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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 [7] had the largest ratio of [1.50000000000000000]

# 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 8 8 0.68 14 0.571
2 A 6 6 0.80 14 0.429
3 A 4 4 1.00 14 0.286
4 A 5 5 1.06 14 0.357
5 A 9 9 0.82 14 0.643
6 A 13 13 0.72 14 0.929
7 A 22 21 0.64 14 1.500
8 A 18 17 0.69 14 1.214
9 A 16 15 0.70 14 1.071
10 A 16 15 0.70 14 1.071
11 A 18 17 0.67 14 1.214
12 A 22 21 0.64 14 1.500
13 A 13 13 0.55 14 0.929
14 A 9 9 0.62 14 0.643
15 A 5 5 0.74 14 0.357
16 A 5 5 0.75 14 0.357
17 A 9 9 0.60 14 0.643
18 A 13 13 0.55 14 0.929
19 A 6 5 1.00 14 0.357
20 A 6 5 1.00 14 0.357
21 A 6 5 1.25 14 0.357
22 A 6 5 1.00 14 0.357
23 A 6 5 1.00 14 0.357
24 A 6 5 1.00 14 0.357
25 A 6 5 1.00 12 0.417
26 A 6 5 1.00 12 0.417
27 A 6 5 1.00 12 0.417
28 A 6 5 1.00 12 0.417
29 A 4 4 1.00 14 0.286
30 A 5 4 0.89 21 0.190
31 A 6 5 0.90 21 0.238
32 A 5 4 0.93 19 0.211
33 A 6 5 0.92 19 0.263
34 A 6 5 1.14 21 0.238
35 A 9 8 1.19 21 0.381
36 A 10 9 1.25 21 0.429
37 A 7 6 1.27 21 0.286
38 A 7 6 1.28 21 0.286
39 A 1 1 1.00 12 0.083
40 A 5 4 0.92 21 0.190
41 A 5 4 0.88 21 0.190
42 A 5 4 0.88 21 0.190
43 A 5 4 0.90 23 0.174
44 A 6 5 0.90 23 0.217
45 A 5 4 0.91 21 0.190
46 A 6 5 0.90 21 0.238
47 A 7 6 0.95 23 0.261
48 A 9 8 1.09 23 0.348
49 A 7 6 1.12 23 0.261
50 A 7 6 0.99 23 0.261
51 A 5 4 1.09 14 0.286
52 A 5 4 0.89 23 0.174
53 A 5 4 0.89 23 0.174
54 A 5 4 0.88 23 0.174
55 A 5 4 0.93 23 0.174
56 A 7 6 1.04 23 0.261
57 A 5 4 0.97 21 0.190
58 A 7 6 0.97 21 0.286
59 A 7 6 1.09 23 0.261
60 A 10 9 1.15 23 0.391
61 A 10 9 1.25 23 0.391
62 A 8 7 1.25 23 0.304
63 A 7 6 1.23 23 0.261
64 A 6 5 1.00 14 0.357
65 A 5 4 0.96 23 0.174
66 A 6 5 0.93 23 0.217
67 A 5 4 0.92 23 0.174
68 A 9 8 1.04 23 0.348
69 A 8 7 1.01 23 0.304
70 A 6 5 1.03 21 0.238
71 A 9 8 1.11 21 0.381
72 A 9 8 1.05 23 0.348
73 A 12 11 1.08 23 0.478
74 A 11 10 1.17 23 0.435
75 A 9 8 1.17 23 0.348
76 A 7 6 1.20 14 0.429
77 A 6 5 0.99 23 0.217
78 A 7 6 1.02 23 0.261
79 A 7 6 1.03 23 0.261
80 A 10 9 1.03 23 0.391
81 A 9 8 1.01 23 0.348
82 A 7 6 1.09 21 0.286
83 A 11 10 1.16 21 0.476
84 A 11 10 1.14 23 0.435
85 A 14 13 1.06 23 0.565
86 A 12 11 1.16 23 0.478
87 A 10 9 1.21 23 0.391
88 A 8 7 1.22 14 0.500
89 A 7 6 1.04 23 0.261
90 A 8 7 1.01 23 0.304
91 A 9 8 1.02 23 0.348
92 A 9 8 1.07 25 0.320
93 A 8 7 0.96 25 0.280
94 A 6 5 0.97 23 0.217
95 A 9 8 0.98 23 0.348
96 A 9 8 1.06 25 0.320
97 A 12 11 1.11 25 0.440
