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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 [309] had the largest ratio of [.484800000000000009]

# 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 4 3 1.00 33 0.091
2 A 4 3 1.00 33 0.091
3 A 4 3 1.00 33 0.091
4 A 4 3 1.00 31 0.097
5 A 5 5 1.00 33 0.152
6 A 2 2 1.18 33 0.061
7 A 4 3 1.00 33 0.091
8 A 4 3 1.00 33 0.091
9 A 4 3 1.00 33 0.091
10 A 8 5 1.00 35 0.143
11 A 7 5 1.00 35 0.143
12 A 6 5 1.00 35 0.143
13 A 5 5 1.00 33 0.152
14 A 4 4 1.00 35 0.114
15 A 3 3 1.00 35 0.086
16 A 7 4 1.00 35 0.114
17 A 9 4 1.00 35 0.114
18 A 11 4 1.00 35 0.114
19 N/A 0 0 1.00 35 0.000
20 N/A 0 0 1.00 33 0.000
21 N/A 0 0 1.00 35 0.000
22 A 3 3 1.00 35 0.086
23 A 7 4 1.00 35 0.114
24 N/A 0 0 1.00 35 0.000
25 N/A 0 0 1.00 33 0.000
26 N/A 0 0 1.00 35 0.000
27 A 4 4 1.00 35 0.114
28 A 9 5 1.00 35 0.143
29 A 4 3 1.00 33 0.091
30 A 4 3 1.00 33 0.091
31 A 4 3 1.00 33 0.091
32 A 4 3 1.00 31 0.097
33 A 5 5 1.00 33 0.152
34 A 3 2 1.00 33 0.061
35 A 4 3 1.00 33 0.091
36 A 4 3 1.00 33 0.091
37 A 4 3 1.00 33 0.091
38 A 19 8 1.00 35 0.229
39 A 15 8 1.00 35 0.229
40 A 11 8 1.00 35 0.229
41 A 7 7 1.00 33 0.212
42 A 4 4 1.00 35 0.114
43 A 4 3 1.00 35 0.086
44 A 8 6 1.00 35 0.171
45 A 6 5 1.00 35 0.143
46 A 5 5 1.00 35 0.143
47 N/A 0 0 1.00 35 0.000
48 N/A 0 0 1.00 33 0.000
49 N/A 0 0 1.00 35 0.000
50 A 3 3 1.00 35 0.086
51 A 7 5 1.00 35 0.143
52 N/A 0 0 1.00 35 0.000
53 N/A 0 0 1.00 33 0.000
54 N/A 0 0 1.00 35 0.000
55 A 4 4 1.00 35 0.114
56 A 10 6 1.00 35 0.171
57 A 3 2 1.00 30 0.067
58 A 3 2 1.00 30 0.067
59 A 3 2 1.00 30 0.067
60 A 3 2 1.00 28 0.071
61 A 3 2 1.00 22 0.091
62 A 7 4 1.00 30 0.133
63 A 3 3 1.00 30 0.100
64 A 3 2 1.00 30 0.067
65 A 3 2 1.00 30 0.067
66 A 3 2 1.00 30 0.067
67 A 15 10 1.00 32 0.312
68 A 12 10 1.00 32 0.312
69 A 9 8 1.00 30 0.267
70 A 6 6 1.00 24 0.250
71 A 9 5 1.00 32 0.156
72 A 4 4 1.00 32 0.125
73 A 9 8 1.00 32 0.250
74 A 12 10 1.00 32 0.312
75 A 15 10 1.00 32 0.312
76 N/A 0 0 1.00 32 0.000
77 N/A 0 0 1.00 30 0.000
78 N/A 0 0 1.00 24 0.000
79 N/A 0 0 1.00 32 0.000
80 N/A 0 0 1.00 32 0.000
81 N/A 0 0 1.00 32 0.000
82 N/A 0 0 1.00 32 0.000
83 N/A 0 0 1.00 30 0.000
84 N/A 0 0 1.00 24 0.000
85 N/A 0 0 1.00 32 0.000
86 N/A 0 0 1.00 32 0.000
87 N/A 0 0 1.00 32 0.000
88 A 4 3 1.00 30 0.100
89 A 4 3 1.00 30 0.100
90 A 4 3 1.00 30 0.100
91 A 4 3 1.00 28 0.107
92 A 5 5 1.00 30 0.167
93 A 2 2 1.19 30 0.067
94 A 4 3 1.00 30 0.100
95 A 4 3 1.00 30 0.100
96 A 4 3 1.00 30 0.100
97 A 8 5 1.00 32 0.156
98 A 7 5 1.00 32 0.156
99 A 6 5 1.00 32 0.156
100 A 5 5 1.00 30 0.167
101 A 4 4 1.00 32 0.125
102 A 3 3 1.00 32 0.094
103 A 7 4 1.00 32 0.125
