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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 [408] had the largest ratio of [.8824]

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 3 2 1.00 24 0.083
2 A 3 3 1.00 29 0.103
3 A 2 2 1.00 29 0.069
4 A 2 2 1.00 29 0.069
5 A 1 0 1.00 27 0.000
6 A 2 2 1.00 29 0.069
7 A 2 2 1.00 29 0.069
8 A 2 2 1.00 29 0.069
9 A 3 2 1.00 27 0.074
10 A 3 2 1.00 27 0.074
11 A 1 0 1.00 25 0.000
12 A 7 7 1.00 27 0.259
13 A 8 8 1.00 27 0.296
14 A 9 8 1.00 27 0.296
15 A 3 2 1.00 46 0.043
16 A 3 2 1.00 46 0.043
17 A 1 0 1.00 44 0.000
18 A 2 1 1.00 46 0.022
19 A 2 1 1.00 46 0.022
20 A 2 1 1.00 46 0.022
21 A 5 4 1.00 11 0.364
22 A 5 4 1.00 17 0.235
23 A 2 2 1.00 7 0.286
24 A 3 2 1.00 13 0.154
25 A 5 5 1.00 11 0.454
26 A 7 7 1.00 16 0.438
27 A 6 6 1.00 9 0.667
28 A 2 2 1.00 7 0.286
29 A 3 2 1.00 29 0.069
30 A 2 1 1.00 29 0.034
31 A 2 1 1.00 29 0.034
32 A 1 0 1.00 27 0.000
33 A 10 6 1.00 29 0.207
34 A 11 7 1.00 29 0.241
35 A 3 2 1.00 32 0.062
36 A 2 1 1.00 32 0.031
37 A 2 1 1.00 32 0.031
38 A 1 0 1.00 30 0.000
39 A 4 3 1.00 32 0.094
40 A 5 4 1.00 32 0.125
41 A 2 1 1.00 17 0.059
42 A 2 1 1.00 17 0.059
43 A 2 1 1.00 17 0.059
44 A 1 0 1.00 15 0.000
45 A 16 9 1.00 17 0.529
46 A 18 11 1.00 17 0.647
47 A 2 1 1.00 17 0.059
48 A 2 1 1.00 17 0.059
49 A 2 1 1.00 17 0.059
50 A 1 0 1.00 15 0.000
51 A 15 9 1.00 17 0.529
52 A 17 11 1.00 17 0.647
53 A 2 1 1.00 22 0.045
54 A 2 1 1.00 22 0.045
55 A 2 1 1.00 22 0.045
56 A 1 0 1.00 20 0.000
57 A 16 9 1.00 22 0.409
58 A 18 11 1.00 22 0.500
59 A 2 2 1.00 51 0.039
60 A 2 2 1.00 51 0.039
61 B 1 0 4.36 49 0.000
62 A 2 2 1.00 51 0.039
63 A 2 2 1.00 51 0.039
64 A 2 2 1.00 51 0.039
65 A 6 5 1.00 13 0.385
66 A 5 3 1.00 19 0.158
67 A 5 3 1.00 19 0.158
68 A 5 3 1.00 19 0.158
69 A 1 0 1.00 17 0.000
70 A 5 2 1.00 19 0.105
71 A 7 3 1.00 19 0.158
72 A 10 3 1.00 19 0.158
73 B 15 7 2.25 17 0.412
74 A 6 5 1.00 15 0.333
75 A 6 5 1.00 15 0.333
76 A 4 4 1.00 13 0.308
77 A 2 2 1.00 11 0.182
78 A 6 6 1.00 15 0.400
79 A 7 6 1.00 15 0.400
80 A 7 6 1.00 15 0.400
81 A 2 2 1.00 13 0.154
82 A 3 3 1.00 13 0.231
83 A 4 3 1.00 13 0.231
84 A 2 2 1.00 19 0.105
85 A 2 2 1.00 11 0.182
86 A 3 3 1.00 11 0.273
87 A 4 3 1.00 11 0.273
88 A 2 2 1.00 13 0.154
89 A 3 3 1.00 13 0.231
90 A 4 3 1.00 13 0.231
91 A 2 2 1.00 11 0.182
92 A 3 3 1.00 11 0.273
93 A 4 3 1.00 11 0.273
94 A 3 2 1.00 15 0.133
95 A 4 3 1.00 13 0.231
96 A 4 4 1.00 17 0.235
