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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 [227] had the largest ratio of [1.11765000000000003]

# 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 4 0.89 21 0.190
2 A 5 4 0.89 21 0.190
3 A 5 4 0.91 21 0.190
4 A 5 4 0.96 19 0.211
5 A 5 4 0.96 19 0.211
6 A 7 6 1.13 21 0.286
7 A 9 8 1.20 21 0.381
8 A 10 9 1.27 21 0.429
9 A 7 6 1.29 21 0.286
10 A 7 6 1.31 21 0.286
11 A 1 1 1.00 12 0.083
12 A 5 4 0.92 21 0.190
13 A 5 4 0.89 21 0.190
14 A 5 4 0.88 21 0.190
15 A 5 4 0.89 23 0.174
16 A 5 4 0.90 23 0.174
17 A 5 4 0.89 21 0.190
18 A 5 4 0.92 21 0.190
19 A 8 7 1.46 23 0.304
20 A 10 9 1.34 23 0.391
21 A 9 8 1.19 23 0.348
22 A 7 6 1.19 23 0.261
23 A 7 6 1.17 23 0.261
24 A 5 4 1.10 14 0.286
25 A 5 4 0.90 23 0.174
26 A 5 4 0.89 23 0.174
27 A 5 4 0.89 23 0.174
28 A 5 4 0.93 23 0.174
29 A 6 5 0.97 23 0.217
30 A 5 4 0.98 21 0.190
31 A 6 5 0.98 21 0.238
32 A 7 6 1.15 23 0.261
33 A 8 7 1.20 23 0.304
34 A 10 9 1.20 23 0.391
35 A 8 7 1.21 23 0.304
36 A 7 6 1.20 23 0.261
37 A 6 5 1.00 14 0.357
38 A 5 4 0.96 23 0.174
39 A 6 5 1.01 23 0.217
40 A 5 4 0.92 23 0.174
41 A 8 7 0.95 23 0.304
42 A 6 5 0.94 23 0.217
43 A 6 5 0.99 21 0.238
44 A 7 6 1.07 21 0.286
45 A 9 8 1.07 23 0.348
46 A 11 10 1.12 23 0.435
47 A 12 11 1.12 23 0.478
48 A 11 10 1.12 23 0.435
49 A 9 8 1.12 23 0.348
50 A 7 6 1.21 14 0.429
51 A 6 5 1.01 23 0.217
52 A 7 6 1.02 23 0.261
53 A 8 7 1.32 23 0.304
54 A 8 7 1.07 23 0.304
55 A 8 7 0.99 23 0.304
56 A 7 6 1.03 21 0.286
57 A 8 7 1.12 21 0.333
58 A 12 11 1.11 23 0.478
59 A 12 11 1.11 23 0.478
60 A 14 13 1.10 23 0.565
61 A 12 11 1.10 23 0.478
62 A 10 9 1.17 23 0.391
63 A 8 7 1.22 14 0.500
64 A 7 6 1.06 23 0.261
65 A 8 7 1.01 23 0.304
66 A 9 8 1.20 23 0.348
67 A 9 8 1.03 25 0.320
68 A 8 7 0.95 25 0.280
69 A 6 5 0.97 23 0.217
70 A 9 8 0.98 23 0.348
71 A 9 8 1.06 25 0.320
72 A 12 11 1.13 25 0.440
73 A 12 11 1.12 25 0.440
74 A 10 9 1.09 25 0.360
75 A 9 8 1.03 25 0.320
76 A 8 7 0.97 16 0.438
77 A 6 5 0.97 25 0.200
78 A 7 6 0.95 25 0.240
79 A 8 7 1.05 25 0.280
80 A 10 9 0.89 25 0.360
81 A 9 8 0.89 25 0.320
82 A 7 6 0.98 23 0.261
83 A 11 10 0.98 23 0.435
84 A 11 10 1.01 25 0.400
85 A 15 14 1.04 25 0.560
86 A 14 13 1.04 25 0.520
87 A 13 12 1.02 25 0.480
88 A 11 10 0.99 25 0.400
89 A 9 8 0.98 16 0.500
90 A 7 6 0.98 25 0.240
91 A 8 7 0.90 25 0.280
