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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 [115] had the largest ratio of [1.90908999999999995]

# 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 10 10 1.00 8 1.250
2 C 11 11 1.26 8 1.375
3 A 7 7 1.00 8 0.875
4 C 7 7 1.33 8 0.875
5 A 4 4 1.00 8 0.500
6 A 3 3 1.00 6 0.500
7 C 3 3 1.36 6 0.500
8 A 4 4 1.00 8 0.500
9 C 7 7 1.48 8 0.875
10 A 7 7 1.00 8 0.875
11 C 11 11 1.36 8 1.375
12 A 10 10 1.00 8 1.250
13 A 12 11 1.00 12 0.917
14 A 10 9 0.95 12 0.750
15 A 10 9 0.96 12 0.750
16 A 8 7 0.88 12 0.583
17 A 8 7 0.89 12 0.583
18 A 10 9 0.95 12 0.750
19 A 10 9 0.96 12 0.750
20 A 12 11 1.01 12 0.917
21 A 12 11 1.01 8 1.375
22 A 5 4 1.00 8 0.500
23 A 5 4 1.00 10 0.400
24 C 9 9 1.00 10 0.900
25 A 5 5 1.00 10 0.500
26 A 5 5 1.00 10 0.500
27 C 13 13 0.83 14 0.929
28 C 9 9 0.93 14 0.643
29 A 5 5 1.00 14 0.357
30 C 5 5 1.13 14 0.357
31 C 9 9 1.00 14 0.643
32 C 13 13 0.88 14 0.929
33 A 12 11 0.86 8 1.375
34 A 14 13 0.74 10 1.300
35 A 12 11 0.81 10 1.100
36 A 12 11 0.80 10 1.100
37 A 12 12 0.57 10 1.200
38 A 6 6 0.71 10 0.600
39 A 6 6 0.71 10 0.600
40 A 7 6 1.00 12 0.500
41 A 12 12 1.08 12 1.000
42 A 10 10 1.09 12 0.833
43 A 8 8 1.07 12 0.667
44 A 6 6 1.00 12 0.500
45 A 3 3 1.00 12 0.250
46 A 5 5 1.08 12 0.417
47 A 7 7 1.12 12 0.583
48 A 9 9 1.14 12 0.750
49 A 11 11 1.12 12 0.917
50 A 10 9 1.11 8 1.125
51 A 8 7 1.07 8 0.875
52 A 6 5 1.00 8 0.625
53 A 4 3 1.00 8 0.375
54 A 6 5 1.00 8 0.625
55 A 8 7 1.00 8 0.875
56 A 10 9 1.08 8 1.125
57 A 12 12 1.00 12 1.000
58 A 10 10 1.00 12 0.833
59 A 8 8 1.00 12 0.667
60 A 6 6 1.00 12 0.500
61 A 5 5 1.00 12 0.417
62 A 7 7 1.15 12 0.583
63 A 9 9 1.20 12 0.750
64 A 11 11 1.23 12 0.917
65 A 5 5 1.00 12 0.417
66 A 5 5 1.00 12 0.417
67 A 8 7 1.22 14 0.500
68 A 7 6 1.15 14 0.429
69 A 7 6 1.03 11 0.545
70 C 12 12 1.40 11 1.091
71 A 7 6 1.05 11 0.545
72 C 11 11 1.47 9 1.222
73 C 12 12 2.00 9 1.333
74 A 6 5 1.00 11 0.455
75 C 11 11 1.67 11 1.000
76 A 7 6 1.00 11 0.545
77 C 12 12 1.35 11 1.091
78 A 7 6 1.00 11 0.545
79 C 11 11 1.32 11 1.000
80 A 10 9 1.65 13 0.692
81 C 24 23 1.12 13 1.769
82 A 8 7 1.69 13 0.538
83 C 15 14 1.22 11 1.273
84 C 8 8 1.15 11 0.727
85 A 6 5 1.17 13 0.385
86 C 8 8 1.20 13 0.615
87 A 6 5 1.12 13 0.385
88 C 8 8 1.17 13 0.615
89 A 6 5 1.07 13 0.385
90 A 9 9 1.00 11 0.818
91 A 5 4 1.03 11 0.364
92 C 6 5 1.31 11 0.455
93 A 5 4 1.05 11 0.364
94 A 4 4 1.00 9 0.444
95 A 2 2 1.00 9 0.222
96 A 4 3 1.00 11 0.273
97 A 4 4 1.00 11 0.364
98 A 4 3 1.09 11 0.273
99 A 6 6 1.00 11 0.545
100 A 5 4 1.00 11 0.364
101 A 8 8 1.15 11 0.727
102 A 6 5 0.99 13 0.385
103 A 6 5 0.99 13 0.385
104 A 6 5 0.98 13 0.385
105 A 4 3 1.00 13 0.231
106 A 5 5 1.00 8 0.625
107 A 6 5 1.29 13 0.385
108 A 6 5 1.26 13 0.385
109 A 21 20 1.05 13 1.538
110 A 15 14 1.01 13 1.077
111 A 9 8 1.00 13 0.615
112 A 4 3 1.00 11 0.273
113 A 9 8 0.88 11 0.727
114 C 15 14 0.95 13 1.077
115 C 21 21 1.63 11 1.909
116 C 15 15 1.32 11 1.364
117 C 11 11 1.42 11 1.000
118 A 4 4 1.26 11 0.364
119 C 4 4 1.50 9 0.444
120 A 3 3 1.00 6 0.500
121 C 9 9 1.68 9 1.000
122 C 13 13 1.34 11 1.182
