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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 [175] had the largest ratio of [1.37500000000000000]

# 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 6 0.333
2 A 3 3 1.00 8 0.375
3 A 4 3 0.89 8 0.375
4 A 5 5 1.11 8 0.625
5 A 4 3 0.86 8 0.375
6 A 7 7 1.15 8 0.875
7 A 4 3 0.85 8 0.375
8 A 9 9 1.17 8 1.125
9 A 6 6 1.08 8 0.750
10 A 4 4 1.00 8 0.500
11 A 4 4 1.00 8 0.500
12 A 2 2 1.00 8 0.250
13 A 2 2 1.00 8 0.250
14 A 4 4 1.00 8 0.500
15 A 4 4 1.00 8 0.500
16 A 6 6 1.02 8 0.750
17 A 6 6 1.07 10 0.600
18 A 4 4 1.00 10 0.400
19 A 4 4 1.00 10 0.400
20 A 2 2 1.00 10 0.200
21 A 2 2 1.00 10 0.200
22 A 4 4 1.00 10 0.400
23 A 4 4 1.00 10 0.400
24 A 6 6 1.01 10 0.600
25 A 8 8 1.06 12 0.667
26 A 6 6 1.00 12 0.500
27 A 6 6 1.00 12 0.500
28 A 4 4 1.00 12 0.333
29 A 4 4 1.00 12 0.333
30 A 6 6 1.00 12 0.500
31 A 6 6 1.00 12 0.500
32 A 8 8 1.04 12 0.667
33 A 2 2 1.00 12 0.167
34 A 2 2 1.00 12 0.167
35 C 2 2 0.11 12 0.167
36 C 2 2 0.23 12 0.167
37 C 2 2 0.21 12 0.167
38 A 2 2 1.00 12 0.167
39 A 2 2 1.00 8 0.250
40 A 2 2 1.00 10 0.200
41 A 3 3 1.00 21 0.143
42 A 4 3 1.00 15 0.200
43 A 4 3 1.00 15 0.200
44 A 4 3 1.00 13 0.231
45 A 2 2 1.00 6 0.333
46 A 4 3 1.00 13 0.231
47 A 4 3 1.00 15 0.200
48 A 4 3 1.00 15 0.200
49 A 5 4 0.87 17 0.235
50 A 5 4 0.89 17 0.235
51 A 5 4 0.94 17 0.235
52 A 4 3 1.00 15 0.200
53 A 3 3 1.00 8 0.375
54 A 4 3 1.00 17 0.176
55 A 5 4 0.94 17 0.235
56 A 5 4 0.89 17 0.235
57 A 5 4 0.87 17 0.235
58 A 9 9 1.17 17 0.529
59 A 7 7 1.15 17 0.412
60 A 5 5 1.11 17 0.294
61 A 3 3 1.00 8 0.375
62 A 5 4 0.87 13 0.308
63 A 4 4 1.00 15 0.267
64 A 6 6 1.09 17 0.353
65 A 8 8 1.13 17 0.471
66 A 5 4 0.97 17 0.235
67 A 5 4 0.97 17 0.235
68 A 5 4 0.94 17 0.235
69 A 5 4 0.97 17 0.235
70 A 4 3 1.00 15 0.200
71 A 5 4 0.89 15 0.267
72 A 5 4 1.05 15 0.267
73 A 4 4 1.00 8 0.500
74 A 4 3 0.93 15 0.200
75 A 4 3 1.00 17 0.176
76 A 6 5 0.94 17 0.294
77 A 6 5 0.94 17 0.294
78 A 6 5 0.94 17 0.294
79 A 6 5 0.94 17 0.294
80 A 5 4 0.87 17 0.235
81 A 5 4 0.89 17 0.235
82 A 5 4 0.94 17 0.235
83 A 4 3 1.00 15 0.200
84 A 6 5 1.40 17 0.294
85 A 5 5 1.00 8 0.625
86 A 4 3 1.00 17 0.176
87 A 5 4 0.94 17 0.235
88 A 5 4 0.89 17 0.235
