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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [77] had the largest ratio of [.6923]

Table 2.1:Rubi specific breakdown of results for each integral
# 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 2 1 1.00 20 0.050
2 A 2 1 1.00 22 0.045
3 A 2 1 1.00 22 0.045
4 A 2 1 1.00 25 0.040
5 A 2 1 1.00 27 0.037
6 A 2 1 1.00 27 0.037
7 A 6 6 1.00 15 0.400
8 A 7 7 1.00 15 0.467
9 A 8 7 1.00 15 0.467
10 A 9 7 1.00 15 0.467
11 A 6 6 1.00 15 0.400
12 A 6 6 1.00 16 0.375
13 A 3 3 1.00 11 0.273
14 A 3 3 1.00 15 0.200
15 A 3 3 1.00 13 0.231
16 A 3 3 1.00 13 0.231
17 A 6 6 1.00 15 0.400
18 A 3 3 1.00 19 0.158
19 A 3 3 1.00 21 0.143
20 A 3 3 1.00 31 0.097
21 A 3 3 1.00 36 0.083
22 A 12 10 1.00 35 0.286
23 A 11 9 1.00 33 0.273
24 A 10 8 1.00 36 0.222
25 A 10 10 1.00 19 0.526
26 A 9 9 1.00 18 0.500
27 A 4 4 1.00 27 0.148
28 A 4 4 1.00 28 0.143
29 A 4 4 1.00 24 0.167
30 A 4 4 1.00 24 0.167
31 A 4 4 1.00 26 0.154
32 A 4 4 1.00 26 0.154
33 A 4 4 1.00 28 0.143
34 A 4 4 1.00 30 0.133
35 A 4 4 1.00 29 0.138
36 A 4 4 1.00 29 0.138
37 A 4 4 1.00 29 0.138
38 A 4 4 1.00 32 0.125
39 A 6 6 1.00 13 0.462
40 A 4 4 1.00 49 0.082
41 A 4 4 1.00 57 0.070
42 A 2 2 1.00 31 0.065
43 A 2 2 1.00 42 0.048
44 A 4 4 1.00 42 0.095
45 A 4 4 1.00 45 0.089
46 A 4 4 1.00 45 0.089
47 A 4 4 1.00 44 0.091
48 A 3 3 1.00 20 0.150
49 A 6 6 1.00 20 0.300
50 A 2 2 1.00 16 0.125
51 A 5 5 1.00 20 0.250
52 A 3 3 1.00 18 0.167
53 A 2 1 1.00 30 0.033
54 A 2 1 1.00 30 0.033
55 A 2 1 1.00 28 0.036
56 A 2 1 1.00 30 0.033
57 A 7 7 1.00 30 0.233
58 A 8 8 1.00 30 0.267
59 A 8 8 1.00 17 0.471
60 A 10 9 1.00 17 0.529
61 A 10 9 0.99 17 0.529
62 A 10 9 0.99 22 0.409
63 A 10 9 1.00 22 0.409
64 A 10 9 1.00 22 0.409
65 A 9 8 1.00 17 0.471
66 A 9 8 1.00 19 0.421
67 A 8 7 1.00 18 0.389
68 A 7 5 1.00 16 0.312
69 A 13 9 1.00 15 0.600
70 A 8 6 1.00 16 0.375
71 A 14 10 1.00 15 0.667
72 A 9 6 1.00 16 0.375
73 A 15 10 1.00 15 0.667
74 A 10 6 1.00 16 0.375
75 A 16 10 1.00 15 0.667
76 A 7 5 1.00 15 0.333
77 A 13 9 1.00 13 0.692
78 A 7 5 1.00 21 0.238
79 A 13 9 1.00 20 0.450
80 A 8 6 1.00 21 0.286
81 A 14 10 1.00 20 0.500
