[prev] [prev-tail] [tail] [up]

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 [401] had the largest ratio of [40]

# 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 3 1.00 10 0.300
2 A 4 3 1.00 10 0.300
3 A 3 3 1.00 10 0.300
4 A 2 2 1.00 8 0.250
5 A 2 2 1.00 10 0.200
6 A 3 3 1.00 10 0.300
7 A 4 3 1.00 10 0.300
8 A 5 3 1.00 10 0.300
9 A 7 5 1.00 12 0.417
10 A 6 5 1.00 12 0.417
11 A 5 5 1.00 12 0.417
12 A 4 4 1.00 12 0.333
13 A 5 5 1.00 12 0.417
14 A 6 5 1.00 12 0.417
15 A 7 5 1.00 12 0.417
16 A 3 3 1.00 10 0.300
17 A 6 3 1.00 16 0.188
18 A 5 3 1.00 16 0.188
19 A 4 3 1.00 16 0.188
20 A 3 2 1.00 14 0.143
21 A 3 3 1.00 16 0.188
22 A 4 4 1.00 16 0.250
23 A 5 4 1.00 16 0.250
24 A 7 5 1.00 18 0.278
25 A 6 5 1.00 18 0.278
26 A 5 5 1.00 18 0.278
27 A 4 4 1.00 18 0.222
28 A 5 5 1.00 18 0.278
29 A 6 5 1.00 18 0.278
30 A 7 5 1.00 18 0.278
31 A 3 3 1.00 16 0.188
32 A 3 3 1.00 18 0.167
33 A 3 3 1.00 22 0.136
34 A 4 4 1.00 25 0.160
35 A 3 2 1.00 22 0.091
36 A 3 2 1.00 22 0.091
37 A 3 2 1.00 22 0.091
38 A 3 2 1.00 20 0.100
39 A 3 2 1.00 14 0.143
40 A 3 3 1.00 22 0.136
41 A 4 3 1.00 22 0.136
42 A 3 2 1.00 22 0.091
43 A 3 2 1.00 22 0.091
44 A 6 6 1.00 24 0.250
45 A 8 7 1.00 24 0.292
46 A 9 7 1.00 22 0.318
47 A 4 3 1.00 16 0.188
48 A 4 4 1.00 24 0.167
49 A 4 4 1.00 24 0.167
50 A 7 7 1.00 24 0.292
51 A 11 9 1.00 24 0.375
52 A 19 7 1.00 24 0.292
53 A 15 7 1.00 24 0.292
54 A 11 7 1.00 22 0.318
55 A 5 3 1.00 16 0.188
56 A 5 5 1.00 24 0.208
57 A 5 5 1.00 24 0.208
58 A 9 9 1.00 24 0.375
59 A 16 12 1.00 24 0.500
60 A 13 7 1.00 22 0.318
61 A 6 3 1.00 16 0.188
62 A 6 5 1.00 24 0.208
63 A 6 6 1.00 24 0.250
64 A 2 2 1.00 6 0.333
65 A 3 3 1.00 8 0.375
66 A 4 3 1.00 8 0.375
67 A 3 3 1.00 9 0.333
68 A 4 4 1.00 11 0.364
69 A 5 4 1.00 11 0.364
70 A 2 2 1.00 10 0.200
71 A 2 2 1.00 27 0.074
72 A 2 2 1.00 18 0.111
73 A 2 2 1.00 10 0.200
74 A 2 2 1.00 10 0.200
75 A 1 1 1.00 10 0.100
76 A 1 1 1.00 8 0.125
77 A 2 2 1.00 10 0.200
78 A 2 2 1.00 10 0.200
79 A 2 2 1.00 14 0.143
80 A 2 2 1.00 14 0.143
81 A 2 2 1.00 14 0.143
82 A 1 1 1.00 12 0.083
83 A 2 2 1.00 14 0.143
84 A 2 2 1.00 14 0.143
85 A 7 7 1.00 16 0.438
86 A 11 9 1.00 16 0.562
87 A 14 7 1.00 16 0.438
88 A 14 6 1.00 24 0.250
89 A 11 6 1.00 24 0.250
90 A 8 6 1.00 22 0.273
