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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 [496] had the largest ratio of [.916699999999999959]

# 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 2 1.00 14 0.143
2 A 4 2 1.00 14 0.143
3 A 3 2 1.00 14 0.143
4 A 2 2 1.00 12 0.167
5 A 3 3 1.00 14 0.214
6 A 4 4 1.00 14 0.286
7 A 5 4 1.00 14 0.286
8 A 6 4 1.00 16 0.250
9 A 4 3 1.00 16 0.188
10 A 4 4 1.00 16 0.250
11 A 2 1 1.00 14 0.071
12 A 5 4 1.00 16 0.250
13 A 5 5 1.00 16 0.312
14 A 7 6 1.00 16 0.375
15 A 7 7 1.00 16 0.438
16 A 12 4 1.00 16 0.250
17 A 8 4 1.00 16 0.250
18 A 6 4 1.00 16 0.250
19 A 3 3 1.00 14 0.214
20 A 8 4 1.00 16 0.250
21 A 8 4 1.00 16 0.250
22 A 12 5 1.00 16 0.312
23 A 9 5 1.00 14 0.357
24 A 7 4 1.00 14 0.286
25 A 5 3 1.00 12 0.250
26 N/A 0 0 1.00 14 0.000
27 N/A 0 0 1.00 14 0.000
28 A 6 6 1.00 16 0.375
29 A 5 5 1.00 16 0.312
30 A 2 2 1.00 14 0.143
31 N/A 0 0 1.00 16 0.000
32 N/A 0 0 1.00 16 0.000
33 A 15 8 1.00 16 0.500
34 A 9 6 1.00 16 0.375
35 A 6 4 1.00 14 0.286
36 N/A 0 0 1.00 16 0.000
37 N/A 0 0 1.00 16 0.000
38 A 8 5 1.00 16 0.312
39 A 7 5 1.00 16 0.312
40 A 6 5 1.00 16 0.312
41 A 5 4 1.00 16 0.250
42 A 6 5 1.00 16 0.312
43 A 7 5 1.00 16 0.312
44 A 8 5 1.00 16 0.312
45 A 10 8 1.00 18 0.444
46 A 9 7 1.00 18 0.389
47 A 8 6 1.00 18 0.333
48 A 7 5 1.00 18 0.278
49 A 7 6 1.00 18 0.333
50 A 9 7 1.00 18 0.389
51 A 9 8 1.00 18 0.444
52 A 11 7 1.00 18 0.389
53 A 23 7 1.00 18 0.389
54 A 20 7 1.00 18 0.389
55 A 14 6 1.00 18 0.333
56 A 12 5 1.00 18 0.278
57 A 12 5 1.00 18 0.278
58 A 18 6 1.00 18 0.333
59 A 19 7 1.00 18 0.389
60 A 7 5 1.00 12 0.417
61 A 6 5 1.00 12 0.417
62 A 5 4 1.00 12 0.333
63 A 6 5 1.00 12 0.417
64 A 7 5 1.00 12 0.417
65 N/A 0 0 1.00 16 0.000
66 N/A 0 0 1.00 16 0.000
67 N/A 0 0 1.00 10 0.000
68 A 2 1 1.00 18 0.056
69 A 2 1 1.00 20 0.050
70 A 3 1 1.00 20 0.050
71 A 4 3 1.00 22 0.136
72 N/A 0 0 1.00 18 0.000
73 A 8 3 1.00 16 0.188
74 A 5 3 1.00 16 0.188
75 A 3 2 1.00 14 0.143
76 N/A 0 0 1.00 14 0.000
77 N/A 0 0 1.00 16 0.000
78 A 3 2 1.00 12 0.167
79 A 3 2 1.00 12 0.167
80 A 3 2 1.00 12 0.167
81 A 3 2 1.00 10 0.200
82 A 3 2 1.00 12 0.167
