7 1.00 31 0.226
113 A 10 6 1.00 28 0.214
114 A 12 7 1.00 31 0.226
115 A 12 7 1.00 31 0.226
116 A 12 7 1.00 31 0.226
117 A 13 8 1.00 31 0.258
118 A 13 8 1.00 31 0.258
119 A 13 8 1.00 31 0.258
120 A 11 7 1.00 31 0.226
121 A 11 7 1.00 31 0.226
122 A 11 7 1.00 28 0.250
123 A 13 7 1.00 31 0.226
124 A 13 7 1.00 31 0.226
125 A 7 6 1.00 33 0.182
126 A 6 4 1.00 35 0.114
127 A 6 4 1.00 35 0.114
128 A 4 3 1.00 32 0.094
129 A 6 4 1.00 35 0.114
130 A 6 4 1.00 35 0.114
131 A 1 1 1.00 42 0.024
132 A 5 4 1.32 35 0.114
133 A 4 3 1.34 35 0.086
134 A 4 3 1.37 33 0.091
135 A 6 5 1.62 35 0.143
136 A 6 6 1.57 35 0.171
137 A 6 6 1.44 35 0.171
138 A 7 7 1.17 35 0.200
139 A 6 6 1.13 35 0.171
140 A 5 5 1.40 32 0.156
141 A 5 5 1.52 35 0.143
142 A 5 5 1.00 35 0.143
143 A 4 4 1.00 35 0.114
144 A 5 5 1.00 35 0.143
145 A 6 5 1.00 35 0.143

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