98 A 10 9 1.13 25 0.360
99 A 9 8 1.03 25 0.320
100 A 8 7 0.98 16 0.438
101 A 6 5 0.97 25 0.200
102 A 7 6 0.95 25 0.240
103 A 8 7 1.03 25 0.280
104 A 10 9 0.91 25 0.360
105 A 9 8 0.90 25 0.320
106 A 7 6 0.98 23 0.261
107 A 11 10 0.98 23 0.435
108 A 11 10 1.01 25 0.400
109 A 15 14 1.04 25 0.560
110 A 13 12 1.02 25 0.480
111 A 11 10 0.99 25 0.400
112 A 9 8 0.98 16 0.500
113 A 7 6 0.98 25 0.240
114 A 8 7 0.89 25 0.280
115 A 10 9 0.89 25 0.360
116 A 7 6 1.05 25 0.240
117 A 6 5 0.98 25 0.200
118 A 4 3 1.00 23 0.130
119 A 6 5 1.00 23 0.217
120 A 7 6 1.07 25 0.240
121 A 9 8 1.12 25 0.320
122 A 8 7 1.12 25 0.280
123 A 7 6 1.04 25 0.240
124 A 5 4 1.00 16 0.250
125 A 4 3 1.00 25 0.120
126 A 5 4 0.97 25 0.160
127 A 6 5 1.02 25 0.200
128 A 8 7 0.98 25 0.280
129 A 7 6 0.98 25 0.240
130 A 5 4 0.97 23 0.174
131 A 7 6 0.98 23 0.261
132 A 9 8 1.05 25 0.320
133 A 12 11 1.13 25 0.440
134 A 10 9 1.13 25 0.360
135 A 8 7 1.06 25 0.280
136 A 6 5 0.98 16 0.312
137 A 5 4 0.97 25 0.160
138 A 6 5 0.93 25 0.200
139 A 7 6 0.94 25 0.240
140 A 9 8 0.97 25 0.320
141 A 8 7 1.02 25 0.280
142 A 6 5 1.03 23 0.217
143 A 10 9 1.09 23 0.391
144 A 11 10 1.06 25 0.400
145 A 14 13 1.10 25 0.520
146 A 11 10 1.13 25 0.400
147 A 10 9 1.10 25 0.360
148 A 8 7 1.07 16 0.438
149 A 6 5 1.00 25 0.200
150 A 7 6 0.95 25 0.240
151 A 8 7 0.89 25 0.280
152 A 6 6 1.00 23 0.261
153 A 6 5 1.21 25 0.200
154 A 8 7 1.03 23 0.304
155 A 7 6 0.99 23 0.261
156 A 5 4 1.00 21 0.190
157 A 6 5 1.00 21 0.238
158 A 5 4 1.00 23 0.174
159 A 5 4 1.00 23 0.174
160 A 5 4 1.00 14 0.286
161 A 5 4 1.00 23 0.174
162 A 6 5 0.98 23 0.217
163 A 7 6 1.02 23 0.261
164 A 6 6 1.00 25 0.240
165 A 6 5 1.00 23 0.217
166 A 6 5 1.00 14 0.357
167 A 6 5 1.00 23 0.217
168 A 7 6 1.22 23 0.261
169 A 7 6 1.07 23 0.261
170 A 6 6 1.00 23 0.261
171 A 6 6 1.00 21 0.286
172 A 6 6 1.00 21 0.286
173 A 6 6 1.00 23 0.261
174 N/A 2 0 1.00 25 0.000
175 A 6 6 1.00 23 0.261
176 A 7 6 1.00 25 0.240
177 A 6 6 1.00 25 0.240
178 N/A 4 0 1.00 27 0.000
179 A 7 6 0.78 14 0.429
180 A 7 6 0.82 14 0.429
181 A 7 6 0.91 14 0.429
182 A 6 6 0.94 14 0.429
183 A 8 8 1.00 14 0.571
184 A 10 10 1.03 14 0.714
185 A 8 8 0.89 21 0.381
186 A 6 6 0.94 21 0.286
187 A 4 4 1.00 19 0.211
188 A 5 5 1.08 19 0.263
189 A 7 7 1.06 21 0.333
190 A 11 11 0.98 21 0.524
191 A 9 9 0.84 21 0.429
192 A 7 7 0.85 21 0.333
193 A 5 5 0.92 21 0.238
194 A 1 1 1.00 12 0.083
195 A 3 3 1.00 21 0.143
196 A 7 7 1.00 21 0.333
197 A 9 9 0.84 21 0.429
198 A 6 5 0.93 23 0.217