97 A 4 4 1.00 19 0.210
98 A 4 4 1.00 17 0.235
99 A 11 10 1.00 17 0.588
100 A 9 9 1.00 17 0.529
101 A 7 7 1.00 15 0.467
102 A 7 7 1.00 13 0.538
103 A 11 10 1.06 17 0.588
104 A 11 10 0.99 17 0.588
105 A 11 10 1.00 17 0.588
106 A 16 12 1.00 17 0.706
107 A 14 10 1.00 17 0.588
108 A 14 10 1.00 15 0.667
109 A 10 7 1.00 13 0.538
110 A 18 13 1.00 17 0.765
111 A 18 13 1.00 17 0.765
112 A 3 2 1.00 22 0.091
113 A 2 1 1.00 22 0.045
114 A 2 1 1.00 22 0.045
115 A 1 0 1.00 20 0.000
116 A 4 3 1.00 22 0.136
117 A 5 4 1.00 22 0.182
118 A 6 5 1.00 22 0.227
119 A 2 1 1.00 24 0.042
120 A 2 1 1.00 24 0.042
121 A 2 1 1.00 24 0.042
122 A 2 1 1.00 22 0.045
123 A 8 7 1.00 24 0.292
124 A 10 9 1.00 24 0.375
125 A 12 10 1.00 24 0.417
126 A 2 1 1.00 26 0.038
127 A 2 1 1.00 26 0.038
128 A 2 1 1.00 26 0.038
129 A 2 1 1.00 24 0.042
130 A 9 8 1.00 26 0.308
131 A 11 10 1.00 26 0.385
132 A 14 5 1.00 46 0.109
133 A 14 5 1.00 46 0.109
134 A 8 3 1.00 46 0.065
135 A 14 5 1.00 44 0.114
136 A 14 5 1.00 42 0.119
137 A 14 5 1.00 46 0.109
138 A 14 5 0.99 46 0.109
139 A 14 6 1.00 26 0.231
140 A 14 6 1.00 26 0.231
141 A 14 6 1.00 26 0.231
142 A 8 4 1.00 26 0.154
143 A 14 6 1.00 24 0.250
144 A 14 6 1.00 22 0.273
145 A 14 6 1.00 26 0.231
146 A 14 6 1.00 26 0.231
147 A 23 7 1.00 26 0.269
148 A 23 7 1.00 26 0.269
149 A 14 6 1.00 26 0.231
150 A 17 5 1.00 26 0.192
151 A 23 7 1.00 26 0.269
152 A 23 7 1.00 26 0.269
153 A 23 7 1.00 26 0.269
154 A 2 1 1.00 52 0.019
155 A 4 3 1.00 52 0.058
156 A 1 1 1.00 18 0.056
157 A 3 3 1.00 23 0.130
158 A 3 3 1.00 23 0.130
159 A 3 3 1.00 29 0.103
160 A 1 1 1.00 18 0.056
161 A 4 3 1.00 20 0.150
162 A 4 3 1.00 20 0.150
163 A 4 3 1.00 22 0.136
164 A 1 1 1.00 18 0.056
165 A 3 3 1.00 23 0.130
166 A 3 3 1.00 23 0.130
167 A 3 3 1.00 29 0.103
168 A 1 1 1.00 18 0.056
169 A 1 1 1.00 25 0.040
170 C 7 3 4.30 38 0.079
171 A 1 1 1.00 27 0.037
172 A 1 1 1.00 31 0.032
173 A 2 1 1.00 54 0.019
174 A 3 1 1.00 54 0.019
175 A 5 4 1.00 54 0.074
176 A 1 1 1.00 30 0.033
177 A 1 1 1.00 29 0.034
178 A 1 1 1.00 28 0.036
179 A 1 1 1.00 21 0.048
180 A 1 1 1.00 20 0.050
181 A 1 1 1.00 21 0.048
182 A 1 1 1.00 26 0.038
183 A 1 1 1.00 25 0.040
184 A 2 2 1.00 26 0.077
185 A 1 1 1.00 24 0.042
186 A 1 1 1.00 24 0.042
187 A 1 1 1.00 23 0.043
188 A 1 1 1.00 30 0.033
189 A 1 1 1.00 29 0.034
190 A 1 1 1.00 28 0.036
191 A 1 1 1.00 21 0.048
192 A 1 1 1.00 20 0.050
193 A 2 2 1.00 21 0.095
194 A 1 1 1.00 26 0.038