89 A 11 11 1.18 17 0.647
90 A 9 9 1.17 17 0.529
91 A 7 7 1.14 17 0.412
92 A 5 5 1.11 8 0.625
93 A 5 4 0.84 15 0.267
94 A 6 5 1.16 15 0.333
95 A 6 6 1.09 15 0.400
96 A 8 8 1.13 17 0.471
97 A 10 10 1.15 17 0.588
98 A 6 5 0.96 17 0.294
99 A 5 4 0.91 17 0.235
100 A 6 5 0.96 17 0.294
101 A 5 4 0.91 17 0.235
102 A 5 4 0.94 17 0.235
103 A 5 4 0.91 17 0.235
104 A 4 3 1.00 15 0.200
105 A 6 5 0.98 15 0.333
106 A 5 4 0.92 17 0.235
107 A 6 5 0.81 17 0.294
108 A 5 4 0.84 15 0.267
109 A 6 6 1.00 8 0.750
110 A 5 4 0.85 15 0.267
111 A 4 3 1.00 17 0.176
112 A 5 4 0.89 17 0.235
113 A 5 4 0.94 17 0.235
114 A 5 4 0.89 17 0.235
115 A 6 5 0.96 17 0.294
116 A 5 4 0.89 17 0.235
117 A 6 5 0.96 17 0.294
118 A 6 5 1.05 17 0.294
119 A 5 4 0.84 15 0.267
120 A 6 5 0.85 15 0.333
121 A 7 6 0.92 15 0.400
122 A 6 5 0.87 15 0.333
123 A 6 5 0.96 15 0.333
124 A 6 5 0.91 13 0.385
125 A 3 3 1.18 6 0.500
126 A 4 3 1.00 13 0.231
127 A 6 5 0.87 15 0.333
128 A 5 4 0.89 15 0.267
129 A 6 5 0.84 15 0.333
130 A 6 5 1.00 15 0.333
131 A 6 5 0.83 15 0.333
132 A 6 5 0.89 15 0.333
133 A 5 4 0.84 17 0.235
134 A 7 6 1.39 17 0.353
135 A 5 4 0.84 17 0.235
136 A 6 5 1.39 17 0.294
137 A 5 4 0.78 15 0.267
138 A 3 3 1.00 8 0.375
139 A 5 4 1.00 13 0.308
140 A 6 5 0.91 15 0.333
141 A 5 4 0.86 17 0.235
142 A 6 5 1.16 17 0.294
143 A 5 4 0.87 17 0.235
144 A 8 7 1.26 17 0.412
145 A 7 6 0.78 17 0.353
146 A 7 6 1.07 17 0.353
147 A 7 6 0.77 17 0.353
148 A 7 6 1.16 15 0.400
149 A 7 7 1.07 8 0.875
150 A 4 4 1.00 15 0.267
151 A 5 4 1.00 15 0.267
152 A 5 4 0.89 15 0.267
153 A 6 5 1.16 17 0.294
154 A 6 5 0.81 17 0.294
155 A 6 5 1.05 17 0.294
156 A 6 5 0.84 17 0.294
157 A 5 4 0.85 17 0.235
158 A 7 6 1.26 17 0.353
159 A 5 4 0.87 17 0.235
160 A 6 5 1.22 17 0.294
161 A 5 4 0.92 15 0.267
162 A 5 5 1.00 8 0.625
163 A 5 4 1.00 15 0.267
164 A 4 3 1.00 17 0.176
165 A 5 4 1.00 15 0.267
166 A 6 5 0.87 15 0.333
167 A 5 4 0.84 17 0.235
168 A 6 5 1.07 17 0.294
169 A 5 4 0.85 17 0.235
170 A 8 7 1.17 17 0.412
171 A 7 6 0.86 17 0.353
172 A 8 7 1.17 17 0.412
173 A 7 6 0.78 17 0.353
174 A 8 7 1.28 15 0.467
175 A 11 11 1.05 8 1.375
176 A 6 6 1.09 15 0.400
177 A 5 4 1.00 17 0.235
178 A 6 6 1.09 17 0.353
179 A 5 4 1.00 15 0.267
180 A 6 5 0.92 15 0.333
