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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 [112] had the largest ratio of [1.41667000000000010]

# 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 F 0 0 N/A 0.000 N/A
2 F 0 0 N/A 0.000 N/A
3 F 0 0 N/A 0.000 N/A
4 F 0 0 N/A 0.000 N/A
5 N/A 1 0 1.00 20 0.000
6 N/A 1 0 1.00 20 0.000
7 A 5 4 1.06 8 0.500
8 A 4 4 1.21 8 0.500
9 A 5 4 1.08 8 0.500
10 A 3 3 1.14 6 0.500
11 A 2 2 1.00 4 0.500
12 C 9 8 1.33 8 1.000
13 A 5 4 1.00 8 0.500
14 A 2 2 1.00 8 0.250
15 A 6 5 1.00 8 0.625
16 A 3 3 1.09 8 0.375
17 A 7 6 1.06 8 0.750
18 A 6 6 1.18 10 0.600
19 A 5 5 1.15 10 0.500
20 A 4 4 1.12 8 0.500
21 A 3 3 1.18 6 0.500
22 C 10 9 1.28 10 0.900
23 C 8 7 1.18 10 0.700
24 A 3 3 1.00 10 0.300
25 C 10 9 1.04 10 0.900
26 A 5 5 1.01 10 0.500
27 A 11 11 1.47 10 1.100
28 A 10 9 1.30 10 0.900
29 A 6 6 1.19 8 0.750
30 A 4 4 1.14 6 0.667
31 C 11 10 1.23 10 1.000
32 C 9 8 1.11 10 0.800
33 C 11 10 1.10 10 1.000
34 C 14 13 1.04 10 1.300
35 C 14 13 1.09 10 1.300
36 A 14 14 1.65 10 1.400
37 A 10 10 1.48 10 1.000
38 A 11 11 1.37 10 1.100
39 A 7 7 1.19 8 0.875
40 A 5 5 1.21 6 0.833
41 C 12 11 1.29 10 1.100
42 C 10 9 1.12 10 0.900
43 C 12 11 1.11 10 1.100
44 C 14 13 1.06 10 1.300
45 A 4 3 0.85 10 0.300
46 A 4 3 0.88 10 0.300
47 A 4 3 0.88 10 0.300
48 A 4 3 0.93 10 0.300
49 A 4 3 0.93 10 0.300
50 A 7 6 1.00 8 0.750
51 A 4 3 1.00 6 0.500
52 N/A 1 0 1.00 10 0.000
53 N/A 1 0 1.00 10 0.000
54 A 3 2 0.91 10 0.200
55 A 3 2 0.94 10 0.200
56 A 3 2 0.94 10 0.200
57 A 3 2 0.98 10 0.200
58 A 3 2 0.98 10 0.200
59 A 4 3 1.00 8 0.375
60 A 6 5 1.00 6 0.833
61 N/A 1 0 1.00 10 0.000
62 N/A 1 0 1.00 10 0.000
63 A 6 5 1.37 10 0.500
64 A 10 9 1.33 10 0.900
65 A 9 8 1.26 10 0.800
66 A 10 9 1.10 8 1.125
67 A 6 5 1.08 6 0.833
68 N/A 1 0 1.00 10 0.000
69 N/A 1 0 1.00 10 0.000
70 A 5 4 1.34 10 0.400
71 A 7 6 1.23 10 0.600
72 A 10 9 1.25 10 0.900
73 A 7 6 1.09 8 0.750
74 A 8 7 1.16 6 1.167
75 N/A 1 0 1.00 10 0.000
76 N/A 1 0 1.00 10 0.000
77 A 6 5 1.15 16 0.312
78 A 8 7 1.13 16 0.438
79 A 5 4 1.12 16 0.250
80 A 7 6 1.13 16 0.375
81 A 4 3 1.07 16 0.188
82 A 8 7 1.10 16 0.438
83 A 2 2 1.04 18 0.111
84 A 2 2 1.04 18 0.111
85 A 2 2 1.02 18 0.111
86 A 2 2 1.02 18 0.111
87 A 2 2 1.00 18 0.111
88 N/A 2 0 1.00 18 0.000
89 N/A 2 0 1.00 18 0.000
90 N/A 2 0 1.00 18 0.000
91 N/A 2 0 1.00 18 0.000
92 N/A 1 0 1.00 18 0.000
93 N/A 1 0 1.00 18 0.000
94 N/A 1 0 1.00 18 0.000
95 N/A 1 0 1.00 18 0.000
96 N/A 1 0 1.00 18 0.000
