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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 [321] had the largest ratio of [1]

# 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 2 1.00 17 0.118
2 A 2 2 1.00 21 0.095
3 A 1 1 1.00 21 0.048
4 A 2 2 1.00 24 0.083
5 A 2 2 1.00 27 0.074
6 A 1 1 1.00 28 0.036
7 A 3 3 1.00 24 0.125
8 A 3 3 1.32 27 0.111
9 A 6 6 1.47 26 0.231
10 F 0 0 N/A 0.000 N/A
11 A 5 5 1.00 19 0.263
12 A 5 5 1.00 19 0.263
13 A 4 4 1.00 21 0.190
14 A 5 5 1.00 25 0.200
15 A 5 5 1.00 26 0.192
16 A 4 4 1.00 28 0.143
17 A 6 6 0.74 25 0.240
18 A 7 7 1.45 26 0.269
19 A 9 9 1.37 27 0.333
20 F 0 0 N/A 0.000 N/A
21 A 3 3 1.00 24 0.125
22 A 3 3 1.00 24 0.125
23 A 3 3 1.00 24 0.125
24 A 2 2 1.00 22 0.091
25 A 7 7 1.04 24 0.292
26 A 9 9 1.13 24 0.375
27 A 7 6 1.00 26 0.231
28 A 4 3 1.00 26 0.115
29 A 5 4 1.00 26 0.154
30 A 9 8 1.10 26 0.308
31 A 11 11 1.58 26 0.423
32 A 11 11 1.55 27 0.407
33 A 11 11 1.55 34 0.324
34 A 15 15 1.49 26 0.577
35 A 14 14 1.56 26 0.538
36 F 0 0 N/A 0.000 N/A
37 A 3 3 1.00 16 0.188
38 A 7 7 1.45 26 0.269
39 B 12 12 3.28 26 0.462
40 A 12 12 1.32 26 0.462
41 A 14 14 1.28 26 0.538
42 A 17 17 1.29 26 0.654
43 A 21 21 1.56 26 0.808
44 A 18 18 1.61 26 0.692
45 F 0 0 N/A 0.000 N/A
46 A 4 4 1.05 16 0.250
47 A 12 12 1.56 26 0.462
48 A 9 9 1.45 26 0.346
49 A 10 10 1.35 26 0.385
50 A 6 6 1.48 26 0.231
51 A 14 14 1.29 26 0.538
52 A 16 16 1.26 26 0.615
53 A 18 18 1.25 26 0.692
54 A 12 12 1.44 26 0.462
55 A 9 9 1.45 26 0.346
56 A 3 3 1.00 24 0.125
57 A 2 2 1.00 16 0.125
58 A 6 6 1.47 26 0.231
59 A 12 12 1.30 26 0.462
60 A 14 14 1.30 26 0.538
61 A 9 9 1.37 26 0.346
62 A 11 11 1.58 26 0.423
63 F 0 0 N/A 0.000 N/A
64 A 3 3 1.00 16 0.188
65 A 14 14 1.52 26 0.538
66 A 16 16 1.45 26 0.615
67 A 18 18 1.41 26 0.692
68 A 11 11 1.37 26 0.423
69 A 11 11 1.31 26 0.423
70 F 0 0 N/A 0.000 N/A
71 A 4 4 1.07 16 0.250
72 A 18 18 1.60 26 0.692
73 A 19 19 1.54 26 0.731
74 A 22 22 1.50 26 0.846
75 A 2 2 1.00 17 0.118
76 A 4 4 1.06 19 0.211
77 B 3 3 5.04 15 0.200
78 B 1 1 2.42 17 0.059
79 A 3 3 1.00 29 0.103
80 A 3 3 1.00 29 0.103
81 B 12 12 3.24 27 0.444
82 B 12 12 3.19 26 0.462
83 B 12 12 3.24 34 0.353
84 A 16 16 1.49 27 0.593
85 A 14 14 1.56 27 0.519
86 F 0 0 N/A 0.000 N/A
87 A 3 3 1.00 16 0.188
88 A 3 3 1.32 27 0.111
89 A 11 11 1.58 27 0.407
90 A 11 11 1.31 27 0.407
91 A 13 13 1.26 27 0.481
92 A 15 15 1.27 27 0.556
93 A 19 19 1.56 27 0.704
94 A 17 17 1.61 27 0.630
95 F 0 0 N/A 0.000 N/A