181 A 8 7 1.26 17 0.412
182 A 6 5 0.81 17 0.294
183 A 8 7 1.16 17 0.412
184 A 6 5 0.88 17 0.294
185 A 5 4 1.00 9 0.444
186 A 7 6 1.00 9 0.667
187 A 4 3 1.00 19 0.158
188 A 4 3 1.00 19 0.158
189 A 4 3 1.00 19 0.158
190 A 4 3 1.00 19 0.158
191 A 4 3 1.00 19 0.158
192 A 4 3 1.00 19 0.158
193 A 4 3 1.00 19 0.158
194 A 10 10 1.09 21 0.476
195 A 10 10 1.09 21 0.476
196 A 8 8 1.05 21 0.381
197 A 8 8 1.05 21 0.381
198 A 6 6 1.00 21 0.286
199 A 6 6 1.00 21 0.286
200 A 6 6 1.00 21 0.286
201 A 6 6 1.00 21 0.286
202 A 8 8 1.04 21 0.381
203 A 8 8 1.08 21 0.381
204 A 6 5 0.98 21 0.238
205 A 6 5 0.98 21 0.238
206 A 6 5 0.98 21 0.238
207 A 6 5 0.98 21 0.238
208 A 6 5 0.98 21 0.238
209 A 6 5 0.98 21 0.238
210 A 6 5 0.98 21 0.238
211 A 12 12 1.10 21 0.571
212 A 12 12 1.10 21 0.571
213 A 10 10 1.08 21 0.476
214 A 10 10 1.08 21 0.476
215 A 8 8 1.05 21 0.381
216 A 8 8 1.05 21 0.381
217 A 8 8 1.03 21 0.381
218 A 8 8 1.03 21 0.381
219 A 8 8 1.04 21 0.381
220 A 8 8 1.08 21 0.381
221 A 5 4 0.92 19 0.211
222 A 10 9 0.94 19 0.474
223 A 10 9 0.93 19 0.474
224 A 9 8 0.94 19 0.421
225 A 9 8 0.92 19 0.421
226 A 8 7 0.88 19 0.368
227 A 8 7 0.86 19 0.368
228 A 9 8 0.95 19 0.421
229 A 9 8 0.94 19 0.421
230 A 10 9 0.98 19 0.474
231 A 10 9 0.97 19 0.474
232 A 10 10 1.10 21 0.476
233 A 8 8 1.06 21 0.381
234 A 8 8 1.06 21 0.381
235 A 6 6 1.00 21 0.286
236 A 6 6 1.00 21 0.286
237 A 6 6 1.00 21 0.286
238 A 6 6 1.00 21 0.286
239 A 8 8 1.05 21 0.381
240 A 8 8 1.05 21 0.381
241 A 10 10 1.07 21 0.476
242 A 11 10 0.99 21 0.476
243 A 10 9 1.02 21 0.429
244 A 10 9 1.00 21 0.429
245 A 9 8 1.02 21 0.381
246 A 9 8 1.02 21 0.381
247 A 9 8 1.06 21 0.381
248 F 0 0 N/A 0.000 N/A
249 A 10 9 1.06 21 0.429
250 A 10 9 1.08 21 0.429
251 A 11 10 1.07 21 0.476
252 A 4 3 1.00 19 0.158
253 A 5 4 1.00 11 0.364
254 A 5 4 1.00 11 0.364
255 A 5 4 1.00 11 0.364
256 A 5 4 1.00 11 0.364
257 A 8 8 1.05 25 0.320
258 A 6 6 1.00 25 0.240
259 A 4 4 1.00 25 0.160
260 A 6 6 1.00 25 0.240
261 A 8 8 1.03 25 0.320
262 A 13 12 1.33 25 0.480
263 A 11 10 1.40 25 0.400
264 A 2 2 1.00 25 0.080
265 A 4 4 1.00 25 0.160
266 A 6 6 1.07 25 0.240
267 A 8 8 1.03 25 0.320
268 A 6 6 1.00 25 0.240
269 A 6 6 1.00 25 0.240
270 A 8 8 1.08 25 0.320