104 A 9 4 1.00 32 0.125
105 A 11 4 1.00 32 0.125
106 A 1 1 1.04 29 0.034
107 A 1 1 1.00 18 0.056
108 A 1 1 1.00 20 0.050
109 N/A 0 0 1.00 32 0.000
110 N/A 0 0 1.00 30 0.000
111 N/A 0 0 1.00 32 0.000
112 A 3 3 1.00 32 0.094
113 A 7 4 1.00 32 0.125
114 N/A 0 0 1.00 32 0.000
115 N/A 0 0 1.00 30 0.000
116 N/A 0 0 1.00 32 0.000
117 A 4 4 1.00 32 0.125
118 A 9 5 1.00 32 0.156
119 A 4 3 1.00 32 0.094
120 A 4 3 1.00 32 0.094
121 A 4 3 1.00 32 0.094
122 A 4 3 1.00 30 0.100
123 A 5 5 1.00 32 0.156
124 A 2 2 1.18 32 0.062
125 A 4 3 1.00 32 0.094
126 A 4 3 1.00 32 0.094
127 A 4 3 1.00 32 0.094
128 A 8 5 1.00 34 0.147
129 A 7 5 1.00 34 0.147
130 A 6 5 1.00 34 0.147
131 A 5 5 1.00 32 0.156
132 A 4 4 1.00 34 0.118
133 A 3 3 1.00 34 0.088
134 A 7 4 1.00 34 0.118
135 A 9 4 1.00 34 0.118
136 A 11 4 1.00 34 0.118
137 N/A 0 0 1.00 34 0.000
138 N/A 0 0 1.00 32 0.000
139 N/A 0 0 1.00 34 0.000
140 A 3 3 0.97 34 0.088
141 A 7 4 0.98 34 0.118
142 N/A 0 0 1.00 34 0.000
143 N/A 0 0 1.00 32 0.000
144 N/A 0 0 1.00 34 0.000
145 A 4 4 0.98 34 0.118
146 A 9 5 0.99 34 0.147
147 A 3 2 1.00 31 0.065
148 A 3 2 1.00 31 0.065
149 A 3 2 1.00 31 0.065
150 A 3 2 1.00 29 0.069
151 A 5 5 1.00 31 0.161
152 A 3 2 1.00 31 0.065
153 A 3 2 1.00 31 0.065
154 A 3 2 1.00 31 0.065
155 A 3 2 1.00 31 0.065
156 A 8 6 1.00 33 0.182
157 A 7 6 1.00 33 0.182
158 A 6 6 1.00 31 0.194
159 A 5 5 1.00 33 0.152
160 A 4 4 1.00 33 0.121
161 A 8 5 1.00 33 0.152
162 A 10 5 1.00 33 0.152
163 A 12 5 1.00 33 0.152
164 A 27 15 1.00 33 0.454
165 A 17 14 1.00 33 0.424
166 A 11 9 1.00 31 0.290
167 A 6 6 1.00 33 0.182
168 A 5 4 1.00 33 0.121
169 A 10 5 1.00 33 0.152
170 A 13 5 1.00 33 0.152
171 A 16 5 1.00 33 0.152
172 A 4 4 1.00 36 0.111
173 A 4 3 1.00 30 0.100
174 A 4 3 1.00 30 0.100
175 A 4 3 1.00 30 0.100
176 A 4 3 1.00 28 0.107
177 A 5 5 1.00 30 0.167
178 A 3 2 1.55 30 0.067
179 A 4 3 1.00 30 0.100
180 A 4 3 1.00 30 0.100
181 A 4 3 1.00 30 0.100
182 A 19 8 1.00 32 0.250
183 A 15 8 1.00 32 0.250
184 A 11 8 1.00 32 0.250
185 A 7 7 1.00 30 0.233
186 A 4 4 1.00 32 0.125
187 A 4 3 1.00 32 0.094
188 A 8 6 1.00 32 0.188
189 A 6 5 1.00 32 0.156
190 A 5 5 1.00 32 0.156
191 N/A 0 0 1.00 32 0.000
192 N/A 0 0 1.00 30 0.000
193 N/A 0 0 1.00 32 0.000
194 A 3 3 1.00 32 0.094
195 A 7 5 1.00 32 0.156
196 N/A 0 0 1.00 32 0.000
197 N/A 0 0 1.00 30 0.000
198 N/A 0 0 1.00 32 0.000
199 A 4 4 1.00 32 0.125
200 A 10 6 1.00 32 0.188
201 A 4 3 1.00 32 0.094
202 A 4 3 1.00 32 0.094
203 A 4 3 1.00 32 0.094
204 A 4 3 1.00 30 0.100
205 A 5 5 1.00 32 0.156
206 A 3 2 1.00 32 0.062
207 A 4 3 1.00 32 0.094
208 A 4 3 1.00 32 0.094
209 A 4 3 1.00 32 0.094
210 A 19 8 1.00 34 0.235