83 A 3 2 1.00 12 0.167
84 A 3 2 1.00 12 0.167
85 A 5 3 1.00 14 0.214
86 A 5 3 1.00 14 0.214
87 A 5 3 1.00 14 0.214
88 A 5 3 1.00 12 0.250
89 A 5 3 1.00 14 0.214
90 A 5 3 1.00 14 0.214
91 A 5 3 1.00 14 0.214
92 A 4 2 1.00 20 0.100
93 A 4 2 1.00 20 0.100
94 A 5 2 1.00 20 0.100
95 A 7 5 1.00 24 0.208
96 A 6 3 1.00 21 0.143
97 A 5 3 1.00 21 0.143
98 A 4 3 1.00 19 0.158
99 A 5 4 1.00 21 0.190
100 A 6 5 1.00 21 0.238
101 A 7 5 1.00 21 0.238
102 A 10 6 1.00 23 0.261
103 A 9 7 1.00 23 0.304
104 A 6 4 1.00 21 0.190
105 A 9 5 1.00 23 0.217
106 A 9 5 1.00 23 0.217
107 A 15 6 1.00 23 0.261
108 A 7 7 1.00 23 0.304
109 A 6 6 1.00 23 0.261
110 A 3 3 1.00 21 0.143
111 N/A 0 0 1.00 23 0.000
112 N/A 0 0 1.00 23 0.000
113 A 10 9 1.00 23 0.391
114 A 9 9 1.00 23 0.391
115 A 4 4 1.00 21 0.190
116 N/A 0 0 1.00 23 0.000
117 N/A 0 0 1.00 23 0.000
118 A 6 3 1.00 21 0.143
119 A 5 3 1.00 21 0.143
120 A 4 3 1.00 21 0.143
121 A 3 3 1.00 19 0.158
122 A 4 4 1.00 21 0.190
123 A 5 5 1.00 21 0.238
124 A 6 5 1.00 21 0.238
125 A 9 5 1.00 21 0.238
126 A 7 5 1.00 21 0.238
127 A 4 4 1.00 19 0.210
128 A 9 5 1.00 21 0.238
129 A 9 5 1.00 21 0.238
130 A 14 5 1.00 21 0.238
131 A 10 5 1.00 21 0.238
132 A 5 4 1.00 19 0.210
133 A 12 5 1.00 21 0.238
134 A 12 5 1.00 21 0.238
135 A 21 6 1.00 21 0.286
136 A 10 6 1.00 21 0.286
137 A 8 5 1.00 21 0.238
138 A 6 4 1.00 19 0.210
139 N/A 0 0 1.00 21 0.000
140 N/A 0 0 1.00 21 0.000
141 A 16 9 1.00 21 0.429
142 A 10 7 1.00 21 0.333
143 A 7 5 1.00 19 0.263
144 N/A 0 0 1.00 21 0.000
145 N/A 0 0 1.00 21 0.000
146 A 23 10 1.00 21 0.476
147 A 13 8 1.00 21 0.381
148 A 8 5 1.00 19 0.263
149 N/A 0 0 1.00 21 0.000
150 N/A 0 0 1.00 21 0.000
151 N/A 0 0 1.00 23 0.000
152 A 12 5 1.00 23 0.217
153 A 9 5 1.00 23 0.217
154 A 5 3 1.00 21 0.143
155 N/A 0 0 1.00 23 0.000
156 N/A 0 0 1.00 23 0.000
157 A 6 3 1.00 18 0.167
158 A 5 3 1.00 18 0.167
159 A 4 3 1.00 16 0.188
160 A 5 4 1.00 18 0.222
161 A 6 5 1.00 18 0.278
162 A 7 5 1.00 18 0.278
163 A 10 6 1.00 20 0.300
164 A 9 7 1.00 20 0.350
165 A 6 4 1.00 18 0.222
166 A 10 5 1.00 20 0.250
167 A 11 7 1.00 20 0.350
168 A 14 8 1.00 20 0.400
169 A 12 7 1.00 20 0.350
