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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 [205] had the largest ratio of [1.25000000000000000]

# 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 5 4 1.00 20 0.200
2 A 5 4 1.00 20 0.200
3 A 5 5 1.00 20 0.250
4 A 3 2 1.00 20 0.100
5 A 3 3 1.00 18 0.167
6 A 5 5 1.00 20 0.250
7 A 6 6 1.00 20 0.300
8 A 7 6 1.00 20 0.300
9 A 8 6 1.00 20 0.300
10 A 3 3 1.00 8 0.375
11 A 4 4 1.00 8 0.500
12 A 5 4 1.00 8 0.500
13 A 8 3 1.00 22 0.136
14 A 9 5 1.00 22 0.227
15 A 7 5 1.00 22 0.227
16 A 4 4 1.00 22 0.182
17 A 3 2 1.00 20 0.100
18 A 8 4 1.00 22 0.182
19 A 10 5 1.00 22 0.227
20 A 12 5 1.00 22 0.227
21 A 14 5 1.00 22 0.227
22 A 8 3 1.00 22 0.136
23 A 9 4 1.00 22 0.182
24 A 9 5 1.00 22 0.227
25 A 4 2 1.00 22 0.091
26 A 4 3 1.00 20 0.150
27 A 8 4 1.00 22 0.182
28 A 10 5 1.00 22 0.227
29 A 12 5 1.00 22 0.227
30 A 14 5 1.00 22 0.227
31 N/A 0 0 1.00 14 0.000
32 A 7 6 1.00 14 0.429
33 A 6 6 1.00 14 0.429
34 A 5 5 1.00 14 0.357
35 A 4 4 1.00 12 0.333
36 N/A 0 0 1.00 14 0.000
37 N/A 0 0 1.00 14 0.000
38 N/A 0 0 1.00 20 0.000
39 A 10 6 1.00 20 0.300
40 A 8 5 1.00 20 0.250
41 A 6 4 1.00 20 0.200
42 A 2 2 1.00 18 0.111
43 N/A 0 0 1.00 20 0.000
44 N/A 0 0 1.00 20 0.000
45 N/A 0 0 1.00 22 0.000
46 A 7 7 1.00 22 0.318
47 A 6 6 1.00 22 0.273
48 A 3 3 1.00 22 0.136
49 A 3 3 1.00 20 0.150
50 N/A 0 0 1.00 22 0.000
51 N/A 0 0 1.00 22 0.000
52 A 10 8 1.00 22 0.364
53 A 9 8 1.00 22 0.364
54 A 8 8 1.00 22 0.364
55 A 8 8 1.00 22 0.364
56 A 9 8 1.00 22 0.364
57 A 10 8 1.00 22 0.364
58 A 18 7 1.00 24 0.292
59 A 16 7 1.00 24 0.292
60 A 14 7 1.00 24 0.292
61 A 14 7 1.00 24 0.292
62 A 16 7 1.00 24 0.292
63 A 18 7 1.00 24 0.292
64 A 18 7 1.00 24 0.292
65 A 16 7 1.00 24 0.292
66 A 14 7 1.00 24 0.292
67 A 14 7 1.00 24 0.292
68 A 16 7 1.00 24 0.292
69 A 18 7 1.00 24 0.292
70 A 8 3 1.00 22 0.136
71 A 9 5 1.00 22 0.227
72 A 7 5 1.00 22 0.227
73 A 4 4 1.00 22 0.182
74 A 3 2 1.00 20 0.100
75 A 8 4 1.00 22 0.182
76 A 10 5 1.00 22 0.227
77 A 12 5 1.00 22 0.227
78 A 14 5 1.00 22 0.227
79 A 5 3 1.00 24 0.125
80 A 7 3 1.00 24 0.125
81 A 6 3 1.00 24 0.125
82 A 5 3 1.00 24 0.125
83 A 4 3 1.00 22 0.136
84 A 5 4 1.00 24 0.167
85 A 6 5 1.00 24 0.208
86 A 7 5 1.00 24 0.208
87 A 8 5 1.00 24 0.208
88 A 11 3 1.00 24 0.125
89 A 17 3 1.00 24 0.125
90 A 14 3 1.00 24 0.125
91 A 11 3 1.00 24 0.125
92 A 8 3 1.00 22 0.136
93 A 11 4 1.00 24 0.167
94 A 14 5 1.00 24 0.208
95 A 17 5 1.00 24 0.208
96 A 20 5 1.00 24 0.208
97 N/A 0 0 1.00 20 0.000
98 A 17 8 1.00 20 0.400