92 A 10 9 0.90 25 0.360
93 A 7 6 1.02 25 0.240
94 A 6 5 0.97 25 0.200
95 A 4 3 1.00 23 0.130
96 A 6 5 1.00 23 0.217
97 A 7 6 1.07 25 0.240
98 A 9 8 1.14 25 0.320
99 A 9 8 1.11 25 0.320
100 A 8 7 1.10 25 0.280
101 A 7 6 1.05 25 0.240
102 A 5 4 1.00 16 0.250
103 A 4 3 1.00 25 0.120
104 A 5 4 0.97 25 0.160
105 A 6 5 1.04 25 0.200
106 A 8 7 1.01 25 0.280
107 A 7 6 0.98 25 0.240
108 A 5 4 0.97 23 0.174
109 A 7 6 0.98 23 0.261
110 A 9 8 1.06 25 0.320
111 A 12 11 1.13 25 0.440
112 A 11 10 1.11 25 0.400
113 A 10 9 1.11 25 0.360
114 A 8 7 1.03 25 0.280
115 A 6 5 0.97 16 0.312
116 A 5 4 0.97 25 0.160
117 A 6 5 1.02 25 0.200
118 A 7 6 1.05 25 0.240
119 A 9 8 0.96 25 0.320
120 A 8 7 0.92 25 0.280
121 A 6 5 1.00 23 0.217
122 A 9 8 1.06 23 0.348
123 A 11 10 1.09 25 0.400
124 A 14 13 1.12 25 0.520
125 A 14 13 1.09 25 0.520
126 A 11 10 1.08 25 0.400
127 A 10 9 1.06 25 0.360
128 A 8 7 1.08 16 0.438
129 A 6 5 1.02 25 0.200
130 A 7 6 0.96 25 0.240
131 A 8 7 0.98 25 0.280
132 F 0 0 N/A 0.000 N/A
133 A 8 7 1.01 23 0.304
134 A 7 6 0.97 23 0.261
135 A 5 4 0.99 21 0.190
136 A 6 5 0.99 21 0.238
137 A 5 4 0.99 23 0.174
138 A 5 4 0.98 23 0.174
139 A 5 4 0.98 23 0.174
140 A 5 4 0.98 14 0.286
141 A 5 4 0.97 23 0.174
142 A 6 5 0.97 23 0.217
143 A 7 6 1.02 23 0.261
144 A 11 11 0.84 15 0.733
145 A 9 9 0.88 15 0.600
146 A 7 7 0.84 15 0.467
147 A 1 1 1.00 13 0.077
148 A 5 5 1.05 15 0.333
149 A 7 7 0.84 15 0.467
150 A 9 9 0.91 15 0.600
151 A 11 11 0.84 15 0.733
152 A 8 8 0.96 21 0.381
153 A 6 6 0.97 21 0.286
154 A 4 4 1.00 19 0.211
155 A 4 4 1.00 19 0.211
156 A 6 5 1.00 21 0.238
157 A 7 6 0.94 21 0.286
158 A 6 5 0.80 21 0.238
159 A 6 5 0.89 21 0.238
160 A 6 5 1.00 21 0.238
161 A 1 1 1.00 12 0.083
162 A 3 3 1.00 21 0.143
163 A 5 5 0.97 21 0.238
164 A 7 7 0.96 21 0.333
165 A 9 8 1.08 23 0.348
166 A 8 7 1.16 23 0.304
167 A 7 6 1.30 21 0.286
168 A 5 4 1.05 21 0.190
169 A 5 4 0.90 23 0.174
170 A 5 4 0.91 23 0.174
171 A 5 4 0.90 23 0.174
172 A 5 4 0.90 23 0.174
173 A 5 4 0.91 23 0.174
174 A 5 4 1.10 14 0.286
175 A 5 4 1.21 23 0.174
176 A 6 5 1.39 23 0.217
177 A 7 6 1.19 23 0.261
178 A 5 4 1.01 14 0.286
179 A 5 4 0.98 14 0.286
180 A 8 7 1.10 23 0.304
181 A 6 5 0.96 23 0.217
182 A 4 3 1.00 21 0.143
183 A 5 4 0.96 21 0.190
184 A 5 4 0.93 23 0.174
185 A 5 4 0.93 23 0.174
186 A 5 4 0.94 23 0.174
187 A 5 4 0.96 23 0.174
188 A 4 3 1.00 23 0.130