91 A 3 3 1.00 16 0.188
92 A 0 0 0.00 0 0.000
93 A 0 0 0.00 0 0.000
94 A 26 7 1.00 24 0.292
95 A 20 7 1.00 24 0.292
96 A 12 7 1.00 22 0.318
97 A 4 4 1.00 16 0.250
98 A 0 0 0.00 0 0.000
99 A 0 0 0.00 0 0.000
100 A 33 7 1.00 24 0.292
101 A 17 8 1.00 22 0.364
102 A 5 4 1.00 16 0.250
103 A 0 0 0.00 0 0.000
104 A 0 0 0.00 0 0.000
105 A 17 9 1.00 26 0.346
106 A 12 9 1.00 24 0.375
107 A 5 5 1.00 18 0.278
108 A 0 0 0.00 0 0.000
109 A 0 0 0.00 0 0.000
110 A 0 0 0.00 0 0.000
111 A 20 9 1.00 26 0.346
112 A 14 9 1.00 24 0.375
113 A 6 5 1.00 18 0.278
114 A 0 0 0.00 0 0.000
115 A 0 0 0.00 0 0.000
116 A 0 0 0.00 0 0.000
117 A 23 9 1.00 26 0.346
118 A 16 9 1.00 24 0.375
119 A 7 5 1.00 18 0.278
120 A 0 0 0.00 0 0.000
121 A 0 0 0.00 0 0.000
122 A 0 0 0.00 0 0.000
123 A 18 7 1.00 26 0.269
124 A 14 7 1.00 26 0.269
125 A 10 7 1.00 24 0.292
126 A 4 4 1.00 18 0.222
127 A 0 0 0.00 0 0.000
128 A 33 8 1.00 26 0.308
129 A 25 8 1.00 26 0.308
130 A 15 8 1.00 24 0.333
131 A 5 5 1.00 18 0.278
132 A 0 0 0.00 0 0.000
133 A 59 8 1.00 26 0.308
134 A 41 8 1.00 26 0.308
135 A 21 9 1.00 24 0.375
136 A 6 5 1.00 18 0.278
137 A 0 0 0.00 0 0.000
138 A 6 4 1.00 24 0.167
139 A 5 4 1.00 24 0.167
140 A 4 4 1.00 24 0.167
141 A 3 3 1.00 24 0.125
142 A 4 4 1.00 24 0.167
143 A 5 4 1.00 24 0.167
144 A 6 4 1.00 24 0.167
145 A 28 15 1.00 26 0.577
146 A 21 15 1.00 26 0.577
147 A 15 15 1.00 26 0.577
148 A 10 12 1.00 26 0.462
149 A 14 14 1.00 26 0.538
150 A 19 15 1.00 26 0.577
151 A 25 15 1.00 26 0.577
152 A 0 0 0.00 0 0.000
153 A 0 0 0.00 0 0.000
154 A 0 0 0.00 0 0.000
155 A 0 0 0.00 0 0.000
156 A 0 0 0.00 0 0.000
157 A 0 0 0.00 0 0.000
158 A 0 0 0.00 0 0.000
159 A 0 0 0.00 0 0.000
160 A 0 0 0.00 0 0.000
161 A 0 0 0.00 0 0.000
162 A 2 2 1.00 22 0.091
163 A 0 0 0.00 0 0.000
164 A 0 0 0.00 0 0.000
165 A 0 0 0.00 0 0.000
166 A 0 0 0.00 0 0.000
167 A 0 0 0.00 0 0.000
168 A 0 0 0.00 0 0.000
169 A 0 0 0.00 0 0.000
170 A 14 6 1.00 24 0.250
171 A 11 6 1.00 24 0.250
172 A 8 6 1.00 22 0.273
173 A 3 3 1.00 16 0.188
174 A 0 0 0.00 0 0.000
175 A 6 5 1.00 30 0.167
176 A 8 6 1.00 30 0.200
177 A 7 6 1.00 30 0.200
178 A 6 5 1.00 28 0.179
179 A 3 3 1.00 23 0.130
180 A 4 4 1.00 30 0.133
181 A 7 7 1.00 30 0.233
182 A 11 9 1.00 30 0.300
183 A 30 15 1.00 32 0.469