199 A 6 5 0.96 23 0.217
200 A 6 5 0.97 21 0.238
201 A 6 5 1.04 21 0.238
202 A 6 5 0.98 23 0.217
203 A 6 5 0.96 23 0.217
204 A 5 4 0.96 23 0.174
205 A 5 4 0.98 23 0.174
206 A 5 4 1.01 23 0.174
207 A 5 4 1.09 14 0.286
208 A 5 4 1.11 23 0.174
209 A 5 4 1.09 23 0.174
210 A 5 4 1.01 23 0.174
211 A 6 5 0.94 23 0.217
212 A 6 5 1.06 23 0.217
213 A 6 5 1.36 21 0.238
214 A 6 5 1.03 21 0.238
215 A 6 5 0.93 23 0.217
216 A 6 5 0.92 23 0.217
217 A 9 8 1.18 23 0.348
218 A 7 6 1.17 23 0.261
219 A 6 5 1.14 23 0.217
220 A 6 5 1.00 14 0.357
221 A 8 7 1.17 23 0.304
222 A 9 8 1.20 23 0.348
223 A 11 10 1.17 23 0.435
224 A 6 5 0.94 23 0.217
225 A 6 5 1.10 23 0.217
226 A 6 5 1.09 21 0.238
227 A 6 5 0.97 21 0.238
228 A 6 5 0.91 23 0.217
229 A 6 5 0.91 23 0.217
230 A 8 7 1.09 23 0.304
231 A 7 6 1.19 23 0.261
232 A 7 6 1.16 23 0.261
233 A 7 6 1.20 14 0.429
234 A 8 7 1.11 23 0.304
235 A 10 9 1.07 23 0.391
236 A 12 11 1.03 23 0.478
237 A 6 5 1.04 23 0.217
238 A 6 5 1.04 23 0.217
239 A 6 5 1.03 21 0.238
240 A 6 5 0.96 21 0.238
241 A 6 5 0.92 23 0.217
242 A 6 5 0.92 23 0.217
243 A 9 8 1.20 23 0.348
244 A 9 8 1.17 23 0.348
245 A 8 7 1.19 23 0.304
246 A 8 7 1.22 14 0.500
247 A 9 8 1.14 23 0.348
248 A 11 10 1.10 23 0.435
249 A 13 12 1.06 23 0.522
250 A 5 4 0.98 14 0.286
251 A 5 4 1.01 14 0.286
252 A 5 4 1.09 14 0.286
253 A 1 1 1.00 12 0.083
254 A 6 5 1.00 14 0.357
255 A 7 6 1.20 14 0.429
256 A 8 7 1.22 14 0.500
257 A 10 10 0.81 17 0.588
258 A 8 7 1.27 17 0.412
259 A 8 8 0.81 17 0.471
260 A 6 5 1.00 15 0.333
261 A 8 7 1.00 15 0.467
262 A 9 8 1.00 17 0.471
263 A 8 7 1.18 17 0.412
264 A 9 8 0.79 17 0.471
265 A 7 6 1.06 16 0.375
266 A 8 7 1.25 17 0.412
267 A 10 10 0.76 17 0.588
268 A 6 5 1.00 15 0.333
269 A 9 8 1.14 15 0.533
270 A 10 9 0.70 17 0.529
271 A 8 7 1.03 16 0.438
272 A 9 8 1.04 16 0.500
273 A 8 7 1.44 17 0.412
274 A 9 8 0.68 17 0.471
275 A 6 5 1.00 15 0.333
276 A 9 8 1.29 15 0.533
277 A 9 8 0.61 17 0.471
278 A 8 7 1.27 17 0.412
279 A 8 7 1.00 17 0.412
280 A 6 5 1.00 15 0.333
281 A 10 9 1.28 15 0.600
282 A 9 8 0.53 17 0.471
283 A 6 5 1.08 16 0.312
284 A 7 6 1.10 16 0.375
285 A 8 7 1.15 16 0.438
286 A 9 8 1.17 16 0.500
287 A 7 6 1.09 10 0.600
288 A 6 5 1.00 10 0.500
289 A 6 5 1.18 10 0.500
290 A 8 7 1.11 12 0.583
291 A 7 6 1.12 12 0.500
292 A 6 5 1.15 12 0.417
293 A 6 5 0.97 25 0.200
294 A 8 7 0.99 25 0.280
295 A 7 6 1.03 23 0.261
296 A 7 6 1.03 23 0.261
297 A 9 8 0.97 25 0.320
298 A 11 10 1.02 25 0.400
299 A 12 11 1.05 25 0.440