96 A 4 4 1.05 16 0.250
97 A 11 11 1.56 27 0.407
98 A 9 9 1.45 27 0.333
99 A 9 9 1.34 27 0.333
100 A 7 7 1.47 27 0.259
101 A 14 14 1.28 27 0.519
102 A 16 16 1.24 27 0.593
103 A 18 18 1.23 27 0.667
104 A 11 11 1.44 27 0.407
105 A 9 9 1.45 27 0.333
106 A 6 6 0.74 25 0.240
107 A 2 2 1.00 16 0.125
108 A 9 9 1.37 27 0.333
109 A 11 11 1.28 27 0.407
110 A 13 13 1.29 27 0.481
111 A 12 12 1.37 27 0.444
112 A 10 10 1.36 27 0.370
113 B 12 12 3.28 27 0.444
114 F 0 0 N/A 0.000 N/A
115 A 3 3 1.00 16 0.188
116 A 14 14 1.49 27 0.519
117 A 16 16 1.44 27 0.593
118 A 17 17 1.38 27 0.630
119 A 12 12 1.36 27 0.444
120 A 12 12 1.30 27 0.444
121 F 0 0 N/A 0.000 N/A
122 A 4 4 1.07 16 0.250
123 A 18 18 1.61 27 0.667
124 A 19 19 1.53 27 0.704
125 A 21 21 1.49 27 0.778
126 A 5 5 1.00 19 0.263
127 A 6 6 1.13 21 0.286
128 A 1 1 1.36 17 0.059
129 A 1 1 0.73 19 0.053
130 A 12 11 0.88 28 0.393
131 A 9 8 0.90 28 0.286
132 A 6 5 0.96 28 0.179
133 A 5 4 1.13 28 0.143
134 A 7 6 1.11 28 0.214
135 A 5 4 1.20 28 0.143
136 A 6 5 1.16 28 0.179
137 A 15 14 0.83 28 0.500
138 A 13 12 0.83 28 0.429
139 A 10 9 0.84 28 0.321
140 A 7 6 0.86 28 0.214
141 A 6 5 0.98 28 0.179
142 A 9 8 0.98 28 0.286
143 A 9 8 1.06 28 0.286
144 A 6 5 1.17 28 0.179
145 A 7 6 1.14 28 0.214
146 A 14 13 1.11 28 0.464
147 A 15 14 1.10 28 0.500
148 A 2 2 1.00 9 0.222
149 A 3 3 1.00 23 0.130
150 A 11 10 0.96 28 0.357
151 A 8 7 1.02 28 0.250
152 A 5 4 1.13 28 0.143
153 A 4 3 1.59 28 0.107
154 A 4 3 1.44 28 0.107
155 A 5 4 1.20 28 0.143
156 A 9 8 1.16 28 0.286
157 A 10 9 0.92 29 0.310
158 A 8 7 0.96 29 0.241
159 A 5 4 1.08 29 0.138
160 A 2 2 1.00 29 0.069
161 A 5 4 1.06 29 0.138
162 A 8 7 1.05 29 0.241
163 A 10 9 1.05 29 0.310
164 A 12 11 0.91 29 0.379
165 A 10 9 0.93 29 0.310
166 A 7 6 1.00 29 0.207
167 A 3 3 1.24 29 0.103
168 A 3 3 1.08 29 0.103
169 A 9 8 0.98 29 0.276
170 A 11 10 0.99 29 0.345
171 A 13 12 1.00 29 0.414
172 A 14 13 1.00 29 0.448
173 A 2 2 1.00 21 0.095
174 A 2 2 1.00 23 0.087
175 A 4 3 2.00 21 0.143
176 A 4 3 1.76 23 0.130
177 A 4 3 1.90 19 0.158
178 A 4 3 2.00 21 0.143
179 A 2 2 1.43 19 0.105
180 A 2 2 1.48 21 0.095
181 A 2 2 1.60 31 0.065
182 A 1 1 1.00 11 0.091
183 A 2 2 1.00 21 0.095
184 A 1 1 1.00 22 0.045
185 A 2 2 1.00 22 0.091
186 A 1 1 1.00 17 0.059
187 A 1 1 1.00 24 0.042
188 A 1 1 1.00 24 0.042
189 A 1 1 1.00 17 0.059
190 A 5 4 1.00 19 0.211
191 A 1 1 1.00 19 0.053
192 A 5 4 1.00 21 0.190
193 A 3 3 1.00 15 0.200
194 A 3 3 1.00 23 0.130