99 A 14 8 1.00 20 0.400
100 A 11 7 1.00 20 0.350
101 A 8 6 1.00 18 0.333
102 N/A 0 0 1.00 20 0.000
103 N/A 0 0 1.00 20 0.000
104 N/A 0 0 1.00 16 0.000
105 A 8 8 1.00 16 0.500
106 A 7 7 1.00 16 0.438
107 A 6 6 1.00 16 0.375
108 A 3 2 1.00 14 0.143
109 N/A 0 0 1.00 16 0.000
110 N/A 0 0 1.00 16 0.000
111 N/A 0 0 1.00 22 0.000
112 A 31 7 1.00 22 0.318
113 A 25 9 1.00 22 0.409
114 A 17 7 1.00 22 0.318
115 A 12 5 1.00 20 0.250
116 N/A 0 0 1.00 22 0.000
117 N/A 0 0 1.00 22 0.000
118 A 18 7 1.00 24 0.292
119 A 16 7 1.00 24 0.292
120 A 14 7 1.00 24 0.292
121 A 14 7 1.00 24 0.292
122 A 16 7 1.00 24 0.292
123 A 18 7 1.00 24 0.292
124 A 10 7 1.00 26 0.269
125 A 9 7 1.00 26 0.269
126 A 8 7 1.00 26 0.269
127 A 8 7 1.00 26 0.269
128 A 9 7 1.00 26 0.269
129 A 10 7 1.00 26 0.269
130 A 26 7 1.00 26 0.269
131 A 23 7 1.00 26 0.269
132 A 20 7 1.00 26 0.269
133 A 20 7 1.00 26 0.269
134 A 23 7 1.00 26 0.269
135 A 26 7 1.00 26 0.269
136 A 8 3 1.00 22 0.136
137 A 9 4 1.00 22 0.182
138 A 9 5 1.00 22 0.227
139 A 4 2 1.00 22 0.091
140 A 4 3 1.00 20 0.150
141 A 8 4 1.00 22 0.182
142 A 10 5 1.00 22 0.227
143 A 12 5 1.00 22 0.227
144 A 14 5 1.00 22 0.227
145 A 11 3 1.00 24 0.125
146 A 17 3 1.00 24 0.125
147 A 14 3 1.00 24 0.125
148 A 11 3 1.00 24 0.125
149 A 8 3 1.00 22 0.136
150 A 11 4 1.00 24 0.167
151 A 14 5 1.00 24 0.208
152 A 17 5 1.00 24 0.208
153 A 20 5 1.00 24 0.208
154 A 8 3 1.00 24 0.125
155 A 12 3 1.00 24 0.125
156 A 10 3 1.00 24 0.125
157 A 8 3 1.00 24 0.125
158 A 6 3 1.00 22 0.136
159 A 8 4 1.00 24 0.167
160 A 10 5 1.00 24 0.208
161 A 12 5 1.00 24 0.208
162 A 14 5 1.00 24 0.208
163 N/A 0 0 1.00 22 0.000
164 A 13 11 1.00 22 0.500
165 A 12 12 1.00 22 0.546
166 A 9 8 1.00 22 0.364
167 A 8 8 1.00 20 0.400
168 N/A 0 0 1.00 22 0.000
169 N/A 0 0 1.00 22 0.000
170 N/A 0 0 1.00 22 0.000
171 A 16 9 1.00 22 0.409
172 A 13 8 1.00 22 0.364
173 A 10 7 1.00 22 0.318
174 A 5 5 1.00 20 0.250
175 N/A 0 0 1.00 22 0.000
176 N/A 0 0 1.00 22 0.000
177 N/A 0 0 1.00 16 0.000
178 A 15 8 1.00 16 0.500
179 A 13 10 1.00 16 0.625
180 A 9 7 1.00 16 0.438
181 A 7 7 1.00 14 0.500
182 N/A 0 0 1.00 16 0.000
183 N/A 0 0 1.00 16 0.000
184 A 18 7 1.00 24 0.292
185 A 16 7 1.00 24 0.292
186 A 14 7 1.00 24 0.292
187 A 14 7 1.00 24 0.292
188 A 16 7 1.00 24 0.292
189 A 18 7 1.00 24 0.292
190 A 26 7 1.00 26 0.269
191 A 23 7 1.00 26 0.269
192 A 20 7 1.00 26 0.269
193 A 20 7 1.00 26 0.269
194 A 23 7 1.00 26 0.269
195 A 26 7 1.00 26 0.269
196 A 18 7 1.00 26 0.269
197 A 16 7 1.00 26 0.269
198 A 14 7 1.00 26 0.269
199 A 14 7 1.00 26 0.269