184 A 24 15 1.00 32 0.469
185 A 16 10 1.00 32 0.312
186 A 8 7 1.00 30 0.233
187 A 4 4 1.00 25 0.160
188 A 5 5 1.00 32 0.156
189 A 9 9 1.00 32 0.281
190 A 16 12 1.00 32 0.375
191 A 14 8 1.00 32 0.250
192 A 12 8 1.00 32 0.250
193 A 10 8 1.00 32 0.250
194 A 8 7 1.00 30 0.233
195 A 4 4 1.00 25 0.160
196 A 0 0 0.00 0 0.000
197 A 0 0 0.00 0 0.000
198 A 27 14 1.00 31 0.452
199 A 20 14 1.00 31 0.452
200 A 14 14 1.00 31 0.452
201 A 9 11 1.00 31 0.355
202 A 13 13 1.00 31 0.419
203 A 18 14 1.00 31 0.452
204 A 20 14 1.00 23 0.609
205 A 14 14 1.00 23 0.609
206 A 9 11 1.00 23 0.478
207 A 13 13 1.00 23 0.565
208 A 18 14 1.00 23 0.609
209 A 0 0 0.00 0 0.000
210 A 12 8 1.00 32 0.250
211 A 10 8 1.00 32 0.250
212 A 8 7 1.00 30 0.233
213 A 4 4 1.00 25 0.160
214 A 0 0 0.00 0 0.000
215 A 0 0 0.00 0 0.000
216 A 0 0 0.00 0 0.000
217 A 14 8 1.00 29 0.276
218 A 11 8 1.00 29 0.276
219 A 8 6 1.00 27 0.222
220 A 3 3 1.00 22 0.136
221 A 8 4 1.00 29 0.138
222 A 12 7 1.00 29 0.241
223 A 15 8 1.00 29 0.276
224 A 19 12 1.00 31 0.387
225 A 10 8 1.00 29 0.276
226 A 4 4 1.00 24 0.167
227 A 10 5 1.00 31 0.161
228 A 14 9 1.00 31 0.290
229 A 23 13 1.00 31 0.419
230 A 12 9 1.00 29 0.310
231 A 5 5 1.00 24 0.208
232 A 12 6 1.00 31 0.194
233 A 17 7 1.00 31 0.226
234 A 0 0 0.00 0 0.000
235 A 0 0 0.00 0 0.000
236 A 0 0 0.00 0 0.000
237 A 0 0 0.00 0 0.000
238 A 0 0 0.00 0 0.000
239 A 0 0 0.00 0 0.000
240 A 0 0 0.00 0 0.000
241 A 0 0 0.00 0 0.000
242 A 14 8 1.00 25 0.320
243 A 11 8 1.00 25 0.320
244 A 8 7 1.00 23 0.304
245 A 3 3 1.00 22 0.136
246 A 7 8 1.00 25 0.320
247 A 11 10 1.00 25 0.400
248 A 14 10 1.00 25 0.400
249 A 15 10 1.00 25 0.400
250 A 12 10 1.00 25 0.400
251 A 9 8 1.00 23 0.348
252 A 4 3 1.00 22 0.136
253 A 11 9 1.00 25 0.360
254 A 15 10 1.00 25 0.400
255 A 18 10 1.00 25 0.400
256 A 16 8 1.00 27 0.296
257 A 13 8 1.00 27 0.296
258 A 8 5 1.00 25 0.200
259 A 12 10 1.00 27 0.370
260 A 15 9 1.00 27 0.333
261 A 16 11 1.00 27 0.407
262 A 13 9 1.00 27 0.333
263 A 8 4 1.00 24 0.167
264 A 14 11 1.00 27 0.407
265 A 17 12 1.00 27 0.444
266 A 19 13 1.00 27 0.482
267 A 16 12 1.00 27 0.444
268 A 6 6 1.00 25 0.240
269 A 18 13 1.00 27 0.482
270 A 21 14 1.00 27 0.518
271 A 31 13 1.00 27 0.482
272 A 28 10 1.00 27 0.370
273 A 18 7 1.00 24 0.292