195 A 4 4 1.00 23 0.174
196 A 3 3 1.00 15 0.200
197 A 5 4 1.00 17 0.235
198 A 3 3 1.00 17 0.176
199 A 5 4 1.00 19 0.211
200 A 6 6 1.35 19 0.316
201 A 10 9 1.28 17 0.529
202 A 10 9 1.27 18 0.500
203 A 3 3 1.00 18 0.167
204 A 3 3 1.00 19 0.158
205 A 4 3 1.00 17 0.176
206 A 3 3 1.89 17 0.176
207 A 2 2 1.00 17 0.118
208 A 2 2 1.00 17 0.118
209 A 4 3 1.00 27 0.111
210 B 4 4 2.08 28 0.143
211 A 4 3 1.00 21 0.143
212 B 4 4 2.09 22 0.182
213 A 3 3 1.00 15 0.200
214 A 13 13 1.04 20 0.650
215 A 11 11 1.03 20 0.550
216 A 9 9 1.01 20 0.450
217 A 7 7 1.00 20 0.350
218 A 9 9 1.01 20 0.450
219 A 11 11 1.06 20 0.550
220 A 11 11 1.08 19 0.579
221 A 9 9 1.05 19 0.474
222 A 7 7 1.00 19 0.368
223 A 5 5 1.00 19 0.263
224 A 7 7 1.00 19 0.368
225 A 9 9 1.05 19 0.474
226 A 18 18 1.88 22 0.818
227 A 14 14 1.72 22 0.636
228 A 9 9 1.53 22 0.409
229 A 2 2 1.00 22 0.091
230 A 7 7 1.10 22 0.318
231 A 12 12 1.38 22 0.545
232 A 16 16 1.62 22 0.727
233 A 18 18 1.88 23 0.783
234 A 13 13 1.72 23 0.565
235 A 10 10 1.53 23 0.435
236 A 5 5 1.00 23 0.217
237 A 5 5 1.02 23 0.217
238 A 12 12 1.44 23 0.522
239 A 16 16 1.55 23 0.696
240 A 21 21 1.76 23 0.913
241 A 10 10 1.03 19 0.526
242 A 8 8 1.02 19 0.421
243 A 6 6 1.01 19 0.316
244 A 4 4 1.00 19 0.211
245 A 6 6 1.00 19 0.316
246 A 8 8 1.03 19 0.421
247 A 10 10 1.06 17 0.588
248 A 8 8 1.04 17 0.471
249 A 6 6 1.01 17 0.353
250 A 4 4 1.02 17 0.235
251 A 6 6 1.01 17 0.353
252 A 8 8 1.04 17 0.471
253 A 9 9 1.05 22 0.409
254 A 7 7 1.03 22 0.318
255 A 5 5 1.00 22 0.227
256 A 1 1 1.00 22 0.045
257 A 5 5 0.98 22 0.227
258 A 7 7 1.03 22 0.318
259 A 9 9 1.05 22 0.409
260 A 7 7 1.03 21 0.333
261 A 5 5 1.01 21 0.238
262 A 3 3 1.00 21 0.143
263 A 3 3 1.00 21 0.143
264 A 7 7 1.02 21 0.333
265 A 9 9 1.05 21 0.429
266 F 0 0 N/A 0.000 N/A
267 F 0 0 N/A 0.000 N/A
268 F 0 0 N/A 0.000 N/A
269 A 3 3 1.00 21 0.143
270 F 0 0 N/A 0.000 N/A
271 F 0 0 N/A 0.000 N/A
272 F 0 0 N/A 0.000 N/A
273 F 0 0 N/A 0.000 N/A
274 F 0 0 N/A 0.000 N/A
275 A 6 6 0.71 22 0.273
276 F 0 0 N/A 0.000 N/A
277 F 0 0 N/A 0.000 N/A
278 F 0 0 N/A 0.000 N/A
279 F 0 0 N/A 0.000 N/A
280 A 9 9 1.04 23 0.391
281 A 7 7 1.02 23 0.304
282 A 5 5 0.99 23 0.217
283 A 1 1 1.00 23 0.043
284 A 5 5 0.98 23 0.217
285 A 7 7 1.02 23 0.304
286 A 9 9 1.04 23 0.391
287 A 7 7 1.02 22 0.318
288 A 5 5 1.00 22 0.227
289 A 3 3 1.00 22 0.136
290 A 3 3 1.01 22 0.136
291 A 7 7 1.02 22 0.318
292 A 9 9 1.04 22 0.409
293 A 11 11 1.06 22 0.500
294 A 2 2 1.00 17 0.118