271 A 13 12 1.33 25 0.480
272 A 13 12 1.37 25 0.480
273 A 2 2 1.00 25 0.080
274 A 6 6 1.14 25 0.240
275 A 8 8 1.18 25 0.320
276 A 10 10 1.09 25 0.400
277 A 8 8 1.05 25 0.320
278 A 6 6 1.00 25 0.240
279 A 6 6 1.00 25 0.240
280 A 8 8 1.05 25 0.320
281 A 10 10 1.10 25 0.400
282 A 13 12 1.33 25 0.480
283 A 13 12 1.37 25 0.480
284 A 2 2 1.00 25 0.080
285 A 6 6 1.14 25 0.240
286 A 8 8 1.18 25 0.320
287 A 15 14 1.30 21 0.667
288 A 2 2 1.00 13 0.154
289 A 11 10 1.51 13 0.769
290 A 13 12 1.37 13 0.923
291 A 8 8 1.02 25 0.320
292 A 6 6 1.00 25 0.240
293 A 4 4 1.00 25 0.160
294 A 6 6 1.00 25 0.240
295 A 8 8 1.06 25 0.320
296 A 11 10 1.41 25 0.400
297 A 2 2 1.00 25 0.080
298 A 4 4 1.00 25 0.160
299 A 6 6 1.07 25 0.240
300 A 11 10 1.42 21 0.476
301 A 13 12 1.35 21 0.571
302 A 13 12 1.34 21 0.571
303 A 15 14 1.29 21 0.667
304 A 2 2 1.00 21 0.095
305 A 2 2 1.00 21 0.095
306 A 2 2 1.00 12 0.167
307 A 2 2 1.00 21 0.095
308 A 2 2 1.00 21 0.095
309 A 2 2 1.00 21 0.095
310 A 2 2 1.00 21 0.095
311 A 2 2 1.00 12 0.167
312 A 2 2 1.00 21 0.095
313 A 2 2 1.00 21 0.095
314 A 2 2 1.00 21 0.095
315 A 2 2 1.00 21 0.095
316 A 2 2 1.00 12 0.167
317 A 2 2 1.00 21 0.095
318 A 2 2 1.00 21 0.095
319 A 2 2 1.00 21 0.095
320 A 2 2 1.00 21 0.095
321 A 2 2 1.00 12 0.167
322 A 2 2 1.00 21 0.095
323 A 2 2 1.00 21 0.095
324 A 11 10 0.57 21 0.476
325 A 11 10 1.36 21 0.476
326 A 13 12 1.31 21 0.571
327 A 13 12 0.65 21 0.571
328 A 13 12 0.65 21 0.571
329 A 11 10 0.57 21 0.476
330 A 11 10 1.35 21 0.476
331 A 13 12 1.31 21 0.571
332 A 13 12 0.65 21 0.571
333 A 13 12 0.65 21 0.571
334 A 2 2 1.00 13 0.154
335 A 2 2 1.00 13 0.154
336 A 2 2 1.00 17 0.118
337 A 2 2 1.00 19 0.105
338 A 2 2 1.00 19 0.105
339 A 2 2 1.00 21 0.095
340 A 6 5 0.93 19 0.263
341 A 6 5 0.96 19 0.263
342 A 4 3 1.00 17 0.176
343 A 5 4 1.00 17 0.235
344 A 5 4 1.00 19 0.211
345 A 2 2 1.00 19 0.105
346 A 2 2 1.00 19 0.105
347 A 2 2 1.00 10 0.200
348 A 2 2 1.00 19 0.105
349 A 2 2 1.00 19 0.105
350 A 2 2 1.00 23 0.087
351 A 2 2 1.00 23 0.087
352 A 2 2 1.00 23 0.087
353 A 2 2 1.00 23 0.087
354 A 2 2 1.00 23 0.087
355 A 6 5 0.92 19 0.263
356 A 6 5 0.98 19 0.263
357 A 4 3 1.00 17 0.176
358 A 5 4 1.00 17 0.235
359 A 5 4 1.00 19 0.211
360 A 5 4 1.00 19 0.211