82 A 9 6 1.00 21 0.286
83 A 15 10 1.00 20 0.500
84 A 10 6 1.00 21 0.286
85 A 16 10 1.00 20 0.500
86 A 3 2 1.00 11 0.182
87 A 3 2 1.00 12 0.167
88 A 2 1 1.00 15 0.067
89 A 3 2 1.00 14 0.143
90 A 2 1 1.00 17 0.059
91 A 3 2 1.00 19 0.105
92 A 2 1 1.00 20 0.050
93 A 2 2 1.00 14 0.143
94 A 4 3 1.00 17 0.176
95 A 4 3 1.00 19 0.158
96 A 3 2 1.00 20 0.100
97 A 4 3 1.00 21 0.143
98 A 3 2 1.00 22 0.091
99 A 4 3 1.00 24 0.125
100 A 3 2 1.00 25 0.080
101 A 3 2 1.00 25 0.080
102 A 8 6 1.00 26 0.231
103 A 9 7 1.00 26 0.269
104 A 10 7 1.00 26 0.269
105 A 10 7 1.00 11 0.636
106 A 3 3 1.00 12 0.250
107 A 13 9 1.00 15 0.600
108 A 10 7 1.00 14 0.500
109 A 9 6 1.00 17 0.353
110 A 14 10 1.00 19 0.526
111 A 13 9 1.00 20 0.450
112 A 2 2 1.00 14 0.143
113 A 12 8 1.00 17 0.471
114 A 5 5 1.00 19 0.263
115 A 15 11 1.00 20 0.550
116 A 13 9 1.00 21 0.429
117 A 12 8 1.00 22 0.364
118 A 16 12 1.00 24 0.500
119 A 15 11 1.00 25 0.440
120 A 2 2 1.00 19 0.105
121 A 11 8 1.00 17 0.471
122 A 9 7 1.00 20 0.350
123 A 15 11 1.00 19 0.579
124 A 11 8 1.00 31 0.258
125 A 8 6 1.00 31 0.194
126 A 9 7 1.00 31 0.226
127 A 10 8 1.00 31 0.258
128 A 17 12 1.00 30 0.400
129 A 14 10 1.00 30 0.333
130 A 15 11 1.00 30 0.367
131 A 16 12 1.00 30 0.400
132 A 2 2 1.00 21 0.095
133 A 2 2 1.00 21 0.095
134 A 2 1 1.00 19 0.053
135 A 2 2 1.00 19 0.105
136 A 2 2 1.00 21 0.095
137 A 2 2 1.00 21 0.095
138 A 2 2 1.00 21 0.095
139 A 13 9 1.00 36 0.250
140 A 13 9 1.00 41 0.220
141 A 13 9 1.00 46 0.196
142 A 19 13 1.00 35 0.371
143 A 19 13 1.00 40 0.325
144 A 19 13 1.00 45 0.289
145 A 8 6 1.00 36 0.167
146 A 8 6 1.00 41 0.146
147 A 10 8 1.00 46 0.174
148 A 14 10 1.00 35 0.286
149 A 14 10 1.00 40 0.250
150 A 16 12 1.00 45 0.267
151 A 9 7 1.00 36 0.194
152 A 9 7 1.00 41 0.171
153 A 9 7 1.00 46 0.152
154 A 15 11 1.00 35 0.314
155 A 15 11 1.00 40 0.275
156 A 15 11 1.00 45 0.244
157 A 10 8 1.00 36 0.222
158 A 10 8 1.00 41 0.195
159 A 10 8 1.00 46 0.174
160 A 16 12 1.00 35 0.343
161 A 16 12 1.00 40 0.300
162 A 16 12 1.00 45 0.267
163 A 1 1 1.00 23 0.043
164 A 1 1 1.00 26 0.038
165 A 1 1 1.00 28 0.036
166 A 1 1 1.00 31 0.032
167 A 1 1 1.00 15 0.067
168 A 3 2 1.00 11 0.182