300 A 11 10 1.02 25 0.400
301 A 9 8 0.98 25 0.320
302 A 8 7 0.98 16 0.438
303 A 8 7 0.97 25 0.280
304 A 9 8 0.98 25 0.320
305 A 10 9 1.02 25 0.360
306 A 6 5 0.95 25 0.200
307 A 9 8 0.99 25 0.320
308 A 8 7 1.01 23 0.304
309 A 8 7 1.00 23 0.304
310 A 9 8 0.97 25 0.320
311 A 11 10 0.99 25 0.400
312 A 14 13 1.04 25 0.520
313 A 13 12 1.01 25 0.480
314 A 11 10 0.99 25 0.400
315 A 9 8 0.98 16 0.500
316 A 10 9 0.96 25 0.360
317 A 9 8 0.98 25 0.320
318 A 11 10 1.00 25 0.400
319 A 10 9 1.00 16 0.562
320 A 6 5 0.98 25 0.200
321 A 7 6 1.05 25 0.240
322 A 6 5 1.00 23 0.217
323 A 7 6 1.03 23 0.261
324 A 9 8 1.01 25 0.320
325 A 11 10 1.05 25 0.400
326 A 10 9 1.05 25 0.360
327 A 9 8 1.02 25 0.320
328 A 8 7 0.98 25 0.280
329 A 5 4 1.00 16 0.250
330 A 8 7 0.97 25 0.280
331 A 9 8 1.02 25 0.320
332 A 10 9 1.05 25 0.360
333 A 6 5 1.00 25 0.200
334 A 7 6 1.03 25 0.240
335 A 7 6 1.03 23 0.261
336 A 8 7 1.16 23 0.304
337 A 11 10 1.10 25 0.400
338 A 13 12 1.10 25 0.480
339 A 10 9 1.05 25 0.360
340 A 9 8 1.11 25 0.320
341 A 6 5 0.98 25 0.200
342 A 6 5 0.98 16 0.312
343 A 8 7 1.01 25 0.280
344 A 9 8 1.00 25 0.320
345 A 10 9 0.99 25 0.360
346 A 6 5 0.98 25 0.200
347 A 8 7 1.09 25 0.280
348 A 8 7 1.08 23 0.304
349 A 10 9 1.20 23 0.391
350 A 13 12 1.13 25 0.480
351 A 15 14 1.12 25 0.560
352 A 12 11 1.15 25 0.440
353 A 8 7 1.05 25 0.280
354 A 8 7 1.04 25 0.280
355 A 8 7 1.07 16 0.438
356 A 9 8 1.06 25 0.320
357 A 11 10 1.04 25 0.400
358 A 12 11 1.02 25 0.440
359 A 7 6 1.00 23 0.261
360 A 5 4 1.00 25 0.160
361 A 6 5 0.93 23 0.217
362 A 6 5 0.95 23 0.217
363 A 5 4 1.00 21 0.190
364 A 7 6 0.97 21 0.286
365 A 8 7 0.97 23 0.304
366 A 9 8 1.02 23 0.348
367 A 5 4 1.00 23 0.174
368 A 5 4 1.00 23 0.174
369 A 5 4 1.00 23 0.174
370 A 5 4 1.00 14 0.286
371 A 5 4 1.00 23 0.174
372 A 5 4 1.00 23 0.174
373 A 5 4 1.00 23 0.174
374 A 5 4 0.93 14 0.286
375 A 5 4 0.96 14 0.286
376 A 5 4 0.99 14 0.286
377 A 1 1 1.00 12 0.083
378 A 5 4 1.05 14 0.286
379 A 5 4 1.00 14 0.286
380 A 5 4 1.16 8 0.500
381 A 5 4 0.94 14 0.286
382 A 5 4 0.94 14 0.286
383 A 5 4 0.98 14 0.286
384 A 1 1 1.00 12 0.083
385 A 5 4 0.99 14 0.286
386 A 5 4 0.97 14 0.286
387 A 10 9 0.84 16 0.562
388 A 7 6 1.03 16 0.375
389 A 11 10 1.04 17 0.588
390 A 10 9 0.96 15 0.600
391 A 13 12 0.96 15 0.800
392 A 13 12 0.76 17 0.706
393 A 13 12 1.06 17 0.706
394 A 12 11 1.04 15 0.733
395 A 16 15 1.03 15 1.000
396 A 9 8 0.97 17 0.471
397 A 6 5 1.00 15 0.333
398 A 6 5 0.99 15 0.333
399 A 7 6 1.05 17 0.353
400 A 8 7 0.99 17 0.412