200 A 16 7 1.00 26 0.269
201 A 18 7 1.00 26 0.269
202 A 12 10 1.00 12 0.833
203 A 11 10 1.00 12 0.833
204 A 6 5 1.00 10 0.500
205 A 26 15 1.00 12 1.250
206 A 19 11 1.00 12 0.917
207 A 16 10 1.00 10 1.000
208 N/A 0 0 1.00 14 0.000
209 A 7 6 1.00 14 0.429
210 A 6 6 1.00 14 0.429
211 A 5 5 1.00 14 0.357
212 A 4 4 1.00 12 0.333
213 N/A 0 0 1.00 14 0.000
214 N/A 0 0 1.00 14 0.000
215 N/A 0 0 1.00 20 0.000
216 A 14 8 1.00 20 0.400
217 A 11 7 1.00 20 0.350
218 A 8 6 1.00 18 0.333
219 N/A 0 0 1.00 20 0.000
220 N/A 0 0 1.00 20 0.000
221 N/A 0 0 1.00 22 0.000
222 A 12 12 1.00 22 0.546
223 A 9 8 1.00 22 0.364
224 A 8 8 1.00 20 0.400
225 N/A 0 0 1.00 22 0.000
226 N/A 0 0 1.00 22 0.000
227 N/A 0 0 1.00 20 0.000
228 A 12 6 1.00 20 0.300
229 A 10 6 1.00 20 0.300
230 A 8 5 1.00 20 0.250
231 A 6 4 1.00 18 0.222
232 N/A 0 0 1.00 20 0.000
233 N/A 0 0 1.00 20 0.000
234 N/A 0 0 1.00 22 0.000
235 A 23 14 1.00 22 0.636
236 A 19 15 1.00 22 0.682
237 A 10 10 1.00 20 0.500
238 N/A 0 0 1.00 22 0.000
239 N/A 0 0 1.00 22 0.000
240 N/A 0 0 1.00 22 0.000
241 A 22 18 1.00 22 0.818
242 A 17 13 1.00 22 0.591
243 A 11 10 1.00 20 0.500
244 N/A 0 0 1.00 22 0.000
245 N/A 0 0 1.00 22 0.000
246 N/A 0 0 1.00 20 0.000
247 A 10 6 1.00 20 0.300
248 A 8 5 1.00 20 0.250
249 A 6 4 1.00 20 0.200
250 A 2 2 1.00 18 0.111
251 N/A 0 0 1.00 20 0.000
252 N/A 0 0 1.00 20 0.000
253 N/A 0 0 1.00 16 0.000
254 A 7 7 1.00 16 0.438
255 A 6 6 1.00 16 0.375
256 A 3 2 1.00 14 0.143
257 N/A 0 0 1.00 16 0.000
258 N/A 0 0 1.00 16 0.000
259 N/A 0 0 1.00 22 0.000
260 A 13 8 1.00 22 0.364
261 A 10 7 1.00 22 0.318
262 A 5 5 1.00 20 0.250
263 N/A 0 0 1.00 22 0.000
264 N/A 0 0 1.00 22 0.000
265 N/A 0 0 1.00 22 0.000
266 A 27 14 1.00 22 0.636
267 A 23 14 1.00 22 0.636
268 A 19 15 1.00 22 0.682
269 A 10 10 1.08 20 0.500
270 N/A 0 0 1.00 22 0.000
271 N/A 0 0 1.00 22 0.000
272 N/A 0 0 1.00 24 0.000
273 A 7 7 1.00 24 0.292
274 A 6 6 1.00 24 0.250
275 A 3 3 1.00 22 0.136
276 N/A 0 0 1.00 24 0.000
277 N/A 0 0 1.00 24 0.000
278 N/A 0 0 1.00 24 0.000
279 A 64 24 1.00 24 1.000
280 A 36 22 1.00 24 0.917
281 A 13 12 1.13 22 0.546
282 N/A 0 0 1.00 24 0.000
283 N/A 0 0 1.00 24 0.000
284 N/A 0 0 1.00 20 0.000
285 A 40 18 1.00 20 0.900
286 A 29 19 1.00 20 0.950
287 A 13 12 1.00 18 0.667
288 N/A 0 0 1.00 20 0.000
289 N/A 0 0 1.00 20 0.000
290 N/A 0 0 1.00 22 0.000
291 A 7 7 1.00 22 0.318
292 A 6 6 1.00 22 0.273
293 A 3 3 1.00 22 0.136
294 A 3 3 1.00 20 0.150
295 N/A 0 0 1.00 22 0.000
296 N/A 0 0 1.00 22 0.000
297 N/A 0 0 1.00 22 0.000
298 A 25 9 1.00 22 0.409