189 A 6 5 1.00 14 0.357
190 A 8 7 1.21 23 0.304
191 A 10 9 1.21 23 0.391
192 A 12 11 1.21 23 0.478
193 A 8 7 1.10 23 0.304
194 A 5 4 0.97 23 0.174
195 A 5 4 0.98 21 0.190
196 A 5 4 0.95 21 0.190
197 A 5 4 0.94 23 0.174
198 A 5 4 0.93 23 0.174
199 A 5 4 0.95 23 0.174
200 A 5 4 0.98 23 0.174
201 A 5 4 0.97 23 0.174
202 A 7 6 1.21 14 0.429
203 A 10 9 1.13 23 0.391
204 A 12 11 1.14 23 0.478
205 A 14 13 1.14 23 0.565
206 A 6 5 1.05 23 0.217
207 A 6 5 1.00 23 0.217
208 A 7 6 1.11 21 0.286
209 A 5 4 0.95 21 0.190
210 A 5 4 0.94 23 0.174
211 A 5 4 0.93 23 0.174
212 A 6 5 1.10 23 0.217
213 A 6 5 1.00 23 0.217
214 A 6 5 1.05 23 0.217
215 A 8 7 1.22 14 0.500
216 A 11 10 1.19 23 0.435
217 A 14 13 1.13 23 0.565
218 A 16 15 1.13 23 0.652
219 A 10 9 1.20 14 0.643
220 A 12 12 0.62 17 0.706
221 A 10 10 0.67 17 0.588
222 A 8 8 0.80 17 0.471
223 A 6 6 1.00 17 0.353
224 A 7 7 1.06 17 0.412
225 A 11 11 0.81 17 0.647
226 A 15 15 0.71 17 0.882
227 A 19 19 0.63 17 1.118
228 A 17 16 1.04 25 0.640
229 A 15 14 1.04 25 0.560
230 A 13 12 1.07 23 0.522
231 A 7 6 1.10 23 0.261
232 A 12 11 1.00 25 0.440
233 A 14 13 0.96 25 0.520
234 A 9 8 1.01 25 0.320
235 A 7 6 0.96 25 0.240
236 A 6 5 0.97 25 0.200
237 A 8 7 0.97 16 0.438
238 A 6 5 1.05 25 0.200
239 A 7 6 1.02 25 0.240
240 A 11 10 1.10 25 0.400
241 A 19 18 1.04 25 0.720
242 A 17 16 1.04 25 0.640
243 A 15 14 1.05 23 0.609
244 A 13 12 1.07 23 0.522
245 A 11 10 1.00 25 0.400
246 A 13 12 1.00 25 0.480
247 A 10 9 0.92 25 0.360
248 A 8 7 0.92 25 0.280
249 A 7 6 0.98 25 0.240
250 A 9 8 0.98 16 0.500
251 A 9 8 1.03 25 0.320
252 A 7 6 1.06 25 0.240
253 A 8 7 0.98 25 0.280
254 A 10 9 1.00 16 0.562
255 A 9 8 1.00 10 0.800
256 A 7 6 1.00 10 0.600
257 A 15 14 0.94 25 0.560
258 A 10 9 1.17 25 0.360
259 A 7 6 1.10 23 0.261
260 A 7 6 1.07 23 0.261
261 A 12 11 1.00 25 0.440
262 A 14 13 0.97 25 0.520
263 A 8 7 1.07 25 0.280
264 A 6 5 0.98 25 0.200
265 A 5 4 1.00 25 0.160
266 A 5 4 1.00 16 0.250
267 A 6 5 1.05 25 0.200
268 A 10 9 1.09 25 0.360
269 A 11 10 1.11 25 0.400
270 A 15 14 1.08 25 0.560
271 A 9 8 1.23 25 0.320
272 A 12 11 1.06 23 0.478
273 A 12 11 1.07 23 0.478
274 A 14 13 0.99 25 0.520
275 A 16 15 0.96 25 0.600
276 A 7 6 1.18 25 0.240
277 A 6 5 0.97 25 0.200
278 A 4 3 1.00 25 0.120
279 A 6 5 0.97 16 0.312
280 A 9 8 1.02 25 0.320
281 A 11 10 1.07 25 0.400
282 A 13 12 1.08 25 0.480