170 A 10 6 1.00 20 0.300
171 A 8 5 1.00 18 0.278
172 N/A 0 0 1.00 20 0.000
173 N/A 0 0 1.00 20 0.000
174 A 18 10 1.00 20 0.500
175 A 11 8 1.00 18 0.444
176 N/A 0 0 1.00 20 0.000
177 N/A 0 0 1.00 20 0.000
178 A 35 11 1.00 18 0.611
179 N/A 0 0 1.00 20 0.000
180 N/A 0 0 1.00 20 0.000
181 N/A 0 0 1.00 20 0.000
182 A 18 5 1.00 20 0.250
183 A 10 5 1.00 20 0.250
184 A 5 3 1.00 18 0.167
185 N/A 0 0 1.00 20 0.000
186 N/A 0 0 1.00 20 0.000
187 A 9 9 1.00 29 0.310
188 A 8 8 1.00 29 0.276
189 A 5 4 1.00 27 0.148
190 A 2 2 1.00 22 0.091
191 N/A 0 0 1.00 29 0.000
192 N/A 0 0 1.00 29 0.000
193 A 14 11 1.00 31 0.355
194 A 12 10 1.00 31 0.323
195 A 8 6 1.00 29 0.207
196 A 4 4 1.00 24 0.167
197 N/A 0 0 1.00 31 0.000
198 N/A 0 0 1.00 31 0.000
199 A 19 13 1.00 31 0.419
200 A 17 13 1.00 31 0.419
201 A 11 7 1.00 29 0.241
202 A 2 2 1.00 24 0.083
203 N/A 0 0 1.00 31 0.000
204 N/A 0 0 1.00 31 0.000
205 A 17 10 1.00 29 0.345
206 A 14 11 1.00 29 0.379
207 A 9 7 1.00 27 0.259
208 A 3 3 1.00 22 0.136
209 N/A 0 0 1.00 29 0.000
210 N/A 0 0 1.00 29 0.000
211 A 24 10 1.00 31 0.323
212 A 20 11 1.00 31 0.355
213 A 12 7 1.00 29 0.241
214 A 5 5 1.00 24 0.208
215 N/A 0 0 1.00 31 0.000
216 N/A 0 0 1.00 31 0.000
217 A 40 13 1.00 31 0.419
218 A 30 13 1.00 31 0.419
219 A 19 8 1.00 29 0.276
220 A 6 6 1.00 24 0.250
221 N/A 0 0 1.00 31 0.000
222 N/A 0 0 1.00 31 0.000
223 A 14 9 1.00 26 0.346
224 A 12 8 1.00 26 0.308
225 A 10 6 1.00 24 0.250
226 A 4 4 1.00 19 0.210
227 N/A 0 0 1.00 26 0.000
228 A 19 11 1.00 28 0.393
229 A 16 10 1.00 28 0.357
230 A 13 8 1.00 26 0.308
231 A 6 6 1.00 21 0.286
232 N/A 0 0 1.00 28 0.000
233 A 24 13 1.00 28 0.464
234 A 21 13 1.00 28 0.464
235 A 16 9 1.00 26 0.346
236 A 6 6 1.00 21 0.286
237 N/A 0 0 1.00 28 0.000
238 A 22 9 1.00 26 0.346
239 A 18 8 1.00 26 0.308
240 A 14 7 1.00 24 0.292
241 A 5 5 1.00 19 0.263
242 N/A 0 0 1.00 26 0.000
243 A 29 11 1.00 28 0.393
244 A 24 12 1.00 28 0.429
245 A 17 9 1.00 26 0.346
246 A 7 7 1.00 21 0.333
247 N/A 0 0 1.00 28 0.000
248 A 45 14 1.00 28 0.500
249 A 34 14 1.00 28 0.500
250 A 24 10 1.00 26 0.385
251 A 7 7 1.00 21 0.333
252 N/A 0 0 1.00 28 0.000
253 A 6 6 1.00 29 0.207