274 A 32 12 1.00 27 0.444
275 A 10 8 1.00 26 0.308
276 A 11 9 1.00 26 0.346
277 A 9 7 1.00 34 0.206
278 A 11 9 1.00 34 0.265
279 A 2 2 1.00 26 0.077
280 A 4 4 1.00 25 0.160
281 A 4 4 1.00 30 0.133
282 A 4 4 1.00 29 0.138
283 A 16 8 1.00 19 0.421
284 A 11 5 1.00 19 0.263
285 A 15 10 1.00 19 0.526
286 A 18 9 1.00 19 0.474
287 A 16 13 1.00 19 0.684
288 A 15 14 1.00 19 0.737
289 A 11 10 1.00 17 0.588
290 A 11 4 1.00 16 0.250
291 A 17 14 1.00 19 0.737
292 A 16 14 1.00 19 0.737
293 A 23 8 1.00 19 0.421
294 A 18 5 1.00 19 0.263
295 A 22 10 1.00 19 0.526
296 A 23 10 1.00 19 0.526
297 A 18 7 1.00 17 0.412
298 A 23 10 1.00 19 0.526
299 A 22 14 1.00 19 0.737
300 A 18 11 1.00 19 0.579
301 A 18 4 1.00 16 0.250
302 A 24 16 1.00 19 0.842
303 A 4 3 1.00 23 0.130
304 A 4 3 1.00 27 0.111
305 A 4 3 1.00 27 0.111
306 A 4 4 1.00 27 0.148
307 A 5 4 1.00 27 0.148
308 A 4 3 1.00 27 0.111
309 A 12 6 1.00 16 0.375
310 A 28 19 1.00 29 0.655
311 A 21 12 1.00 29 0.414
312 A 10 5 1.00 27 0.185
313 A 16 5 1.00 29 0.172
314 A 23 12 1.00 29 0.414
315 A 23 16 1.00 29 0.552
316 A 16 9 1.00 29 0.310
317 A 10 5 1.00 26 0.192
318 A 15 9 1.00 29 0.310
319 A 26 18 1.00 29 0.621
320 A 34 18 1.00 29 0.621
321 A 25 12 1.00 29 0.414
322 A 13 7 1.00 27 0.259
323 A 29 12 1.00 29 0.414
324 A 36 18 1.00 29 0.621
325 A 36 13 1.00 29 0.448
326 A 32 10 1.00 29 0.345
327 A 20 9 1.00 26 0.346
328 A 35 11 1.00 29 0.379
329 A 12 6 1.00 22 0.273
330 A 10 5 1.00 22 0.227
331 A 8 4 1.00 20 0.200
332 A 0 0 0.00 0 0.000
333 A 4 4 1.00 32 0.125
334 A 5 5 1.00 36 0.139
335 A 4 4 1.00 38 0.105
336 A 5 5 1.00 38 0.132
337 A 2 2 1.00 26 0.077
338 A 4 4 1.00 27 0.148
339 A 1 1 1.00 38 0.026
340 A 2 2 1.00 39 0.051
341 A 1 1 1.00 34 0.029
342 A 3 3 1.00 35 0.086
343 A 13 7 1.00 24 0.292
344 A 11 6 1.00 24 0.250
345 A 8 9 1.00 22 0.409
346 A 0 0 0.00 0 0.000
347 A 12 6 1.00 25 0.240
348 A 10 5 1.00 25 0.200
349 A 8 4 1.00 23 0.174
350 A 0 0 0.00 0 0.000
351 A 10 5 1.00 18 0.278
352 A 9 4 1.00 18 0.222
353 A 6 3 1.00 16 0.188
354 A 6 3 1.00 15 0.200
355 A 9 4 1.00 18 0.222
356 A 10 5 1.00 18 0.278
357 A 11 5 1.00 18 0.278
358 A 11 7 1.00 24 0.292
359 A 10 7 1.00 24 0.292
360 A 9 7 1.00 22 0.318
361 A 8 6 1.00 21 0.286
362 A 4 4 1.00 24 0.167
363 A 6 6 1.00 24 0.250