123 C 18 18 1.62 11 1.636
124 C 20 20 1.56 11 1.818
125 C 9 8 1.24 11 0.727
126 C 7 6 1.28 11 0.545
127 C 7 6 1.37 11 0.545
128 C 9 8 1.16 11 0.727
129 A 10 9 1.00 13 0.692
130 A 8 7 1.00 13 0.538
131 A 10 9 1.00 13 0.692
132 A 9 8 1.00 13 0.615
133 C 21 20 1.39 13 1.538
134 C 16 15 1.30 13 1.154
135 C 13 12 1.27 13 0.923
136 A 11 11 0.97 13 0.846
137 C 6 6 1.23 11 0.545
138 A 5 5 1.00 8 0.625
139 C 8 8 1.24 11 0.727
140 C 12 12 1.28 13 0.923
141 C 16 16 1.43 13 1.231
142 C 19 19 1.35 13 1.462
143 A 6 6 1.05 14 0.429
144 A 9 8 1.06 24 0.333
145 A 10 9 1.01 26 0.346
146 A 6 5 0.93 11 0.455
147 A 11 10 1.15 11 0.909
148 A 5 4 1.00 9 0.444
149 A 11 10 1.09 7 1.429
150 A 5 4 1.00 11 0.364
151 A 11 10 1.19 11 0.909
152 A 5 4 1.00 11 0.364
153 A 5 4 1.00 13 0.308
154 A 13 12 1.21 13 0.923
155 A 7 6 1.30 11 0.545
156 A 3 3 1.00 9 0.333
157 A 6 5 1.00 13 0.385
158 A 13 12 1.12 13 0.923
159 A 7 6 1.00 13 0.462
160 A 3 3 1.00 13 0.231
161 A 5 5 1.23 15 0.333
162 A 7 7 1.12 15 0.467
163 A 3 3 1.00 9 0.333
164 A 3 3 1.00 15 0.200
165 A 2 2 1.00 11 0.182
166 A 5 4 1.03 11 0.364
167 A 6 5 1.09 11 0.455
168 A 7 6 1.08 11 0.545
169 A 3 3 1.00 7 0.429
170 A 3 3 1.00 9 0.333
171 A 3 3 1.00 9 0.333
172 A 5 4 1.61 17 0.235
173 A 5 4 1.57 17 0.235
174 A 5 4 1.65 15 0.267
175 A 5 4 1.66 13 0.308
176 A 5 4 1.00 17 0.235
177 A 5 4 1.58 17 0.235
178 A 5 4 1.64 17 0.235
179 A 7 6 1.38 19 0.316
180 A 7 6 1.36 19 0.316
181 A 7 6 1.38 17 0.353
182 A 7 6 1.39 15 0.400
183 A 6 5 1.18 19 0.263
184 A 7 6 1.35 19 0.316
185 A 7 6 1.35 19 0.316
186 C 9 8 1.14 17 0.471
187 A 9 8 1.04 17 0.471
188 C 13 12 1.08 17 0.706
189 A 5 4 1.41 19 0.211
190 A 7 6 1.26 21 0.286
191 A 9 8 1.18 21 0.381
192 A 5 4 1.00 15 0.267
193 A 5 4 1.00 21 0.190
194 A 11 10 1.00 19 0.526
195 A 11 10 1.01 19 0.526
196 A 9 8 1.02 19 0.421
197 A 9 8 1.04 19 0.421
198 A 11 10 1.00 19 0.526
199 A 11 10 1.01 19 0.526
200 C 12 11 0.68 23 0.478
201 C 10 9 0.50 23 0.391
202 C 7 6 0.50 21 0.286
203 C 7 6 1.05 21 0.286
204 C 7 6 1.04 23 0.261
205 C 12 11 0.64 21 0.524
206 A 4 3 0.89 16 0.188
207 A 5 4 0.88 16 0.250
208 A 4 3 0.88 16 0.188
209 A 5 4 0.88 14 0.286
210 A 5 4 0.88 14 0.286
211 A 4 3 0.89 16 0.188
212 A 5 4 0.89 16 0.250
213 A 4 3 0.89 16 0.188
214 A 4 3 1.00 10 0.300
215 A 12 11 1.14 8 1.375
216 A 7 6 1.44 8 0.750
217 A 4 3 1.00 10 0.300
218 A 4 3 1.00 10 0.300
219 A 12 11 1.07 8 1.375
220 A 12 11 1.14 8 1.375
221 A 4 3 1.00 10 0.300
222 A 4 3 1.00 10 0.300
223 A 11 10 1.02 8 1.250
224 A 16 15 1.16 8 1.875
225 A 4 3 1.00 10 0.300
226 A 6 5 1.02 14 0.357
227 A 4 3 1.02 14 0.214
228 A 2 2 1.00 18 0.111
229 A 2 2 1.00 18 0.111
230 A 2 2 1.00 16 0.125
231 A 2 2 1.00 16 0.125
232 A 2 2 1.00 18 0.111
233 A 2 2 1.00 18 0.111
234 A 6 5 0.52 25 0.200
235 A 6 5 0.53 25 0.200
236 A 6 5 0.64 25 0.200
237 A 6 5 0.64 25 0.200
238 A 6 5 0.54 25 0.200
239 A 6 5 0.53 25 0.200
240 A 4 3 0.87 9 0.333
241 A 4 3 0.88 9 0.333
242 A 4 3 0.90 7 0.429
243 N/A 4 0 1.00 7 0.000
244 A 4 3 0.87 9 0.333
245 A 4 3 0.88 9 0.333
246 A 4 3 0.90 7 0.429
247 N/A 4 0 1.00 7 0.000

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