254 A 5 5 1.00 29 0.172
255 A 4 4 1.00 27 0.148
256 A 2 2 1.00 22 0.091
257 N/A 0 0 1.00 29 0.000
258 N/A 0 0 1.00 29 0.000
259 A 6 4 1.00 31 0.129
260 A 5 4 1.00 31 0.129
261 A 4 3 1.00 29 0.103
262 A 2 2 1.00 24 0.083
263 A 5 5 1.00 31 0.161
264 A 6 6 1.00 31 0.194
265 A 10 8 1.00 31 0.258
266 A 7 5 1.00 31 0.161
267 A 6 6 1.00 29 0.207
268 A 2 1 1.00 24 0.042
269 A 9 6 1.00 31 0.194
270 A 11 7 1.00 31 0.226
271 A 22 13 1.00 29 0.448
272 A 13 10 1.00 29 0.345
273 A 10 8 1.00 27 0.296
274 A 4 3 1.00 22 0.136
275 N/A 0 0 1.00 29 0.000
276 N/A 0 0 1.00 29 0.000
277 A 20 12 1.00 31 0.387
278 A 16 12 1.00 31 0.387
279 A 7 7 1.00 29 0.241
280 A 3 3 1.00 24 0.125
281 N/A 0 0 1.00 31 0.000
282 N/A 0 0 1.00 31 0.000
283 A 32 16 1.00 31 0.516
284 A 17 12 1.00 31 0.387
285 A 11 7 1.00 29 0.241
286 A 4 3 1.00 24 0.125
287 N/A 0 0 1.00 31 0.000
288 N/A 0 0 1.00 31 0.000
289 A 11 6 1.00 26 0.231
290 A 9 5 1.00 26 0.192
291 A 7 4 1.00 24 0.167
292 A 2 2 1.00 19 0.105
293 N/A 0 0 1.00 26 0.000
294 A 18 11 1.00 28 0.393
295 A 15 10 1.00 28 0.357
296 A 12 8 1.00 26 0.308
297 A 5 5 1.00 21 0.238
298 N/A 0 0 1.00 28 0.000
299 A 21 14 1.00 28 0.500
300 A 16 10 1.00 28 0.357
301 A 13 10 1.00 26 0.385
302 A 3 2 1.00 21 0.095
303 N/A 0 0 1.00 28 0.000
304 A 29 10 1.00 26 0.385
305 A 24 9 1.00 26 0.346
306 A 19 8 1.00 24 0.333
307 A 6 6 1.00 19 0.316
308 N/A 0 0 1.00 26 0.000
309 A 29 13 1.00 28 0.464
310 A 24 14 1.00 28 0.500
311 A 15 11 1.00 26 0.423
312 A 5 5 1.00 21 0.238
313 N/A 0 0 1.00 28 0.000
314 A 39 14 1.00 28 0.500
315 A 31 12 1.00 26 0.462
316 A 7 6 1.00 21 0.286
317 N/A 0 0 1.00 28 0.000
318 N/A 0 0 1.00 24 0.000
319 N/A 0 0 1.00 24 0.000
320 N/A 0 0 1.00 22 0.000
321 A 4 4 1.00 24 0.167
322 A 9 6 1.00 26 0.231
323 A 11 7 1.00 26 0.269
324 A 4 4 1.00 24 0.167
325 A 9 6 1.00 26 0.231
326 A 11 7 1.00 26 0.269
327 A 6 6 1.00 24 0.250
328 A 12 9 1.00 26 0.346
329 A 19 11 1.00 26 0.423
330 A 6 6 1.00 24 0.250
331 A 12 9 1.00 26 0.346
332 A 19 11 1.00 26 0.423
333 A 16 9 1.00 32 0.281
334 A 13 8 1.00 32 0.250
335 A 10 7 1.00 30 0.233
336 A 4 3 1.00 25 0.120
337 N/A 0 0 1.00 32 0.000
338 A 23 14 1.00 34 0.412