195 A 1 1 1.00 25 0.040
196 A 2 2 1.00 26 0.077
197 A 1 1 1.00 22 0.045
198 A 1 1 1.00 24 0.042
199 A 2 2 1.00 23 0.087
200 A 1 1 1.00 23 0.043
201 A 1 1 1.00 19 0.053
202 A 2 1 1.00 22 0.045
203 A 2 1 1.00 23 0.043
204 A 2 1 1.00 22 0.045
205 A 2 1 1.00 23 0.043
206 A 2 1 1.00 24 0.042
207 A 2 1 1.00 25 0.040
208 A 2 1 1.00 31 0.032
209 A 2 1 1.00 32 0.031
210 A 2 1 1.00 35 0.029
211 A 2 1 1.00 36 0.028
212 A 2 1 1.00 24 0.042
213 A 2 1 1.00 31 0.032
214 A 2 1 1.00 35 0.029
215 A 1 1 1.00 22 0.045
216 A 1 1 1.00 18 0.056
217 B 3 2 2.91 26 0.077
218 B 2 1 2.91 28 0.036
219 A 1 1 1.00 18 0.056
220 A 1 1 1.00 20 0.050
221 A 1 1 1.00 21 0.048
222 A 3 3 1.00 52 0.058
223 A 9 5 1.00 38 0.132
224 A 3 2 1.00 32 0.062
225 A 4 3 1.00 33 0.091
226 A 3 2 1.00 34 0.059
227 A 6 6 1.00 43 0.140
228 A 1 1 1.00 16 0.062
229 B 15 7 2.25 25 0.280
230 A 1 1 1.00 56 0.018
231 A 1 1 1.00 51 0.020
232 A 1 1 1.00 49 0.020
233 A 1 1 1.00 46 0.022
234 A 2 2 1.00 48 0.042
235 A 1 1 1.00 49 0.020
236 A 1 1 1.00 48 0.021
237 A 1 1 1.00 48 0.021
238 A 10 5 1.00 35 0.143
239 A 10 5 1.00 35 0.143
240 A 10 5 1.00 35 0.143
241 A 10 5 1.00 33 0.152
242 A 10 5 1.00 32 0.156
243 A 13 6 1.00 35 0.171
244 A 13 6 1.00 35 0.171
245 A 13 6 1.00 35 0.171
246 A 13 6 1.00 35 0.171
247 A 13 6 1.00 35 0.171
248 A 11 6 1.00 33 0.182
249 A 9 5 1.00 32 0.156
250 A 13 6 1.00 35 0.171
251 A 13 6 1.00 35 0.171
252 A 13 6 1.00 35 0.171
253 A 2 2 1.00 40 0.050
254 A 6 5 1.00 20 0.250
255 A 3 2 1.00 20 0.100
256 A 3 2 1.00 20 0.100
257 A 2 1 1.00 16 0.062
258 A 5 4 1.00 22 0.182
259 A 3 2 1.00 21 0.095
260 A 6 5 1.00 26 0.192
261 A 2 1 1.00 20 0.050
262 A 2 1 1.00 11 0.091
263 A 4 3 1.00 22 0.136
264 A 3 2 1.00 21 0.095
265 A 3 2 1.00 25 0.080
266 A 6 6 1.00 22 0.273
267 A 5 5 1.00 31 0.161
268 A 3 2 1.00 21 0.095
269 A 4 3 1.00 33 0.091
270 A 4 4 1.00 14 0.286
271 A 7 6 1.00 33 0.182
272 A 7 6 1.00 29 0.207
273 A 6 5 1.00 44 0.114
274 A 3 2 1.00 15 0.133
275 A 5 4 1.00 15 0.267
276 A 4 3 1.00 18 0.167
277 A 3 2 1.00 20 0.100
278 A 5 4 1.00 26 0.154
279 A 3 2 1.00 13 0.154
280 A 3 2 1.00 18 0.111
281 A 2 1 1.00 26 0.038
282 A 5 5 1.00 19 0.263
283 A 5 5 1.00 24 0.208
284 A 8 6 1.00 20 0.300
285 A 8 6 1.00 18 0.333
286 A 5 3 1.00 19 0.158
287 A 4 3 1.00 13 0.231
288 A 6 5 1.00 22 0.227
289 A 6 5 1.00 24 0.208
290 A 2 1 1.00 29 0.034
291 A 2 1 1.00 30 0.033
292 A 2 1 1.00 19 0.053
293 A 4 4 1.00 16 0.250
294 A 10 5 1.00 36 0.139