97 N/A 1 0 1.00 18 0.000
98 N/A 1 0 1.00 18 0.000
99 N/A 1 0 1.00 18 0.000
100 N/A 2 0 1.00 10 0.000
101 N/A 2 0 1.00 10 0.000
102 A 2 2 0.96 10 0.200
103 A 2 2 1.00 8 0.250
104 N/A 1 0 1.00 10 0.000
105 N/A 1 0 1.00 10 0.000
106 C 7 6 1.02 12 0.500
107 A 6 5 0.95 12 0.417
108 C 7 6 1.05 12 0.500
109 A 7 6 0.97 10 0.600
110 C 9 8 1.15 8 1.000
111 N/A 1 0 1.00 12 0.000
112 A 18 17 1.28 12 1.417
113 C 17 16 1.40 12 1.333
114 A 14 13 1.28 12 1.083
115 C 13 12 1.11 10 1.200
116 A 10 9 1.06 8 1.125
117 N/A 1 0 1.00 12 0.000
118 C 17 16 1.37 12 1.333
119 A 12 11 1.38 12 0.917
120 C 15 14 1.37 12 1.167
121 A 10 9 1.07 10 0.900
122 C 11 10 1.17 8 1.250
123 N/A 1 0 1.00 12 0.000
124 A 4 3 0.91 12 0.250
125 A 4 3 0.93 12 0.250
126 A 4 3 0.92 12 0.250
127 C 10 9 1.11 10 0.900
128 A 8 7 0.95 8 0.875
129 N/A 1 0 1.00 12 0.000
130 N/A 1 0 1.00 12 0.000
131 A 3 2 0.94 12 0.167
132 A 3 2 0.96 12 0.167
133 A 3 2 0.95 12 0.167
134 A 8 7 1.07 10 0.700
135 C 9 8 1.17 8 1.000
136 N/A 1 0 1.00 12 0.000
137 C 13 12 1.47 12 1.000
138 A 13 12 1.33 12 1.000
139 C 13 12 1.14 10 1.200
140 A 10 9 1.08 8 1.125
141 N/A 1 0 1.00 12 0.000
142 A 11 10 1.39 12 0.833
143 C 13 12 1.31 12 1.000
144 A 11 10 1.13 10 1.000
145 C 11 10 1.19 8 1.250
146 N/A 1 0 1.00 12 0.000
147 C 8 7 1.03 16 0.438
148 A 7 6 0.98 14 0.429
149 C 10 9 1.08 12 0.750
150 N/A 1 0 1.00 16 0.000
151 N/A 1 0 1.00 16 0.000
152 A 14 13 1.34 16 0.812
153 C 14 13 1.09 14 0.929
154 A 10 9 1.04 12 0.750
155 N/A 1 0 1.00 16 0.000
156 N/A 1 0 1.00 16 0.000
157 C 16 15 1.36 16 0.938
158 A 10 9 1.04 14 0.643
159 C 12 11 1.09 12 0.917
160 N/A 1 0 1.00 16 0.000
161 N/A 1 0 1.00 16 0.000
162 A 4 3 0.97 16 0.188
163 C 11 10 1.09 14 0.714
164 A 8 7 1.01 12 0.583
165 N/A 1 0 1.00 16 0.000
166 N/A 1 0 1.00 16 0.000
167 A 3 2 0.99 16 0.125
168 A 8 7 1.07 14 0.500
169 C 10 9 1.12 12 0.750
170 N/A 1 0 1.00 16 0.000
171 N/A 1 0 1.00 16 0.000
172 A 13 12 1.41 16 0.750
173 C 14 13 1.13 14 0.929
174 A 10 9 1.09 12 0.750
175 N/A 1 0 1.00 16 0.000
176 N/A 1 0 1.00 16 0.000
177 N/A 1 0 1.00 12 0.000
178 N/A 1 0 1.00 12 0.000
179 N/A 1 0 1.00 12 0.000
180 N/A 1 0 1.00 12 0.000
181 A 4 3 0.93 10 0.300
182 A 4 3 0.93 10 0.300
183 C 8 7 1.15 8 0.875
184 A 6 5 0.96 6 0.833
185 N/A 1 0 1.00 10 0.000
186 N/A 1 0 1.00 10 0.000
187 N/A 1 0 1.00 14 0.000
188 N/A 1 0 1.00 14 0.000
189 N/A 1 0 1.00 14 0.000
190 N/A 1 0 1.00 14 0.000
191 N/A 1 0 1.00 12 0.000

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