339 A 20 14 1.00 34 0.412
340 A 15 10 1.00 32 0.312
341 A 5 5 1.00 27 0.185
342 N/A 0 0 1.00 34 0.000
343 A 30 16 1.00 34 0.471
344 A 23 13 1.00 34 0.382
345 A 17 12 1.00 32 0.375
346 A 4 3 1.00 27 0.111
347 N/A 0 0 1.00 34 0.000
348 A 39 11 1.00 26 0.423
349 A 32 10 1.00 26 0.385
350 A 25 9 1.00 24 0.375
351 A 6 5 1.00 19 0.263
352 N/A 0 0 1.00 26 0.000
353 A 36 14 1.00 32 0.438
354 A 30 15 1.00 32 0.469
355 A 18 12 1.00 30 0.400
356 A 5 5 1.00 25 0.200
357 N/A 0 0 1.00 32 0.000
358 A 49 15 1.00 34 0.441
359 A 38 13 1.00 32 0.406
360 A 8 7 1.00 27 0.259
361 N/A 0 0 1.00 34 0.000
362 A 22 14 1.00 34 0.412
363 A 17 10 1.00 34 0.294
364 A 14 10 1.00 32 0.312
365 A 4 3 1.00 27 0.111
366 N/A 0 0 1.00 34 0.000
367 A 31 16 1.00 36 0.444
368 A 25 16 1.00 36 0.444
369 A 19 12 1.00 34 0.353
370 A 8 8 1.00 29 0.276
371 N/A 0 0 1.00 36 0.000
372 A 40 17 1.00 36 0.472
373 A 28 14 1.00 36 0.389
374 A 22 13 1.00 34 0.382
375 A 4 3 1.00 29 0.103
376 N/A 0 0 1.00 36 0.000
377 A 46 12 1.00 32 0.375
378 A 38 11 1.00 32 0.344
379 A 30 10 1.00 30 0.333
380 A 7 6 1.00 25 0.240
381 N/A 0 0 1.00 32 0.000
382 A 45 15 1.00 28 0.536
383 A 37 16 1.00 28 0.571
384 A 21 13 1.00 26 0.500
385 A 8 7 1.00 21 0.333
386 N/A 0 0 1.00 28 0.000
387 A 53 15 1.00 34 0.441
388 A 42 13 1.00 32 0.406
389 A 8 7 1.00 27 0.259
390 N/A 0 0 1.00 34 0.000
391 A 30 15 1.00 34 0.441
392 A 22 10 1.00 34 0.294
393 A 18 11 1.00 32 0.344
394 A 4 3 1.00 27 0.111
395 N/A 0 0 1.00 34 0.000
396 A 38 18 1.00 36 0.500
397 A 31 18 1.00 36 0.500
398 A 24 14 1.00 34 0.412
399 A 9 8 1.00 29 0.276
400 N/A 0 0 1.00 36 0.000
401 A 55 18 1.00 36 0.500
402 A 40 15 1.00 36 0.417
403 A 31 14 1.00 34 0.412
404 A 4 3 1.00 29 0.103
405 N/A 0 0 1.00 36 0.000
406 A 61 15 1.00 34 0.441
407 A 50 14 1.00 34 0.412
408 A 39 13 1.00 32 0.406
409 A 7 6 1.00 27 0.222
410 N/A 0 0 1.00 34 0.000
411 A 53 18 1.00 34 0.529
412 A 44 19 1.00 34 0.559
413 A 25 15 1.00 32 0.469
414 A 9 8 1.00 27 0.296
415 N/A 0 0 1.00 34 0.000
416 A 71 17 1.00 28 0.607
417 A 55 15 1.00 26 0.577
418 A 7 6 1.00 21 0.286
419 N/A 0 0 1.00 28 0.000
420 A 18 8 1.00 26 0.308
421 A 15 7 1.00 26 0.269