169 A 3 2 1.00 15 0.133
170 A 3 2 1.00 30 0.067
171 A 3 2 1.00 30 0.067
172 A 3 2 1.00 30 0.067
173 A 3 2 1.00 30 0.067
174 A 3 2 1.00 30 0.067
175 A 3 2 1.00 30 0.067
176 A 3 2 1.00 30 0.067
177 A 3 2 1.00 30 0.067
178 A 3 2 1.00 30 0.067
179 A 3 2 1.00 30 0.067
180 A 9 8 1.00 30 0.267
181 A 9 8 1.00 30 0.267
182 A 9 8 1.00 30 0.267
183 A 9 8 1.00 30 0.267
184 A 9 8 1.00 30 0.267
185 A 9 8 1.00 28 0.286
186 A 8 7 1.00 27 0.259
187 A 8 7 1.00 30 0.233
188 A 8 7 1.00 30 0.233
189 A 8 7 1.00 30 0.233
190 A 8 7 1.00 30 0.233
191 A 8 7 1.00 30 0.233
192 A 8 7 1.00 30 0.233
193 A 8 7 1.00 30 0.233
194 A 8 7 1.00 30 0.233
195 A 8 7 1.00 30 0.233
196 A 8 7 1.00 30 0.233
197 A 8 7 1.00 30 0.233
198 A 3 2 1.00 30 0.067
199 A 3 2 1.00 30 0.067
200 A 3 2 1.00 30 0.067
201 A 3 2 1.00 30 0.067
202 A 3 2 1.00 30 0.067
203 A 3 2 1.00 30 0.067
204 A 3 2 1.00 30 0.067
205 A 3 2 1.00 30 0.067
206 A 3 2 1.00 30 0.067
207 A 9 8 1.00 30 0.267
208 A 12 10 1.00 30 0.333
209 A 9 8 1.00 30 0.267
210 A 11 10 1.00 30 0.333
211 A 9 8 1.00 30 0.267
212 A 10 9 1.00 28 0.321
213 A 9 9 1.00 27 0.333
214 A 9 8 1.00 30 0.267
215 A 9 8 1.00 30 0.267
216 A 9 8 1.00 30 0.267
217 A 9 8 1.00 30 0.267
218 A 9 8 1.00 30 0.267
219 A 9 8 1.00 30 0.267
220 A 9 8 1.00 30 0.267
221 A 9 8 1.00 30 0.267
222 A 9 8 1.00 30 0.267
223 A 3 2 1.00 30 0.067
224 A 3 2 1.00 30 0.067
225 A 3 2 1.00 30 0.067
226 A 3 2 1.00 30 0.067
227 A 3 2 1.00 30 0.067
228 A 3 2 1.00 30 0.067
229 A 3 2 1.00 30 0.067
230 A 3 2 1.00 30 0.067
231 A 3 2 1.00 30 0.067
232 A 3 2 1.00 30 0.067
233 A 10 9 1.00 30 0.300
234 A 14 10 1.00 30 0.333
235 A 10 9 1.00 30 0.300
236 A 13 10 1.00 30 0.333
237 A 10 9 1.00 30 0.300
238 A 12 10 1.00 30 0.333
239 A 10 10 1.00 30 0.333
240 A 10 10 1.00 28 0.357
241 A 9 9 1.00 27 0.333
242 A 9 9 1.00 30 0.300
243 A 9 9 1.00 30 0.300
244 A 10 9 1.00 30 0.300
245 A 10 9 1.00 30 0.300
246 A 10 8 1.00 30 0.267
247 A 10 8 1.00 30 0.267
248 A 10 8 1.00 30 0.267
249 A 10 8 1.00 30 0.267
250 A 10 8 1.00 30 0.267
251 A 8 7 1.00 16 0.438
252 A 5 4 1.00 16 0.250
253 A 8 7 1.00 16 0.438
254 A 6 6 1.00 14 0.429
255 A 6 5 1.00 16 0.312
256 A 6 5 1.00 16 0.312
