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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 [259] had the largest ratio of [.933332999999999968]

# 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 8 7 1.32 21 0.333
2 A 7 6 0.89 21 0.286
3 A 7 6 1.36 21 0.286
4 A 6 5 1.04 19 0.263
5 A 7 6 0.92 19 0.316
6 A 6 5 0.92 21 0.238
7 A 7 6 1.16 21 0.286
8 A 5 4 0.89 21 0.190
9 A 8 7 1.21 23 0.304
10 A 7 6 0.90 23 0.261
11 A 8 7 1.15 23 0.304
12 A 6 5 0.94 21 0.238
13 A 7 6 0.90 21 0.286
14 A 6 5 0.89 23 0.217
15 A 8 7 1.07 23 0.304
16 A 5 4 0.89 23 0.174
17 A 9 8 1.46 23 0.348
18 A 7 6 0.90 23 0.261
19 A 11 10 1.55 23 0.435
20 A 6 5 0.90 21 0.238
21 A 7 6 0.90 21 0.286
22 A 6 5 0.88 23 0.217
23 A 11 10 1.59 23 0.435
24 A 5 4 0.89 23 0.174
25 A 9 8 1.28 23 0.348
26 A 8 7 1.01 23 0.304
27 A 8 7 1.24 23 0.304
28 A 6 5 0.98 21 0.238
29 A 8 7 0.96 21 0.333
30 A 6 5 0.96 23 0.217
31 A 8 7 1.11 23 0.304
32 A 6 5 1.00 23 0.217
33 A 11 10 1.16 23 0.435
34 A 8 7 1.02 23 0.304
35 A 10 9 1.15 23 0.391
36 A 7 6 1.03 21 0.286
37 A 10 9 1.09 21 0.429
38 A 7 6 1.00 23 0.261
39 A 10 9 1.06 23 0.391
40 A 7 6 1.02 23 0.261
41 A 13 12 1.14 23 0.522
42 A 9 8 1.01 23 0.348
43 A 12 11 1.19 23 0.478
44 A 8 7 1.07 21 0.333
45 A 12 11 1.13 21 0.524
46 A 8 7 1.04 23 0.304
47 A 12 11 1.13 23 0.478
48 A 8 7 1.02 23 0.304
49 A 9 8 1.21 21 0.381
50 C 4 4 1.24 21 0.190
51 A 8 7 1.25 21 0.333
52 C 4 4 1.31 19 0.211
53 C 4 4 1.20 19 0.211
54 A 6 5 0.93 21 0.238
55 C 4 4 1.17 21 0.190
56 A 5 4 0.86 21 0.190
57 A 9 8 1.08 23 0.348
58 C 4 4 1.17 23 0.174
59 A 8 7 1.11 23 0.304
60 C 4 4 1.21 21 0.190
61 C 4 4 1.17 21 0.190
62 A 6 5 0.89 23 0.217
63 C 4 4 1.17 23 0.174
64 A 5 4 0.86 23 0.174
65 A 9 8 0.99 23 0.348
66 C 4 4 1.19 23 0.174
67 A 8 7 0.99 23 0.304
68 C 4 4 1.16 21 0.190
69 C 4 4 1.12 21 0.190
70 A 6 5 0.89 23 0.217
71 C 4 4 1.11 23 0.174
72 A 5 4 0.86 23 0.174
73 A 5 4 0.95 23 0.174
74 N/A 3 0 1.00 23 0.000
75 A 6 5 0.95 23 0.217
76 N/A 3 0 1.00 21 0.000
77 N/A 3 0 1.00 21 0.000
78 A 13 12 1.01 23 0.522
79 N/A 3 0 1.00 23 0.000
80 A 5 4 0.93 23 0.174
81 A 6 5 1.25 21 0.238
82 A 4 3 0.93 21 0.143
83 A 5 4 1.45 21 0.190
84 A 5 4 0.93 19 0.211
85 A 5 4 1.10 19 0.211