401 A 9 8 0.99 15 0.533
402 A 6 5 0.95 15 0.333
403 A 10 9 1.11 17 0.529
404 A 10 9 1.11 15 0.600
405 A 6 5 0.98 15 0.333
406 A 7 6 1.13 29 0.207
407 A 7 6 1.23 27 0.222
408 A 7 6 1.05 29 0.207
409 A 7 6 1.01 29 0.207
410 A 7 6 1.00 25 0.240
411 A 7 6 1.00 23 0.261
412 A 6 5 1.00 14 0.357
413 A 7 6 1.00 23 0.261
414 A 7 6 1.00 23 0.261
415 A 7 6 1.00 23 0.261
416 A 7 6 1.00 23 0.261
417 A 7 6 1.00 21 0.286
418 A 7 6 1.00 21 0.286
419 A 7 6 1.00 23 0.261
420 N/A 2 0 1.00 27 0.000
421 A 8 7 1.00 23 0.304
422 A 7 6 1.00 25 0.240
423 A 8 7 1.00 25 0.280
424 N/A 4 0 1.00 27 0.000
425 A 6 5 1.10 21 0.238
426 A 5 4 1.14 19 0.211
427 A 5 4 0.93 19 0.211
428 A 4 3 0.94 21 0.143
429 A 5 4 0.91 21 0.190
430 A 5 4 0.89 21 0.190
431 A 5 4 0.88 21 0.190
432 A 5 4 0.89 21 0.190
433 A 4 3 0.93 21 0.143
434 A 5 4 1.39 21 0.190
435 A 6 5 1.23 21 0.238
436 A 7 6 1.17 21 0.286
437 A 8 7 1.07 23 0.304
438 A 7 6 1.15 21 0.286
439 A 5 4 1.05 21 0.190
440 A 5 4 0.91 23 0.174
441 A 5 4 0.91 23 0.174
442 A 5 4 0.91 23 0.174
443 A 5 4 0.90 23 0.174
444 A 5 4 0.89 23 0.174
445 A 5 4 0.89 23 0.174
446 A 5 4 0.90 23 0.174
447 A 5 4 1.18 23 0.174
448 A 6 5 1.22 23 0.217
449 A 7 6 1.10 23 0.261
450 A 8 7 1.10 23 0.304
451 A 6 5 0.97 23 0.217
452 A 4 3 1.00 21 0.143
453 A 5 4 0.97 21 0.190
454 A 5 4 0.94 23 0.174
455 A 5 4 0.94 23 0.174
456 A 5 4 0.93 23 0.174
457 A 5 4 0.94 23 0.174
458 A 5 4 0.96 23 0.174
459 A 4 3 1.00 23 0.130
460 A 8 7 1.24 23 0.304
461 A 10 9 1.25 23 0.391
462 A 10 9 1.06 23 0.391
463 A 8 7 1.06 23 0.304
464 A 5 4 0.97 23 0.174
465 A 5 4 0.98 21 0.190
466 A 5 4 0.96 21 0.190
467 A 5 4 0.94 23 0.174
468 A 5 4 0.94 23 0.174
469 A 5 4 0.95 23 0.174
470 A 5 4 0.97 23 0.174
471 A 5 4 0.97 23 0.174
472 A 10 9 1.16 23 0.391
473 A 12 11 1.17 23 0.478
474 A 4 4 1.00 23 0.174
475 A 5 4 1.02 25 0.160
476 A 4 4 1.00 25 0.160
477 A 7 6 1.09 23 0.261
478 A 7 6 1.26 23 0.261
479 A 6 5 1.00 23 0.217
480 A 6 5 1.00 14 0.357
481 A 6 5 1.00 23 0.217
482 A 4 4 1.00 23 0.174
483 A 4 4 1.00 21 0.190
484 A 4 4 1.00 21 0.190
485 A 4 4 1.06 23 0.174
486 N/A 2 0 1.00 27 0.000
487 N/A 2 0 1.00 25 0.000
488 N/A 2 0 1.00 23 0.000
489 N/A 2 0 1.00 23 0.000
490 N/A 2 0 1.00 25 0.000
491 A 5 4 1.03 25 0.160
492 A 5 4 1.04 25 0.160
493 A 5 4 1.00 25 0.160
494 N/A 2 0 1.00 16 0.000
495 N/A 2 0 1.00 25 0.000
496 A 8 8 1.00 23 0.348
497 A 8 7 1.22 25 0.280
498 A 8 8 1.00 25 0.320
499 N/A 4 0 1.00 27 0.000

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