257 A 3 2 1.00 16 0.125
258 A 6 6 1.00 14 0.429
259 A 6 6 1.00 16 0.375
260 A 2 1 1.00 21 0.048
261 A 2 1 1.00 19 0.053
262 A 2 1 1.00 18 0.056
263 A 2 1 1.00 21 0.048
264 A 2 1 1.00 21 0.048
265 A 2 1 1.00 21 0.048
266 A 3 2 1.00 23 0.087
267 A 3 2 1.00 21 0.095
268 A 3 2 1.00 20 0.100
269 A 2 1 1.00 23 0.043
270 A 2 1 1.00 23 0.043
271 A 2 1 1.00 23 0.043
272 A 3 2 1.00 23 0.087
273 A 3 2 1.00 21 0.095
274 A 3 2 1.00 20 0.100
275 A 2 1 1.00 23 0.043
276 A 2 1 1.00 23 0.043
277 A 2 1 1.00 23 0.043
278 A 3 2 1.00 23 0.087
279 A 3 2 1.00 21 0.095
280 A 3 2 1.00 20 0.100
281 A 2 1 1.00 23 0.043
282 A 2 1 1.00 23 0.043
283 A 2 1 1.00 23 0.043
284 A 10 9 1.00 23 0.391
285 A 10 9 1.00 23 0.391
286 A 10 9 1.00 21 0.429
287 A 8 8 1.00 20 0.400
288 A 10 9 1.00 23 0.391
289 A 10 9 1.00 23 0.391
290 A 10 9 1.00 23 0.391
291 A 7 7 1.00 23 0.304
292 A 7 7 1.00 21 0.333
293 A 7 7 1.00 20 0.350
294 A 11 10 1.00 23 0.435
295 A 11 10 1.00 23 0.435
296 A 11 10 1.00 23 0.435
297 A 11 10 1.00 23 0.435
298 A 8 8 1.00 23 0.348
299 A 8 8 1.00 21 0.381
300 A 8 8 1.00 20 0.400
301 A 12 10 1.00 23 0.435
302 A 12 10 1.00 23 0.435
303 A 12 10 1.00 23 0.435
304 A 12 10 1.00 23 0.435
305 A 9 8 1.00 23 0.348
306 A 9 9 1.00 21 0.429
307 A 9 8 1.00 20 0.400
308 A 13 10 1.00 23 0.435
309 A 13 10 1.00 23 0.435
310 A 13 10 1.00 23 0.435
311 A 13 10 1.00 23 0.435
312 A 5 5 1.00 20 0.250
313 A 4 4 1.00 18 0.222
314 A 5 5 1.00 20 0.250
315 A 4 4 1.00 18 0.222
316 A 4 4 1.00 27 0.148
317 A 4 4 1.00 29 0.138
318 A 4 4 1.00 28 0.143
319 A 4 4 1.00 28 0.143
320 A 2 1 1.00 36 0.028
321 A 2 1 1.00 36 0.028
322 A 2 1 1.00 36 0.028
323 A 2 1 1.00 34 0.029
324 A 2 1 1.00 33 0.030
325 A 2 1 1.00 36 0.028
326 A 2 1 1.00 36 0.028
327 A 2 1 1.00 36 0.028
328 A 2 1 1.00 36 0.028
329 A 2 1 1.00 36 0.028
330 A 2 1 1.00 38 0.026
331 A 2 1 1.00 38 0.026
332 A 3 2 1.00 38 0.053
333 A 3 2 1.00 36 0.056
334 A 3 2 1.00 35 0.057
335 A 3 2 1.00 38 0.053
336 A 3 2 1.00 38 0.053
337 A 3 2 1.00 38 0.053
338 A 2 1 1.00 38 0.026
339 A 2 1 1.00 38 0.026
340 A 2 1 1.00 38 0.026
341 A 2 1 1.00 38 0.026
342 A 3 2 1.00 38 0.053
343 A 3 2 1.00 36 0.056