283 A 14 13 1.01 25 0.520
284 A 14 13 1.00 25 0.520
285 A 14 13 1.01 23 0.565
286 A 13 12 0.99 23 0.522
287 A 16 15 0.97 25 0.600
288 A 17 16 0.94 25 0.640
289 A 7 6 1.14 25 0.240
290 A 5 4 0.95 25 0.160
291 A 5 4 0.97 25 0.160
292 A 8 7 1.08 16 0.438
293 A 10 9 1.09 25 0.360
294 A 12 11 1.10 25 0.440
295 A 14 13 1.11 25 0.520
296 A 9 8 1.12 16 0.500
297 A 5 4 1.00 10 0.400
298 F 0 0 N/A 0.000 N/A
299 A 7 6 1.08 23 0.261
300 A 7 6 1.08 21 0.286
301 A 7 6 1.08 21 0.286
302 A 7 6 1.08 23 0.261
303 A 7 6 1.08 23 0.261
304 A 8 7 0.99 23 0.304
305 A 6 5 0.97 23 0.217
306 A 5 4 0.97 23 0.174
307 A 5 4 0.98 14 0.286
308 A 5 4 0.98 23 0.174
309 A 5 4 0.98 23 0.174
310 A 5 4 0.98 23 0.174
311 A 6 5 0.88 21 0.238
312 A 6 5 0.94 21 0.238
313 A 5 4 0.93 19 0.211
314 A 6 5 1.32 19 0.263
315 A 6 5 1.28 21 0.238
316 A 6 5 1.29 21 0.238
317 A 7 6 0.94 21 0.286
318 A 7 6 1.00 21 0.286
319 A 7 6 1.12 21 0.286
320 A 1 1 1.00 12 0.083
321 A 6 5 1.37 21 0.238
322 A 7 6 1.24 21 0.286
323 A 8 7 0.96 21 0.333
324 A 6 5 0.91 23 0.217
325 A 6 5 0.92 23 0.217
326 A 6 5 0.96 21 0.238
327 A 6 5 1.04 21 0.238
328 A 6 5 1.12 23 0.217
329 A 6 5 1.35 23 0.217
330 A 6 5 0.95 23 0.217
331 A 6 5 0.97 23 0.217
332 A 6 5 1.02 23 0.217
333 A 5 4 1.10 14 0.286
334 A 6 5 1.11 23 0.217
335 A 6 5 1.09 23 0.217
336 A 6 5 1.02 23 0.217
337 A 6 5 0.91 23 0.217
338 A 6 5 1.00 23 0.217
339 A 4 3 1.00 21 0.143
340 A 6 5 1.13 21 0.238
341 A 6 5 1.04 23 0.217
342 A 6 5 1.09 23 0.217
343 A 10 9 1.18 23 0.391
344 A 8 7 1.19 23 0.304
345 A 7 6 1.15 23 0.261
346 A 6 5 1.00 14 0.357
347 A 9 8 1.24 23 0.348
348 A 10 9 1.27 23 0.391
349 A 12 11 1.22 23 0.478
350 A 6 5 0.91 23 0.217
351 A 6 5 0.94 23 0.217
352 A 6 5 0.90 21 0.238
353 A 6 5 1.01 21 0.238
354 A 6 5 0.97 23 0.217
355 A 6 5 1.06 23 0.217
356 A 9 8 1.10 23 0.348
357 A 8 7 1.16 23 0.304
358 A 8 7 1.12 23 0.304
359 A 7 6 1.21 14 0.429
360 A 9 8 1.17 23 0.348
361 A 11 10 1.14 23 0.435
362 A 13 12 1.12 23 0.522
363 A 6 5 0.94 23 0.217
364 A 6 5 0.93 23 0.217
365 A 6 5 0.93 21 0.238
366 A 6 5 0.98 21 0.238
367 A 6 5 0.98 23 0.217
368 A 6 5 1.01 23 0.217
369 A 10 9 1.16 23 0.391
370 A 10 9 1.12 23 0.391
371 A 9 8 1.17 23 0.348
372 A 8 7 1.22 14 0.500
373 A 10 9 1.17 23 0.391
374 A 12 11 1.14 23 0.478
375 A 14 13 1.12 23 0.565
376 A 6 5 0.96 25 0.200
377 A 9 8 0.99 25 0.320
378 A 7 6 1.04 23 0.261