211 A 15 8 1.00 34 0.235
212 A 11 8 1.00 34 0.235
213 A 7 7 1.00 32 0.219
214 A 4 4 1.00 34 0.118
215 A 4 3 1.00 34 0.088
216 A 8 6 1.00 34 0.176
217 A 6 5 1.00 34 0.147
218 A 5 5 1.00 34 0.147
219 N/A 0 0 1.00 34 0.000
220 N/A 0 0 1.00 32 0.000
221 N/A 0 0 1.00 34 0.000
222 A 3 3 1.00 34 0.088
223 A 7 5 1.00 34 0.147
224 N/A 0 0 1.00 34 0.000
225 N/A 0 0 1.00 32 0.000
226 N/A 0 0 1.00 34 0.000
227 A 4 4 1.00 34 0.118
228 A 10 6 1.00 34 0.176
229 A 4 4 1.00 36 0.111
230 A 3 2 1.00 27 0.074
231 A 3 2 1.00 27 0.074
232 A 3 2 1.00 27 0.074
233 A 3 2 1.00 25 0.080
234 A 3 2 1.00 19 0.105
235 A 7 4 1.00 27 0.148
236 A 3 3 1.00 27 0.111
237 A 3 2 1.00 27 0.074
238 A 3 2 1.00 27 0.074
239 A 3 2 1.00 27 0.074
240 A 15 10 1.00 29 0.345
241 A 12 10 1.00 29 0.345
242 A 9 8 1.00 27 0.296
243 A 6 6 1.00 21 0.286
244 A 9 5 1.00 29 0.172
245 A 4 4 1.00 29 0.138
246 A 9 8 1.00 29 0.276
247 A 12 10 1.00 29 0.345
248 A 15 10 1.00 29 0.345
249 A 3 3 1.00 14 0.214
250 N/A 0 0 1.00 29 0.000
251 N/A 0 0 1.00 27 0.000
252 N/A 0 0 1.00 21 0.000
253 N/A 0 0 1.00 29 0.000
254 N/A 0 0 1.00 29 0.000
255 N/A 0 0 1.00 29 0.000
256 N/A 0 0 1.00 29 0.000
257 N/A 0 0 1.00 27 0.000
258 N/A 0 0 1.00 21 0.000
259 N/A 0 0 1.00 29 0.000
260 N/A 0 0 1.00 29 0.000
261 N/A 0 0 1.00 29 0.000
262 A 3 2 1.00 29 0.069
263 A 3 2 1.00 29 0.069
264 A 3 2 1.00 29 0.069
265 A 3 2 1.00 27 0.074
266 A 3 2 1.00 21 0.095
267 A 7 4 1.00 29 0.138
268 A 3 3 1.00 29 0.103
269 A 3 2 1.00 29 0.069
270 A 3 2 1.00 29 0.069
271 A 3 2 1.00 29 0.069
272 A 15 10 1.00 31 0.323
273 A 12 10 1.00 31 0.323
274 A 9 8 1.00 29 0.276
275 A 6 6 1.00 23 0.261
276 A 9 5 1.00 31 0.161
277 A 4 4 1.00 31 0.129
278 A 9 8 1.00 31 0.258
279 A 12 10 1.00 31 0.323
280 A 15 10 1.00 31 0.323
281 N/A 0 0 1.00 31 0.000
282 N/A 0 0 1.00 29 0.000
283 N/A 0 0 1.00 23 0.000
284 N/A 0 0 1.00 31 0.000
285 N/A 0 0 1.00 31 0.000
286 N/A 0 0 1.00 31 0.000
287 N/A 0 0 1.00 31 0.000
288 N/A 0 0 1.00 29 0.000
289 N/A 0 0 1.00 23 0.000
290 N/A 0 0 1.00 31 0.000
291 N/A 0 0 1.00 31 0.000
292 N/A 0 0 1.00 31 0.000
293 A 3 2 1.00 31 0.065
294 A 3 2 1.00 31 0.065
295 A 3 2 1.00 31 0.065
296 A 3 2 1.00 29 0.069
297 A 3 2 1.00 23 0.087
298 A 7 4 1.00 31 0.129
299 A 3 2 1.00 31 0.065
300 A 3 2 1.00 31 0.065
301 A 3 2 1.00 31 0.065
302 A 3 2 1.00 31 0.065
303 A 13 11 1.00 33 0.333
304 A 10 9 1.00 31 0.290
305 A 6 6 1.00 25 0.240
306 A 10 6 1.00 33 0.182
307 A 5 5 1.00 33 0.152
308 A 10 9 1.00 33 0.273
309 A 19 16 1.00 33 0.485
310 A 13 11 1.00 31 0.355
311 A 6 6 1.00 25 0.240
312 A 12 7 1.00 33 0.212
313 A 6 6 1.00 33 0.182
314 A 13 11 1.00 33 0.333

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