344 A 3 2 1.00 35 0.057
345 A 3 2 1.00 38 0.053
346 A 3 2 1.00 38 0.053
347 A 3 2 1.00 38 0.053
348 A 2 1 1.00 38 0.026
349 A 2 1 1.00 38 0.026
350 A 13 10 1.00 38 0.263
351 A 13 10 1.00 38 0.263
352 A 13 10 1.00 38 0.263
353 A 13 10 1.00 36 0.278
354 A 10 9 0.99 35 0.257
355 A 10 9 0.99 38 0.237
356 A 10 9 1.00 38 0.237
357 A 10 9 0.99 38 0.237
358 A 10 9 0.99 38 0.237
359 A 11 10 1.00 38 0.263
360 A 11 10 1.00 38 0.263
361 A 11 10 0.99 38 0.263
362 A 11 10 1.00 36 0.278
363 A 9 9 1.00 35 0.257
364 A 11 10 0.99 38 0.263
365 A 11 10 1.00 38 0.263
366 A 11 10 0.99 38 0.263
367 A 11 10 0.99 38 0.263
368 A 12 11 1.00 38 0.290
369 A 10 10 1.00 38 0.263
370 A 8 8 1.00 38 0.210
371 A 8 8 1.00 36 0.222
372 A 8 8 1.00 35 0.229
373 A 12 10 0.99 38 0.263
374 A 12 10 1.00 38 0.263
375 A 12 10 0.99 38 0.263
376 A 12 10 0.99 38 0.263
377 A 2 1 1.00 23 0.043
378 A 2 1 1.00 26 0.038
379 A 3 2 1.00 25 0.080
380 A 3 2 1.00 28 0.071
381 A 3 2 1.00 25 0.080
382 A 3 2 1.00 28 0.071
383 A 3 2 1.00 25 0.080
384 A 3 2 1.00 28 0.071
385 A 9 7 1.00 26 0.269
386 A 12 9 1.00 29 0.310
387 A 15 11 1.00 25 0.440
388 A 18 13 1.00 28 0.464
389 A 14 10 1.00 25 0.400
390 A 14 10 1.00 28 0.357
391 A 15 11 1.00 25 0.440
392 A 15 11 1.00 28 0.393
393 A 16 11 1.00 25 0.440
394 A 16 11 1.00 28 0.393
395 A 2 2 1.00 22 0.091
396 A 2 2 1.00 35 0.057
397 A 2 2 1.00 35 0.057
398 A 2 2 1.00 22 0.091
399 A 3 3 1.00 25 0.120
400 A 6 5 1.00 15 0.333
401 A 6 5 1.00 15 0.333
402 A 7 6 1.00 20 0.300
403 A 7 6 1.00 20 0.300
404 A 7 7 1.00 17 0.412
405 A 7 6 1.00 25 0.240
406 A 11 6 1.00 35 0.171
407 A 11 6 1.00 35 0.171
408 A 8 5 1.00 22 0.227
409 A 11 7 1.00 25 0.280
410 A 17 7 1.00 15 0.467
411 A 17 7 1.00 15 0.467
412 A 14 7 1.00 20 0.350
413 A 14 7 1.00 20 0.350
414 A 15 9 1.00 17 0.529
415 A 14 7 1.00 25 0.280
416 A 13 7 1.00 18 0.389
417 A 4 3 1.00 19 0.158
418 A 4 3 1.00 19 0.158
419 A 4 2 1.00 17 0.118
420 A 1 0 1.00 9 0.000
421 A 2 2 1.00 58 0.034
422 A 1 1 1.00 46 0.022
423 A 10 8 1.00 24 0.333
424 A 1 1 1.00 48 0.021
425 A 1 1 1.00 45 0.022
426 A 1 1 1.00 69 0.014
427 A 1 1 1.00 86 0.012

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