361 A 2 2 1.00 19 0.105
362 A 2 2 1.00 19 0.105
363 A 2 2 1.00 10 0.200
364 A 2 2 1.00 19 0.105
365 A 2 2 1.00 19 0.105
366 A 2 2 1.00 23 0.087
367 A 2 2 1.00 23 0.087
368 A 2 2 1.00 23 0.087
369 A 2 2 1.00 23 0.087
370 A 2 2 1.00 23 0.087
371 A 7 6 0.92 21 0.286
372 A 6 5 0.92 21 0.238
373 A 7 6 0.98 21 0.286
374 A 4 3 1.00 19 0.158
375 A 9 8 0.88 19 0.421
376 A 9 8 0.97 21 0.381
377 A 11 10 1.07 21 0.476
378 A 10 10 1.08 21 0.476
379 A 8 8 1.05 21 0.381
380 A 6 6 1.00 21 0.286
381 A 4 4 1.00 12 0.333
382 A 6 6 1.00 21 0.286
383 A 8 8 1.00 21 0.381
384 A 10 10 1.04 21 0.476
385 A 7 6 0.92 21 0.286
386 A 6 5 0.92 21 0.238
387 A 7 6 0.98 21 0.286
388 A 4 3 1.00 19 0.158
389 A 10 9 0.92 19 0.474
390 A 10 9 0.97 21 0.429
391 A 10 10 1.03 21 0.476
392 A 8 8 1.01 21 0.381
393 A 6 6 1.00 21 0.286
394 A 6 6 1.00 12 0.500
395 A 8 8 1.06 21 0.381
396 A 10 10 1.03 21 0.476
397 A 7 6 0.92 21 0.286
398 A 6 5 0.92 21 0.238
399 A 7 6 0.98 21 0.286
400 A 4 3 1.00 19 0.158
401 A 10 9 0.94 19 0.474
402 A 10 9 0.99 21 0.429
403 A 12 11 1.07 21 0.524
404 A 10 10 1.05 21 0.476
405 A 8 8 1.01 21 0.381
406 A 6 6 1.00 21 0.286
407 A 6 6 1.00 12 0.500
408 A 8 8 0.98 21 0.381
409 A 10 10 1.05 21 0.476
410 A 7 6 0.92 21 0.286
411 A 6 5 0.92 21 0.238
412 A 7 6 0.98 21 0.286
413 A 4 3 1.00 19 0.158
414 A 9 8 0.86 19 0.421
415 A 9 8 0.97 21 0.381
416 A 11 10 1.07 21 0.476
417 A 10 10 1.08 21 0.476
418 A 8 8 1.05 21 0.381
419 A 6 6 1.00 21 0.286
420 A 4 4 1.00 12 0.333
421 A 6 6 1.00 21 0.286
422 A 8 8 1.01 21 0.381
423 A 10 10 1.05 21 0.476
424 A 7 6 0.92 21 0.286
425 A 6 5 0.92 21 0.238
426 A 7 6 0.98 21 0.286
427 A 4 3 1.00 19 0.158
428 A 10 9 0.95 19 0.474
429 A 9 8 1.03 21 0.381
430 A 11 10 1.11 21 0.476
431 A 10 10 1.08 21 0.476
432 A 8 8 1.05 21 0.381
433 A 6 6 1.00 12 0.500
434 A 6 6 1.00 21 0.286
435 A 8 8 0.98 21 0.381
436 A 10 10 1.01 21 0.476
437 A 7 6 0.92 21 0.286
438 A 6 5 0.92 21 0.238
439 A 7 6 0.98 21 0.286
440 A 4 3 1.00 19 0.158
441 A 10 9 0.94 19 0.474
442 A 9 8 1.03 21 0.381
443 A 11 10 1.11 21 0.476
444 A 10 10 1.08 21 0.476
445 A 8 8 1.05 21 0.381
446 A 6 6 1.00 12 0.500
447 A 6 6 1.00 21 0.286
448 A 8 8 0.99 21 0.381
449 A 10 10 1.02 21 0.476
450 A 17 16 1.11 25 0.640