86 A 4 3 0.93 21 0.143
87 A 6 5 1.08 21 0.238
88 A 5 4 0.90 21 0.190
89 A 7 6 1.42 23 0.261
90 A 5 4 0.91 23 0.174
91 A 5 4 1.24 23 0.174
92 A 5 4 1.02 21 0.190
93 A 6 5 1.25 21 0.238
94 A 5 4 0.90 23 0.174
95 A 7 6 1.13 23 0.261
96 A 5 4 0.89 23 0.174
97 A 5 4 1.16 23 0.174
98 A 5 4 0.98 23 0.174
99 A 5 4 1.12 23 0.174
100 A 5 4 1.02 21 0.190
101 A 8 7 1.32 21 0.333
102 A 5 4 0.88 23 0.174
103 A 9 8 1.15 23 0.348
104 A 5 4 0.89 23 0.174
105 A 8 7 1.28 23 0.304
106 A 5 4 0.94 23 0.174
107 A 7 6 1.26 23 0.261
108 A 5 4 0.96 21 0.190
109 A 4 3 1.00 21 0.143
110 A 4 3 1.00 23 0.130
111 A 6 5 0.96 23 0.217
112 A 5 4 0.96 23 0.174
113 A 7 6 1.09 23 0.261
114 A 5 4 0.93 23 0.174
115 A 5 4 0.94 23 0.174
116 A 9 8 1.16 23 0.348
117 A 5 4 0.95 21 0.190
118 A 5 4 0.98 21 0.190
119 A 5 4 0.97 23 0.174
120 A 5 4 0.97 23 0.174
121 A 5 4 0.97 23 0.174
122 A 7 6 1.05 23 0.261
123 A 5 4 0.95 23 0.174
124 A 9 8 1.05 23 0.348
125 A 11 10 1.20 23 0.435
126 A 5 4 0.95 21 0.190
127 A 6 5 1.10 21 0.238
128 A 6 5 1.03 23 0.217
129 A 6 5 0.94 23 0.217
130 A 6 5 0.98 23 0.217
131 A 6 5 1.03 23 0.217
132 A 7 6 1.08 23 0.261
133 A 8 7 1.09 23 0.304
134 A 9 9 0.91 21 0.429
135 C 11 11 1.20 21 0.524
136 A 8 8 1.00 21 0.381
137 C 7 7 1.29 19 0.368
138 A 1 1 1.00 12 0.083
139 C 7 7 1.56 19 0.368
140 A 4 4 1.00 21 0.190
141 C 8 8 1.42 21 0.381
142 A 7 7 1.00 21 0.333
143 C 12 12 1.29 21 0.571
144 A 5 4 0.98 23 0.174
145 A 8 7 1.00 23 0.304
146 A 7 6 1.03 23 0.261
147 A 8 7 1.05 21 0.333
148 A 5 4 1.09 14 0.286
149 A 8 7 1.10 21 0.333
150 A 7 6 1.11 23 0.261
151 A 8 7 1.06 23 0.304
152 A 5 4 1.09 23 0.174
153 A 8 7 1.00 23 0.304
154 A 7 6 1.03 23 0.261
155 A 8 7 0.97 23 0.304
156 A 5 4 0.96 23 0.174
157 A 8 7 0.97 23 0.304
158 A 7 6 0.99 23 0.261
159 A 8 7 1.00 21 0.333
160 A 5 4 1.01 14 0.286
161 A 8 7 1.03 21 0.333
162 A 7 6 1.02 23 0.261
163 A 8 7 0.97 23 0.304
164 A 5 4 1.02 23 0.174
165 A 8 7 1.00 23 0.304
166 A 7 6 1.03 23 0.261
167 A 8 7 0.97 23 0.304
168 A 5 4 0.98 14 0.286
169 A 5 4 0.97 14 0.286
170 A 8 7 1.00 23 0.304
171 A 7 6 1.17 23 0.261
172 A 8 7 1.13 23 0.304
173 A 8 7 1.17 23 0.304
174 A 8 7 1.12 21 0.333
175 A 6 5 1.00 14 0.357
176 A 8 7 1.08 21 0.333