364 A 7 6 1.00 24 0.250
365 A 9 6 1.00 24 0.250
366 A 11 6 1.00 24 0.250
367 A 52 19 1.22 26 0.731
368 A 38 16 1.00 24 0.667
369 A 17 12 1.00 23 0.522
370 F 0 0 N/A 0. N/A
371 F 0 0 N/A 0. N/A
372 F 0 0 N/A 0. N/A
373 A 28 13 1.00 23 0.565
374 F 0 0 N/A 0. N/A
375 A 0 0 0.00 0 0.000
376 A 0 0 0.00 0 0.000
377 A 0 0 0.00 0 0.000
378 A 1 1 1.00 16 0.062
379 A 7 7 1.00 32 0.219
380 A 7 7 1.00 30 0.233
381 A 6 5 1.00 29 0.172
382 A 6 6 1.00 32 0.188
383 A 4 4 1.00 32 0.125
384 A 7 7 1.00 32 0.219
385 A 11 9 1.00 32 0.281
386 A 35 9 1.00 32 0.281
387 A 29 9 1.00 32 0.281
388 A 23 9 1.00 30 0.300
389 A 17 8 1.00 29 0.276
390 A 13 5 1.00 32 0.156
391 A 15 9 1.00 32 0.281
392 A 23 11 1.00 32 0.344
393 A 73 27 1.00 32 0.844
394 A 41 19 1.00 31 0.613
395 A 0 0 0.00 0 0.000
396 A 0 0 0.00 0 0.000
397 A 148 32 1.00 32 1.000
398 A 64 22 1.00 31 0.710
399 A 0 0 0.00 0 0.000
400 A 0 0 0.00 0 0.000
401 A 3 3 1.00 40 0.075
402 A 4 4 1.00 28 0.143
403 A 4 4 1.00 32 0.125
404 A 7 4 1.00 20 0.200
405 A 6 4 1.00 20 0.200
406 A 5 4 1.00 20 0.200
407 A 4 3 1.00 18 0.167
408 A 4 4 1.00 20 0.200
409 A 5 5 1.00 20 0.250
410 A 6 5 1.00 20 0.250
411 A 8 6 1.00 22 0.273
412 A 7 6 1.00 22 0.273
413 A 6 6 1.00 22 0.273
414 A 5 5 1.00 22 0.227
415 A 6 6 1.00 22 0.273
416 A 7 6 1.00 22 0.273
417 A 8 6 1.00 22 0.273
418 A 4 4 1.00 20 0.200
419 A 4 4 1.00 24 0.167
420 A 4 3 1.00 26 0.115
421 A 4 3 1.00 26 0.115
422 A 4 3 1.00 24 0.125
423 A 4 3 1.00 18 0.167
424 A 4 4 1.00 26 0.154
425 A 5 4 1.00 26 0.154
426 A 4 3 1.00 26 0.115
427 A 4 3 1.00 26 0.115
428 A 7 7 1.00 28 0.250
429 A 9 8 1.00 28 0.286
430 A 10 8 1.00 26 0.308
431 A 5 4 1.00 20 0.200
432 A 5 5 1.00 28 0.179
433 A 5 5 1.00 28 0.179
434 A 8 8 1.00 28 0.286
435 A 16 8 1.00 28 0.286
436 A 12 8 1.00 26 0.308
437 A 6 4 1.00 20 0.200
438 A 6 6 1.00 28 0.214
439 A 6 6 1.00 28 0.214
440 A 10 10 1.00 28 0.357
441 A 7 4 1.00 20 0.200
442 A 7 6 1.00 28 0.214
443 A 7 7 1.00 28 0.250
444 A 3 3 1.00 14 0.214
445 A 12 7 1.00 28 0.250
446 A 9 7 1.00 26 0.269
447 A 4 4 1.00 20 0.200
448 A 0 0 0.00 0 0.000
449 A 0 0 0.00 0 0.000
450 A 21 8 1.00 28 0.286
451 A 13 8 1.00 26 0.308
452 A 5 5 1.00 20 0.250
453 A 0 0 0.00 0 0.000
454 A 0 0 0.00 0 0.000
455 A 34 8 1.00 28 0.286
456 A 18 9 1.00 26 0.346