379 A 8 7 1.03 23 0.304
380 A 9 8 1.04 25 0.320
381 A 12 11 1.13 25 0.440
382 A 13 12 1.05 25 0.480
383 A 12 11 1.02 25 0.440
384 A 10 9 0.97 25 0.360
385 A 8 7 0.97 16 0.438
386 A 9 8 0.97 25 0.320
387 A 9 8 0.98 25 0.320
388 A 11 10 1.05 25 0.400
389 A 6 5 0.95 25 0.200
390 A 10 9 0.98 25 0.360
391 A 8 7 1.01 23 0.304
392 A 10 9 1.00 23 0.391
393 A 9 8 1.04 25 0.320
394 A 12 11 1.08 25 0.440
395 A 15 14 1.04 25 0.560
396 A 14 13 1.03 25 0.520
397 A 12 11 0.99 25 0.440
398 A 9 8 0.98 16 0.500
399 A 11 10 0.95 25 0.400
400 A 10 9 0.98 25 0.360
401 A 12 11 1.00 25 0.440
402 A 6 5 0.98 25 0.200
403 A 8 7 1.05 25 0.280
404 A 6 5 1.00 23 0.217
405 A 8 7 1.03 23 0.304
406 A 9 8 1.10 25 0.320
407 A 12 11 1.17 25 0.440
408 A 11 10 1.05 25 0.400
409 A 10 9 1.02 25 0.360
410 A 9 8 0.98 25 0.320
411 A 5 4 1.00 16 0.250
412 A 9 8 0.97 25 0.320
413 A 10 9 1.06 25 0.360
414 A 11 10 1.09 25 0.400
415 A 6 5 1.00 25 0.200
416 A 8 7 1.03 25 0.280
417 A 7 6 1.04 23 0.261
418 A 10 9 1.13 23 0.391
419 A 11 10 1.13 25 0.400
420 A 14 13 1.16 25 0.520
421 A 11 10 1.03 25 0.400
422 A 10 9 1.04 25 0.360
423 A 7 6 0.97 25 0.240
424 A 6 5 0.97 16 0.312
425 A 9 8 1.04 25 0.320
426 A 10 9 1.06 25 0.360
427 A 11 10 1.05 25 0.400
428 A 6 5 0.99 25 0.200
429 A 9 8 1.04 25 0.320
430 A 8 7 1.05 23 0.304
431 A 12 11 1.18 23 0.478
432 A 13 12 1.14 25 0.480
433 A 16 15 1.16 25 0.600
434 A 13 12 1.13 25 0.480
435 A 9 8 1.02 25 0.320
436 A 9 8 1.01 25 0.320
437 A 8 7 1.08 16 0.438
438 A 10 9 1.07 25 0.360
439 A 12 11 1.07 25 0.440
440 A 13 12 1.07 25 0.480
441 A 6 5 0.98 25 0.200
442 A 6 5 0.92 23 0.217
443 A 7 6 0.95 23 0.261
444 A 5 4 0.98 21 0.190
445 A 8 7 0.96 21 0.333
446 A 9 8 1.03 23 0.348
447 A 6 5 0.98 23 0.217
448 A 6 5 0.98 23 0.217
449 A 5 4 0.98 14 0.286
450 A 6 5 0.98 23 0.217
451 A 6 5 0.98 23 0.217
452 A 5 4 0.84 21 0.190
453 A 5 4 0.90 21 0.190
454 A 5 4 0.93 19 0.211
455 A 5 4 0.94 19 0.211
456 A 8 7 0.97 21 0.333
457 A 5 4 0.95 23 0.174
458 A 13 12 0.94 23 0.522
459 A 4 3 1.00 21 0.143
460 A 5 4 0.95 21 0.190
461 A 5 4 0.95 23 0.174
462 N/A 2 0 1.00 27 0.000
463 A 5 4 0.97 25 0.160
464 A 6 5 0.97 25 0.200
465 A 7 6 0.98 23 0.261
466 N/A 2 0 1.00 23 0.000
467 N/A 2 0 1.00 25 0.000
468 N/A 2 0 1.00 25 0.000
469 N/A 2 0 1.00 16 0.000
470 N/A 2 0 1.00 25 0.000

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