295 A 2 2 1.00 17 0.118
296 A 2 2 1.00 17 0.118
297 A 2 2 1.00 15 0.133
298 A 2 2 1.00 17 0.118
299 A 5 5 1.15 17 0.294
300 A 6 6 1.14 17 0.353
301 A 7 7 1.07 17 0.412
302 A 2 2 1.00 19 0.105
303 A 2 2 1.00 19 0.105
304 A 2 2 1.00 17 0.118
305 A 2 2 1.00 9 0.222
306 A 2 2 1.00 19 0.105
307 A 4 4 1.08 19 0.211
308 A 6 6 1.12 19 0.316
309 A 10 10 1.13 19 0.526
310 A 9 9 1.11 19 0.474
311 A 2 2 1.24 19 0.105
312 A 2 2 1.33 19 0.105
313 A 2 2 1.35 19 0.105
314 A 10 9 1.28 17 0.529
315 A 9 8 1.49 9 0.889
316 A 2 2 1.31 19 0.105
317 A 2 2 1.35 19 0.105
318 A 14 13 1.21 19 0.684
319 A 14 13 1.31 19 0.684
320 A 12 11 1.28 17 0.647
321 A 10 9 1.49 9 1.000
322 A 2 2 1.86 19 0.105
323 A 2 2 1.76 19 0.105
324 A 7 6 0.95 20 0.300
325 A 7 6 1.03 20 0.300
326 A 5 4 1.09 20 0.200
327 A 7 6 1.01 20 0.300
328 A 7 6 1.14 20 0.300
329 A 3 3 0.99 20 0.150
330 A 4 4 0.93 20 0.200
331 A 5 5 0.92 20 0.250
332 A 11 10 0.91 22 0.455
333 A 10 9 1.01 22 0.409
334 A 8 7 1.14 22 0.318
335 A 8 7 1.14 22 0.318
336 A 10 9 1.11 22 0.409
337 A 10 9 1.06 22 0.409
338 A 12 11 1.12 22 0.500
339 A 9 9 0.94 22 0.409
340 A 9 9 0.89 22 0.409
341 B 15 14 2.51 22 0.636
342 B 13 12 2.15 22 0.545
343 A 11 10 1.82 22 0.455
344 A 9 8 1.65 22 0.364
345 A 6 5 1.00 22 0.227
346 A 4 4 1.27 22 0.182
347 A 5 5 1.65 22 0.227
348 A 6 6 1.92 22 0.273
349 F 0 0 N/A 0.000 N/A
350 F 0 0 N/A 0.000 N/A
351 F 0 0 N/A 0.000 N/A
352 F 0 0 N/A 0.000 N/A
353 F 0 0 N/A 0.000 N/A
354 F 0 0 N/A 0.000 N/A
355 F 0 0 N/A 0.000 N/A
356 F 0 0 N/A 0.000 N/A
357 F 0 0 N/A 0.000 N/A
358 F 0 0 N/A 0.000 N/A
359 F 0 0 N/A 0.000 N/A
360 F 0 0 N/A 0.000 N/A
361 F 0 0 N/A 0.000 N/A
362 F 0 0 N/A 0.000 N/A
363 F 0 0 N/A 0.000 N/A
364 F 0 0 N/A 0.000 N/A
365 A 7 6 0.97 19 0.316
366 A 7 6 1.04 19 0.316
367 A 5 4 1.09 19 0.211
368 A 6 5 1.03 19 0.263
369 A 8 7 1.17 19 0.368
370 A 3 3 1.00 19 0.158
371 A 4 4 0.94 19 0.211
372 A 5 5 0.93 19 0.263
373 A 11 10 0.91 21 0.476
374 A 10 9 1.01 21 0.429
375 A 8 7 1.14 21 0.333
376 A 8 7 1.14 21 0.333
377 A 10 9 1.11 21 0.429
378 A 10 9 1.06 21 0.429
379 A 12 11 1.12 21 0.524
380 A 11 11 0.94 21 0.524
381 A 10 10 0.90 21 0.476
382 A 15 14 1.34 21 0.667
383 A 13 12 1.16 21 0.571
384 A 11 10 0.88 21 0.476
385 A 9 8 0.92 21 0.381
386 A 6 5 0.41 21 0.238
387 A 4 4 0.61 21 0.190
388 A 5 5 0.78 21 0.238
389 F 0 0 N/A 0.000 N/A
390 F 0 0 N/A 0.000 N/A
391 F 0 0 N/A 0.000 N/A
392 F 0 0 N/A 0.000 N/A
393 F 0 0 N/A 0.000 N/A
394 F 0 0 N/A 0.000 N/A