451 A 15 14 1.10 25 0.560
452 A 13 12 1.12 25 0.480
453 A 2 2 1.00 25 0.080
454 A 4 4 1.00 25 0.160
455 A 6 6 1.08 25 0.240
456 A 10 10 1.03 25 0.400
457 A 8 8 1.00 25 0.320
458 A 6 6 1.00 25 0.240
459 A 8 8 1.00 25 0.320
460 A 10 10 1.06 25 0.400
461 A 10 10 1.04 23 0.435
462 A 8 8 1.00 23 0.348
463 A 6 6 1.00 23 0.261
464 A 8 8 1.00 23 0.348
465 A 10 10 1.01 23 0.435
466 A 15 14 1.04 23 0.609
467 A 13 12 1.07 23 0.522
468 A 2 2 1.00 23 0.087
469 A 4 4 1.00 23 0.174
470 A 6 6 1.05 23 0.261
471 A 8 8 1.08 23 0.348
472 A 19 18 1.11 25 0.720
473 A 17 16 1.11 25 0.640
474 A 15 14 1.10 25 0.560
475 A 15 14 1.13 25 0.560
476 A 2 2 1.00 25 0.080
477 A 12 12 1.03 25 0.480
478 A 10 10 1.01 25 0.400
479 A 8 8 1.00 25 0.320
480 A 8 8 1.00 25 0.320
481 A 10 10 1.04 25 0.400
482 A 12 12 1.07 25 0.480
483 A 4 4 1.00 23 0.174
484 A 4 4 1.00 23 0.174
485 A 4 4 1.00 23 0.174
486 A 4 4 1.00 23 0.174
487 A 4 4 1.00 23 0.174
488 A 4 4 1.00 17 0.235
489 A 4 4 1.00 19 0.211
490 A 4 4 1.00 19 0.211
491 A 4 4 1.00 21 0.190
492 A 6 5 0.94 19 0.263
493 A 7 6 0.98 19 0.316
494 A 4 3 1.00 17 0.176
495 A 6 5 1.00 17 0.294
496 A 5 4 1.00 19 0.211
497 A 4 4 1.00 19 0.211
498 A 4 4 1.00 19 0.211
499 A 4 4 1.00 19 0.211
500 A 4 4 1.00 10 0.400
501 A 4 4 1.00 19 0.211
502 A 4 4 1.00 19 0.211
503 A 4 4 1.00 23 0.174
504 A 4 4 1.00 23 0.174
505 A 4 4 1.00 23 0.174
506 A 4 4 1.00 23 0.174
507 A 9 9 1.17 21 0.429
508 A 7 7 1.08 21 0.333
509 A 7 7 1.12 21 0.333
510 A 5 5 1.00 19 0.263
511 A 4 4 1.00 12 0.333
512 A 7 7 1.10 19 0.368
513 A 7 7 1.07 21 0.333
514 A 9 9 1.09 21 0.429
515 A 9 9 1.14 21 0.429
516 A 7 7 1.05 21 0.333
517 A 7 7 1.08 21 0.333
518 A 5 5 1.00 21 0.238
519 A 5 5 1.00 19 0.263
520 A 6 6 1.00 12 0.500
521 A 7 7 1.10 19 0.368
522 A 9 9 1.06 21 0.429
523 A 9 9 1.15 21 0.429
524 A 7 7 1.12 21 0.333
525 A 7 7 1.07 19 0.368
526 A 4 4 1.00 12 0.333
527 A 5 5 1.00 19 0.263
528 A 7 7 1.07 21 0.333
529 A 7 7 1.03 21 0.333
530 A 9 9 1.14 21 0.429
531 A 7 7 1.07 19 0.368
532 A 6 6 1.00 12 0.500
533 A 5 5 1.00 19 0.263
534 A 5 5 1.00 21 0.238
535 A 7 7 1.03 21 0.333
536 A 7 7 1.03 21 0.333
537 A 9 9 1.04 21 0.429
538 A 4 4 1.00 21 0.190

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