422 A 12 6 1.00 24 0.250
423 A 4 4 1.00 19 0.210
424 N/A 0 0 1.00 26 0.000
425 A 33 14 1.00 32 0.438
426 A 27 13 1.00 32 0.406
427 A 21 11 1.00 30 0.367
428 A 6 6 1.00 25 0.240
429 N/A 0 0 1.00 32 0.000
430 A 34 17 1.00 34 0.500
431 A 26 13 1.00 34 0.382
432 A 22 13 1.00 32 0.406
433 A 4 3 1.00 27 0.111
434 N/A 0 0 1.00 34 0.000
435 A 40 13 1.00 32 0.406
436 A 33 12 1.00 32 0.375
437 A 26 11 1.00 30 0.367
438 A 7 6 1.00 25 0.240
439 N/A 0 0 1.00 32 0.000
440 A 53 22 1.00 34 0.647
441 A 44 23 1.00 34 0.676
442 A 26 19 1.00 32 0.594
443 A 10 9 1.00 27 0.333
444 N/A 0 0 1.00 34 0.000
445 A 57 23 1.00 34 0.676
446 A 43 20 1.00 32 0.625
447 A 9 7 1.00 27 0.259
448 N/A 0 0 1.00 34 0.000
449 A 27 11 1.00 32 0.344
450 A 22 12 1.00 32 0.375
451 A 15 9 1.00 30 0.300
452 A 4 3 1.00 25 0.120
453 N/A 0 0 1.00 32 0.000
454 A 41 17 1.00 28 0.607
455 A 34 18 1.00 28 0.643
456 A 25 14 1.00 26 0.538
457 A 7 7 1.00 21 0.333
458 N/A 0 0 1.00 28 0.000
459 A 48 19 1.00 34 0.559
460 A 37 17 1.00 34 0.500
461 A 28 15 1.00 32 0.469
462 A 4 3 1.00 27 0.111
463 N/A 0 0 1.00 34 0.000
464 A 64 20 1.00 34 0.588
465 A 53 21 1.00 34 0.618
466 A 37 18 1.00 32 0.562
467 A 7 6 1.00 27 0.222
468 N/A 0 0 1.00 34 0.000
469 A 51 25 1.00 36 0.694
470 A 30 20 1.00 34 0.588
471 A 13 11 1.00 29 0.379
472 N/A 0 0 1.00 36 0.000
473 A 57 27 1.00 34 0.794
474 A 9 7 1.00 29 0.241
475 N/A 0 0 1.00 36 0.000
476 A 34 14 1.00 34 0.412
477 A 26 14 1.00 34 0.412
478 A 19 11 1.00 32 0.344
479 A 4 3 1.00 27 0.111
480 N/A 0 0 1.00 34 0.000
481 A 67 22 1.00 34 0.647
482 A 52 22 1.00 34 0.647
483 A 38 17 1.00 32 0.531
484 A 8 8 1.00 27 0.296
485 N/A 0 0 1.00 34 0.000
486 A 62 23 1.00 28 0.821
487 A 47 20 1.00 28 0.714
488 A 36 18 1.00 26 0.692
489 A 3 2 1.00 21 0.095
490 N/A 0 0 1.00 28 0.000
491 A 87 28 1.00 34 0.824
492 A 71 26 1.00 34 0.765
493 A 49 23 1.00 32 0.719
494 A 7 6 1.00 27 0.222
495 N/A 0 0 1.00 34 0.000
496 A 88 33 1.00 36 0.917
497 A 44 22 1.00 34 0.647
498 A 17 12 1.00 29 0.414
499 N/A 0 0 1.00 36 0.000
500 A 65 28 1.00 34 0.824
501 A 9 7 1.00 29 0.241
502 N/A 0 0 1.00 36 0.000

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