299 A 17 7 1.00 22 0.318
300 A 12 5 1.00 20 0.250
301 N/A 0 0 1.00 22 0.000
302 N/A 0 0 1.00 22 0.000
303 N/A 0 0 1.00 16 0.000
304 A 13 10 1.00 16 0.625
305 A 9 7 1.00 16 0.438
306 A 7 7 1.00 14 0.500
307 N/A 0 0 1.00 16 0.000
308 N/A 0 0 1.00 16 0.000
309 N/A 0 0 1.00 22 0.000
310 A 25 16 1.00 22 0.727
311 A 22 18 1.00 22 0.818
312 A 17 13 1.00 22 0.591
313 A 11 10 1.01 20 0.500
314 N/A 0 0 1.00 22 0.000
315 N/A 0 0 1.00 22 0.000
316 N/A 0 0 1.00 24 0.000
317 A 44 19 1.00 24 0.792
318 A 31 19 1.00 24 0.792
319 A 13 12 1.12 22 0.546
320 N/A 0 0 1.00 24 0.000
321 N/A 0 0 1.00 24 0.000
322 N/A 0 0 1.00 24 0.000
323 A 16 9 1.00 24 0.375
324 A 10 7 1.00 24 0.292
325 A 7 5 1.00 22 0.227
326 N/A 0 0 1.00 24 0.000
327 N/A 0 0 1.00 24 0.000
328 A 4 3 1.00 18 0.167
329 A 3 3 1.00 18 0.167
330 A 3 3 1.00 18 0.167
331 A 2 2 1.00 18 0.111
332 A 2 2 1.00 18 0.111
333 A 3 3 1.00 18 0.167
334 A 3 3 1.00 18 0.167
335 A 4 3 1.00 18 0.167
336 A 5 4 1.00 18 0.222
337 A 4 4 1.00 18 0.222
338 A 4 4 1.00 18 0.222
339 A 3 3 1.00 18 0.167
340 A 3 3 1.00 18 0.167
341 A 4 4 1.00 18 0.222
342 A 4 4 1.00 18 0.222
343 A 5 4 1.00 18 0.222
344 A 4 3 1.00 18 0.167
345 A 3 3 1.00 18 0.167
346 A 3 3 1.00 18 0.167
347 A 2 2 1.00 18 0.111
348 A 2 2 1.00 18 0.111
349 A 3 3 1.00 18 0.167
350 A 3 3 1.00 18 0.167
351 A 4 3 1.00 18 0.167
352 A 5 4 1.00 18 0.222
353 A 4 4 1.00 18 0.222
354 A 4 4 1.00 18 0.222
355 A 3 3 1.00 18 0.167
356 A 3 3 1.00 18 0.167
357 A 4 4 1.00 18 0.222
358 A 4 4 1.00 18 0.222
359 A 5 4 1.00 18 0.222
360 A 6 3 1.00 8 0.375
361 A 14 5 1.00 14 0.357
362 A 10 4 1.00 14 0.286
363 A 10 5 1.00 14 0.357
364 A 6 2 1.00 12 0.167
365 A 12 5 1.00 14 0.357
366 A 12 6 1.00 14 0.429
367 A 16 7 1.00 14 0.500
368 A 14 5 1.00 23 0.217
369 A 10 4 1.00 23 0.174
370 A 10 5 1.00 23 0.217
371 A 6 2 1.00 21 0.095
372 A 12 5 1.00 23 0.217
373 A 12 6 1.00 23 0.261
374 A 16 7 1.00 23 0.304
375 A 16 8 1.00 23 0.348
376 A 20 9 1.00 25 0.360
377 A 16 8 1.00 25 0.320
378 A 12 7 1.00 23 0.304
379 N/A 0 0 1.00 25 0.000
380 N/A 0 0 1.00 25 0.000
381 N/A 0 0 1.00 25 0.000
382 A 20 12 1.00 23 0.522
383 A 19 13 1.00 23 0.565
384 A 14 9 1.00 23 0.391
385 A 13 9 1.00 21 0.429
386 N/A 0 0 1.00 23 0.000
387 N/A 0 0 1.00 23 0.000
388 N/A 0 0 1.00 23 0.000
389 A 19 9 1.00 25 0.360
390 A 15 8 1.00 25 0.320
391 A 9 6 1.00 23 0.261
392 N/A 0 0 1.00 25 0.000
393 N/A 0 0 1.00 25 0.000
394 N/A 0 0 1.00 25 0.000
395 A 12 7 1.00 8 0.875
396 A 5 4 1.00 10 0.400
397 A 19 6 1.00 10 0.600

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