177 A 9 8 1.18 23 0.348
178 A 8 7 0.96 23 0.304
179 A 10 9 1.17 23 0.391
180 A 8 7 1.01 23 0.304
181 A 7 6 1.18 23 0.261
182 A 8 7 0.99 23 0.304
183 A 9 8 1.16 23 0.348
184 A 8 7 1.00 21 0.333
185 A 7 6 1.19 14 0.429
186 A 8 7 0.99 21 0.333
187 A 12 11 1.13 23 0.478
188 A 8 7 0.94 23 0.304
189 A 12 11 1.06 23 0.478
190 A 10 9 1.20 23 0.391
191 A 8 7 0.96 23 0.304
192 A 10 9 1.15 23 0.391
193 A 8 7 0.97 23 0.304
194 A 11 10 1.18 23 0.435
195 A 8 7 0.97 21 0.333
196 A 8 7 1.20 14 0.500
197 A 8 7 0.97 21 0.333
198 A 14 13 1.14 23 0.565
199 A 8 7 0.94 23 0.304
200 A 14 13 1.09 23 0.565
201 A 11 10 1.19 14 0.714
202 A 6 5 1.00 12 0.417
203 A 7 6 1.00 10 0.600
204 A 7 6 1.18 12 0.500
205 A 8 7 1.00 10 0.700
206 A 6 5 1.36 12 0.417
207 A 6 5 1.00 10 0.500
208 A 8 7 1.06 17 0.412
209 A 10 9 1.10 17 0.529
210 A 10 9 1.08 17 0.529
211 A 11 10 1.05 17 0.588
212 A 9 8 1.11 15 0.533
213 A 8 7 1.00 12 0.583
214 A 9 8 1.09 15 0.533
215 A 9 8 1.00 17 0.471
216 A 11 10 1.05 17 0.588
217 A 8 7 1.05 17 0.412
218 A 13 12 1.11 17 0.706
219 A 11 10 1.09 17 0.588
220 A 14 13 1.07 17 0.765
221 A 10 9 1.11 15 0.600
222 A 10 9 1.05 12 0.750
223 A 11 10 1.07 15 0.667
224 A 11 10 1.00 17 0.588
225 A 7 6 1.00 10 0.600
226 A 8 7 1.00 12 0.583
227 A 9 8 1.06 10 0.800
228 A 10 9 1.04 12 0.750
229 A 8 7 1.09 17 0.412
230 A 9 8 1.08 17 0.471
231 A 9 8 1.11 17 0.471
232 A 10 9 1.00 17 0.529
233 A 8 7 1.00 15 0.467
234 A 5 4 1.00 12 0.333
235 A 9 8 1.09 15 0.533
236 A 9 8 1.00 17 0.471
237 A 11 10 1.09 17 0.588
238 A 8 7 1.07 17 0.412
239 A 9 8 1.18 17 0.471
240 A 9 8 1.12 17 0.471
241 A 8 7 1.00 17 0.412
242 A 9 8 1.10 15 0.533
243 A 6 5 1.00 12 0.417
244 A 11 10 1.26 15 0.667
245 A 12 11 1.07 17 0.647
246 A 13 12 1.25 17 0.706
247 A 8 7 1.07 17 0.412
248 A 8 7 1.10 17 0.412
249 A 10 9 1.16 17 0.529
250 A 10 9 1.10 17 0.529
251 A 10 9 1.17 15 0.600
252 A 8 7 1.14 12 0.583
253 A 13 12 1.31 15 0.800
254 A 13 12 1.13 17 0.706
255 A 5 4 1.00 10 0.400
256 A 5 4 1.00 12 0.333
257 A 5 4 1.01 14 0.286
258 A 5 4 1.05 8 0.500
259 A 15 14 0.97 15 0.933
260 A 13 12 1.01 15 0.800
261 A 8 7 1.08 15 0.467
262 A 11 10 1.04 15 0.667
263 A 12 11 1.14 15 0.733

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