295 A 2 1 1.00 21 0.048
296 A 5 4 1.00 16 0.250
297 A 2 1 1.00 24 0.042
298 A 2 1 1.00 21 0.048
299 A 2 1 1.00 24 0.042
300 A 6 5 1.00 26 0.192
301 A 3 2 1.00 25 0.080
302 A 2 1 1.00 29 0.034
303 A 6 5 1.00 20 0.250
304 A 14 10 1.00 32 0.312
305 A 4 4 1.00 23 0.174
306 A 6 5 1.00 26 0.192
307 A 4 3 1.00 26 0.115
308 A 8 4 1.00 25 0.160
309 A 6 3 1.00 23 0.130
310 A 7 6 1.00 23 0.261
311 A 5 3 1.18 20 0.150
312 A 3 2 1.00 25 0.080
313 A 3 2 1.00 22 0.091
314 A 2 1 1.00 24 0.042
315 A 7 6 1.00 24 0.250
316 A 6 5 1.00 43 0.116
317 A 7 5 1.25 50 0.100
318 A 3 2 1.00 16 0.125
319 A 6 5 1.00 15 0.333
320 A 5 4 1.00 20 0.200
321 A 3 2 1.00 24 0.083
322 A 5 3 1.00 27 0.111
323 A 5 5 1.00 26 0.192
324 A 3 2 1.00 16 0.125
325 A 11 8 1.32 22 0.364
326 A 5 4 1.00 24 0.167
327 A 4 3 1.00 26 0.115
328 A 5 3 1.00 36 0.083
329 A 4 3 1.00 26 0.115
330 A 10 9 1.00 20 0.450
331 A 6 6 1.00 27 0.222
332 A 7 7 1.00 20 0.350
333 A 8 7 1.00 25 0.280
334 A 8 7 1.00 22 0.318
335 A 2 1 1.00 18 0.056
336 A 5 4 1.00 20 0.200
337 A 10 9 1.00 20 0.450
338 A 16 12 1.00 20 0.600
339 A 3 2 1.00 14 0.143
340 A 2 2 1.00 20 0.100
341 A 14 8 1.00 20 0.400
342 A 4 3 1.00 26 0.115
343 A 4 3 1.00 24 0.125
344 A 6 4 1.00 30 0.133
345 A 4 4 1.00 21 0.190
346 A 2 1 1.00 15 0.067
347 A 4 3 1.00 18 0.167
348 A 3 2 1.00 22 0.091
349 A 3 2 1.00 16 0.125
350 A 6 5 1.00 16 0.312
351 A 3 2 1.00 25 0.080
352 A 3 2 1.00 19 0.105
353 A 2 1 1.00 23 0.043
354 A 5 4 1.00 23 0.174
355 A 5 4 1.00 21 0.190
356 A 10 6 1.00 28 0.214
357 A 2 1 1.00 24 0.042
358 A 6 5 1.00 26 0.192
359 A 2 1 1.00 14 0.071
360 A 5 3 1.00 16 0.188
361 A 5 5 1.00 16 0.312
362 A 7 5 1.00 43 0.116
363 A 17 13 1.00 26 0.500
364 A 18 13 1.00 16 0.812
365 A 3 2 1.00 15 0.133
366 A 3 2 1.00 15 0.133
367 A 3 2 1.00 17 0.118
368 A 3 2 1.00 15 0.133
369 A 4 3 1.00 15 0.200
370 A 4 3 1.00 18 0.167
371 A 3 2 1.00 20 0.100
372 A 7 6 1.00 29 0.207
373 A 4 3 1.00 22 0.136
374 A 6 4 1.00 16 0.250
375 A 6 4 1.00 16 0.250
376 A 5 4 1.00 14 0.286
377 A 4 3 1.00 12 0.250
378 A 4 3 1.00 16 0.188
379 A 6 5 1.00 16 0.312
380 A 4 3 1.00 16 0.188
381 A 4 3 1.00 16 0.188
382 A 4 3 1.00 16 0.188
383 A 8 5 1.00 17 0.294
384 A 8 5 1.00 19 0.263
385 A 8 5 1.00 15 0.333
386 A 8 5 1.00 17 0.294
387 A 16 10 1.00 23 0.435
388 A 17 10 1.00 21 0.476
389 F 0 0 N/A 0 N/A
390 A 15 11 1.00 17 0.647
391 A 13 9 1.00 17 0.529
392 A 13 9 1.00 15 0.600
393 A 9 6 1.00 9 0.667
