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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 [16] had the largest ratio of [1.30000000000000004]

# 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 1.25 27 0.074
2 A 2 2 1.00 8 0.250
3 A 4 3 0.46 10 0.300
4 A 8 8 1.06 10 0.800
5 A 6 6 1.00 10 0.600
6 A 4 4 1.00 10 0.400
7 A 4 4 1.00 10 0.400
8 A 6 6 1.00 10 0.600
9 A 8 8 1.13 10 0.800
10 A 12 12 0.82 10 1.200
11 A 8 8 0.89 10 0.800
12 A 6 6 0.94 10 0.600
13 A 6 6 0.90 10 0.600
14 A 8 8 0.87 10 0.800
15 A 12 12 0.79 10 1.200
16 A 13 13 0.70 10 1.300
17 A 9 9 0.77 10 0.900
18 A 5 5 0.81 10 0.500
19 A 6 5 1.00 10 0.500
20 A 6 5 0.56 10 0.500
21 A 6 5 0.46 10 0.500
22 A 4 4 1.00 14 0.286
23 A 4 4 1.00 14 0.286
24 A 4 4 1.19 14 0.286
25 A 4 4 1.00 14 0.286
26 A 4 4 1.00 14 0.286
27 A 4 4 1.00 14 0.286
28 A 4 4 1.00 12 0.333
29 A 4 4 1.00 12 0.333
30 A 4 4 1.00 12 0.333
31 A 4 4 1.00 12 0.333
32 A 4 4 1.00 14 0.286
33 A 4 4 1.00 14 0.286
34 A 4 3 0.48 10 0.300
35 A 4 3 0.44 10 0.300
36 A 4 3 0.42 10 0.300
37 A 6 5 1.00 10 0.500
38 A 4 3 1.00 10 0.300
39 A 4 3 1.00 10 0.300
40 A 4 3 1.00 10 0.300
41 A 4 3 1.00 10 0.300
42 A 4 3 1.00 10 0.300
43 A 4 3 1.00 10 0.300
44 A 6 5 1.00 10 0.500
45 A 4 3 0.42 10 0.300
46 A 4 3 0.44 10 0.300
47 A 4 3 0.48 8 0.375
48 A 4 3 0.46 10 0.300
49 A 6 5 1.00 11 0.455
50 A 4 3 1.00 10 0.300
51 A 4 3 1.00 11 0.273
52 A 4 3 0.46 10 0.300
53 A 2 2 1.00 10 0.200
54 A 6 5 1.00 11 0.455
55 A 6 5 0.94 11 0.455
56 A 10 9 0.48 11 0.818
57 C 10 9 0.47 11 0.818
58 A 10 9 0.36 11 0.818
59 A 10 9 0.55 11 0.818
60 C 10 9 0.70 11 0.818
61 A 2 2 1.00 9 0.222
62 A 3 3 1.00 11 0.273
63 A 3 3 1.00 11 0.273
64 A 4 3 0.46 10 0.300
65 A 9 8 0.71 10 0.800
66 A 6 5 0.65 10 0.500
67 A 6 5 1.00 10 0.500
68 A 2 2 1.00 8 0.250
69 A 3 3 1.00 10 0.300
70 A 3 3 1.00 10 0.300
71 A 4 3 1.00 11 0.273
72 A 5 4 1.88 11 0.364
73 A 6 5 1.00 11 0.455
74 A 6 5 1.18 11 0.455
75 A 5 4 1.12 9 0.444
76 A 3 3 1.00 11 0.273
77 A 3 3 1.00 11 0.273
78 A 4 3 1.00 10 0.300
79 B 10 9 6.22 10 0.900
80 A 6 5 0.96 10 0.500
81 A 6 5 1.36 10 0.500
82 A 5 4 1.15 8 0.500
83 A 3 3 1.00 10 0.300
84 A 3 3 1.00 10 0.300
85 A 11 11 1.07 11 1.000
86 A 9 9 1.04 11 0.818
87 A 7 7 1.00 11 0.636
88 A 1 1 1.00 9 0.111
89 A 6 5 1.00 11 0.455
90 A 6 5 1.00 11 0.455
91 A 6 5 0.90 11 0.455
92 A 6 5 0.86 11 0.455
93 A 6 5 0.82 11 0.455
94 A 12 12 1.08 13 0.923
95 A 10 10 1.06 13 0.769
96 A 8 8 1.00 13 0.615
97 A 6 6 1.00 13 0.462
98 A 6 6 1.00 13 0.462
99 A 8 8 1.00 13 0.615
100 A 10 10 1.13 13 0.769
101 A 7 7 1.17 10 0.700
102 A 5 5 1.12 10 0.500
103 A 2 2 1.00 10 0.200
104 A 1 1 1.00 8 0.125
105 A 4 3 0.42 10 0.300
106 A 7 6 0.68 10 0.600
107 A 10 9 0.85 10 0.900
108 A 14 14 1.14 12 1.167
109 A 11 11 1.09 12 0.917
110 A 8 8 1.08 12 0.667
111 A 2 2 1.00 12 0.167
112 A 2 2 1.00 12 0.167
113 A 5 5 1.00 12 0.417
114 A 11 11 1.17 12 0.917
115 A 13 13 1.10 12 1.083
116 A 7 7 1.17 10 0.700
117 A 4 4 1.12 10 0.400
118 A 2 2 1.00 10 0.200
119 A 1 1 1.00 8 0.125
120 A 4 3 1.00 10 0.300
121 A 7 6 1.00 10 0.600
122 A 10 9 1.10 10 0.900
123 A 12 11 1.15 10 1.100
124 A 14 14 1.14 12 1.167
125 A 10 10 1.19 12 0.833
126 A 8 8 1.03 12 0.667
127 A 2 2 1.00 12 0.167
128 A 2 2 1.00 12 0.167
129 A 5 5 1.00 12 0.417
130 A 11 11 1.07 12 0.917
131 A 13 13 1.19 12 1.083
132 A 6 6 1.07 10 0.600
133 A 4 4 1.06 10 0.400
134 A 2 2 1.00 10 0.200
135 A 1 1 1.00 8 0.125
136 A 4 3 1.00 10 0.300
137 A 8 7 1.00 10 0.700
138 A 10 9 1.12 10 0.900
139 A 12 11 1.17 10 1.100
140 A 13 13 1.02 12 1.083
141 A 11 11 0.99 12 0.917
142 A 4 4 0.97 12 0.333
143 A 4 4 0.97 12 0.333
144 A 7 7 0.99 12 0.583
145 A 14 14 1.02 12 1.167

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