395 F 0 0 N/A 0.000 N/A
396 F 0 0 N/A 0.000 N/A
397 F 0 0 N/A 0.000 N/A
398 F 0 0 N/A 0.000 N/A
399 F 0 0 N/A 0.000 N/A
400 F 0 0 N/A 0.000 N/A
401 F 0 0 N/A 0.000 N/A
402 F 0 0 N/A 0.000 N/A
403 F 0 0 N/A 0.000 N/A
404 F 0 0 N/A 0.000 N/A
405 A 11 11 1.00 22 0.500
406 A 9 9 1.03 22 0.409
407 A 7 7 1.00 20 0.350
408 A 2 2 1.00 12 0.167
409 A 2 2 1.00 22 0.091
410 A 12 12 0.94 22 0.545
411 A 13 13 0.98 22 0.591
412 A 14 14 1.01 22 0.636
413 A 11 11 1.12 22 0.500
414 A 10 10 1.17 22 0.455
415 A 9 9 1.01 20 0.450
416 A 3 3 1.00 12 0.250
417 A 14 14 0.96 22 0.636
418 A 2 2 1.44 22 0.091
419 A 2 2 1.90 22 0.091
420 B 2 2 2.38 22 0.091
421 A 8 8 1.00 21 0.381
422 A 7 7 0.98 21 0.333
423 A 5 5 1.03 21 0.238
424 A 4 4 1.00 19 0.211
425 A 4 4 1.07 21 0.190
426 A 9 9 0.98 21 0.429
427 A 11 11 0.96 21 0.524
428 A 7 7 1.00 21 0.333
429 A 2 2 1.00 23 0.087
430 A 4 4 1.00 22 0.182
431 A 4 4 1.07 24 0.167
432 A 2 2 1.00 21 0.095
433 A 4 4 1.13 21 0.190
434 A 1 1 1.00 22 0.045
435 A 4 4 1.06 21 0.190
436 F 0 0 N/A 0.000 N/A
437 F 0 0 N/A 0.000 N/A
438 A 17 16 1.13 24 0.667
439 F 0 0 N/A 0.000 N/A
440 F 0 0 N/A 0.000 N/A
441 F 0 0 N/A 0.000 N/A
442 F 0 0 N/A 0.000 N/A
443 F 0 0 N/A 0.000 N/A
444 F 0 0 N/A 0.000 N/A
445 F 0 0 N/A 0.000 N/A
446 F 0 0 N/A 0.000 N/A
447 F 0 0 N/A 0.000 N/A
448 F 0 0 N/A 0.000 N/A
449 F 0 0 N/A 0.000 N/A
450 F 0 0 N/A 0.000 N/A
451 F 0 0 N/A 0.000 N/A
452 F 0 0 N/A 0.000 N/A
453 F 0 0 N/A 0.000 N/A
454 A 6 5 0.98 24 0.208
455 F 0 0 N/A 0.000 N/A
456 F 0 0 N/A 0.000 N/A
457 F 0 0 N/A 0.000 N/A
458 F 0 0 N/A 0.000 N/A
459 F 0 0 N/A 0.000 N/A
460 F 0 0 N/A 0.000 N/A
461 F 0 0 N/A 0.000 N/A
462 F 0 0 N/A 0.000 N/A
463 F 0 0 N/A 0.000 N/A
464 F 0 0 N/A 0.000 N/A
465 F 0 0 N/A 0.000 N/A
466 F 0 0 N/A 0.000 N/A
467 F 0 0 N/A 0.000 N/A
468 F 0 0 N/A 0.000 N/A
469 F 0 0 N/A 0.000 N/A
470 F 0 0 N/A 0.000 N/A
471 F 0 0 N/A 0.000 N/A
472 F 0 0 N/A 0.000 N/A
473 F 0 0 N/A 0.000 N/A
474 A 6 6 0.93 19 0.316
475 A 4 4 0.94 17 0.235
476 A 2 2 1.00 9 0.222
477 A 4 4 1.00 19 0.211
478 F 0 0 N/A 0.000 N/A
479 F 0 0 N/A 0.000 N/A
480 N/A 1 0 1.00 19 0.000
481 A 3 3 1.15 19 0.158
482 A 4 4 1.11 19 0.211
483 A 2 2 1.00 17 0.118
484 A 2 2 1.00 9 0.222
485 A 2 2 1.00 19 0.105
486 A 2 2 1.00 19 0.105
487 A 3 3 1.03 19 0.158
488 A 4 4 1.19 19 0.211
489 A 2 2 1.00 17 0.118
490 A 1 1 1.00 9 0.111
491 A 2 2 1.00 19 0.105
492 A 2 2 1.00 19 0.105
493 A 2 2 1.00 19 0.105

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