394 A 17 12 1.00 17 0.706
395 A 17 12 1.00 17 0.706
396 A 17 12 1.00 17 0.706
397 A 16 12 1.00 17 0.706
398 A 14 10 1.00 17 0.588
399 A 14 10 1.00 15 0.667
400 A 10 7 1.00 9 0.778
401 A 31 14 1.00 17 0.824
402 A 31 14 1.00 17 0.824
403 A 31 14 1.00 17 0.824
404 A 15 11 1.00 17 0.647
405 A 15 10 1.00 17 0.588
406 A 15 10 1.00 15 0.667
407 A 11 7 1.00 9 0.778
408 A 46 15 1.00 17 0.882
409 A 46 15 1.00 17 0.882
410 A 46 15 1.00 17 0.882
411 A 4 4 1.00 14 0.286
412 A 5 5 1.00 13 0.385
413 A 4 4 1.00 16 0.250
414 A 5 5 1.00 18 0.278
415 A 3 2 1.00 14 0.143
416 A 4 3 1.00 16 0.188
417 A 2 2 1.00 11 0.182
418 A 1 0 1.00 17 0.000
419 A 1 1 1.00 11 0.091
420 B 1 0 6.23 73 0.000
421 A 11 7 1.00 13 0.538
422 A 13 9 1.00 19 0.474
423 A 3 2 1.00 15 0.133
424 A 3 2 1.00 11 0.182
425 A 1 0 1.00 11 0.000
426 A 1 0 1.00 11 0.000
427 A 5 4 1.00 16 0.250
428 A 2 1 1.00 16 0.062
429 A 4 3 1.00 15 0.200
430 A 1 1 1.00 15 0.067
431 A 1 1 1.00 20 0.050
432 A 3 2 1.00 15 0.133
433 A 6 5 1.00 13 0.385
434 A 1 1 1.00 22 0.045
435 A 3 2 1.00 18 0.111
436 A 3 3 1.00 20 0.150
437 A 3 2 1.00 16 0.125
438 A 6 6 1.00 17 0.353
439 A 1 1 1.00 17 0.059
440 A 4 3 1.00 25 0.120
441 A 2 2 1.00 20 0.100
442 A 3 2 1.00 18 0.111
443 A 6 5 1.00 15 0.333
444 A 2 1 1.00 11 0.091
445 A 5 5 1.00 13 0.385
446 A 3 2 1.00 20 0.100
447 A 2 1 1.00 16 0.062
448 A 4 3 1.00 16 0.188
449 A 2 1 1.00 16 0.062
450 A 1 1 1.00 9 0.111
451 A 2 2 1.00 7 0.286
452 A 2 2 1.00 11 0.182
453 A 1 1 1.00 7 0.143
454 A 1 1 1.00 9 0.111
455 A 1 1 1.00 9 0.111
456 A 2 2 1.00 10 0.200
457 A 2 1 1.00 13 0.077
458 A 2 1 1.00 11 0.091
459 A 2 1 1.00 14 0.071
460 A 4 4 1.00 16 0.250
461 A 2 1 1.00 7 0.143
462 A 2 1 1.00 11 0.091
463 A 5 5 1.00 13 0.385
464 A 5 5 1.00 13 0.385
465 A 5 4 1.00 14 0.286
466 A 2 1 0.78 13 0.077
467 A 3 2 1.00 20 0.100
468 A 4 4 1.00 18 0.222
469 A 2 1 1.00 12 0.083
470 A 2 1 1.00 10 0.100
471 A 3 2 1.00 16 0.125
472 A 2 1 1.00 11 0.091
473 A 1 1 1.00 7 0.143
474 A 2 1 1.00 15 0.067
475 A 2 1 1.00 12 0.083
476 A 3 3 1.00 16 0.188
477 A 2 1 1.00 11 0.091
478 A 2 1 1.00 17 0.059
479 A 2 1 1.00 29 0.034
480 A 2 1 1.00 18 0.056
481 A 3 2 1.00 14 0.143
482 A 2 1 1.00 24 0.042
483 A 2 1 1.00 11 0.091
484 A 3 2 1.00 18 0.111
485 A 3 3 1.00 15 0.200
486 A 3 3 1.00 16 0.188
487 A 10 7 1.00 15 0.467
488 A 5 2 1.00 50 0.040
489 F 0 0 N/A 0 N/A
490 F 0 0 N/A 0 N/A

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