457 A 6 5 1.00 20 0.250
458 A 0 0 0.00 0 0.000
459 A 0 0 0.00 0 0.000
460 A 18 10 1.00 30 0.333
461 A 13 10 1.00 28 0.357
462 A 6 6 1.00 22 0.273
463 A 0 0 0.00 0 0.000
464 A 0 0 0.00 0 0.000
465 A 21 10 1.00 30 0.333
466 A 15 10 1.00 28 0.357
467 A 7 6 1.00 22 0.273
468 A 0 0 0.00 0 0.000
469 A 0 0 0.00 0 0.000
470 A 15 8 1.00 30 0.267
471 A 11 8 1.00 28 0.286
472 A 5 5 1.00 22 0.227
473 A 0 0 0.00 0 0.000
474 A 26 9 1.00 30 0.300
475 A 16 9 1.00 28 0.321
476 A 6 6 1.00 22 0.273
477 A 0 0 0.00 0 0.000
478 A 42 9 1.00 30 0.300
479 A 22 10 1.00 28 0.357
480 A 7 6 1.00 22 0.273
481 A 0 0 0.00 0 0.000
482 A 7 5 1.00 28 0.179
483 A 6 5 1.00 28 0.179
484 A 5 5 1.00 28 0.179
485 A 4 4 1.00 28 0.143
486 A 5 5 1.00 28 0.179
487 A 6 5 1.00 28 0.179
488 A 7 5 1.00 28 0.179
489 A 29 16 1.00 30 0.533
490 A 22 16 1.00 30 0.533
491 A 16 16 1.00 30 0.533
492 A 11 13 1.00 30 0.433
493 A 15 15 1.00 30 0.500
494 A 20 16 1.00 30 0.533
495 A 26 16 1.00 30 0.533
496 A 0 0 0.00 0 0.000
497 A 0 0 0.00 0 0.000
498 A 0 0 0.00 0 0.000
499 A 0 0 0.00 0 0.000
500 A 0 0 0.00 0 0.000
501 A 0 0 0.00 0 0.000
502 A 0 0 0.00 0 0.000
503 A 0 0 0.00 0 0.000
504 A 0 0 0.00 0 0.000
505 A 0 0 0.00 0 0.000
506 A 3 3 1.00 26 0.115
507 A 0 0 0.00 0 0.000
508 A 0 0 0.00 0 0.000
509 A 0 0 0.00 0 0.000
510 A 0 0 0.00 0 0.000
511 A 0 0 0.00 0 0.000
512 A 0 0 0.00 0 0.000
513 A 0 0 0.00 0 0.000
514 A 12 7 1.00 28 0.250
515 A 9 7 1.00 26 0.269
516 A 4 4 1.00 20 0.200
517 A 0 0 0.00 0 0.000
518 A 9 5 1.00 28 0.179
519 A 11 9 1.00 30 0.300
520 A 12 10 1.00 30 0.333
521 A 10 8 1.00 38 0.210
522 A 12 10 1.00 38 0.263
523 A 15 9 1.00 33 0.273
524 A 12 9 1.00 33 0.273
525 A 9 7 1.00 31 0.226
526 A 4 4 1.00 26 0.154
527 A 9 5 1.00 33 0.152
528 A 13 8 1.00 33 0.242
529 A 16 9 1.00 33 0.273
530 A 20 13 1.00 35 0.371
531 A 11 9 1.00 33 0.273
532 A 5 5 1.00 28 0.179
533 A 11 6 1.00 35 0.171
534 A 15 10 1.00 35 0.286
535 A 24 14 1.00 35 0.400
536 A 13 10 1.00 33 0.303
537 A 6 6 1.00 28 0.214
538 A 13 7 1.00 35 0.200
539 A 18 8 1.00 35 0.229
540 A 0 0 0.00 0 0.000
541 A 0 0 0.00 0 0.000
542 A 0 0 0.00 0 0.000
543 A 0 0 0.00 0 0.000
544 A 0 0 0.00 0 0.000
545 A 0 0 0.00 0 0.000
546 A 0 0 0.00 0 0.000
547 A 0 0 0.00 0 0.000

[prev] [prev-tail] [front] [up]