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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [309] had the largest ratio of [33]

# 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 4 3 1.00 19 0.158
2 A 4 3 1.00 19 0.158
3 A 4 3 1.00 17 0.176
4 A 2 1 1.00 16 0.062
5 A 4 3 1.00 19 0.158
6 A 4 4 1.04 19 0.210
7 A 4 4 1.00 19 0.210
8 A 4 3 1.00 19 0.158
9 A 4 4 1.00 21 0.190
10 A 4 4 1.00 21 0.190
11 A 4 4 1.00 19 0.210
12 A 4 4 1.00 18 0.222
13 A 3 3 1.00 21 0.143
14 A 3 3 1.00 21 0.143
15 A 4 4 1.00 21 0.190
16 A 4 4 1.00 21 0.190
17 A 4 4 1.00 21 0.190
18 A 4 4 1.00 21 0.190
19 A 4 4 1.00 21 0.190
20 A 4 4 1.00 21 0.190
21 A 5 4 1.00 19 0.210
22 A 4 4 1.00 18 0.222
23 A 4 3 1.00 21 0.143
24 A 3 3 1.00 21 0.143
25 A 3 3 1.00 21 0.143
26 A 5 4 1.00 21 0.190
27 A 4 4 1.00 21 0.190
28 A 5 6 1.00 21 0.286
29 A 4 4 1.00 21 0.190
30 A 4 4 1.00 21 0.190
31 A 8 6 1.00 21 0.286
32 A 7 6 1.00 21 0.286
33 A 6 5 1.00 19 0.263
34 A 2 2 1.00 18 0.111
35 A 2 2 1.00 21 0.095
36 A 4 4 1.00 21 0.190
37 A 6 4 1.00 21 0.190
38 A 8 4 1.00 21 0.190
39 A 8 7 1.00 21 0.333
40 A 7 6 1.09 21 0.286
41 A 3 3 1.00 19 0.158
42 A 2 2 1.00 18 0.111
43 A 5 5 1.00 21 0.238
44 A 7 7 1.00 21 0.333
45 A 8 7 1.00 21 0.333
46 A 8 6 1.00 21 0.286
47 A 4 3 1.00 21 0.143
48 A 3 2 1.00 19 0.105
49 A 3 2 1.00 18 0.111
50 A 9 7 1.00 21 0.333
51 A 10 8 1.00 21 0.381
52 A 11 8 1.00 21 0.381
53 A 10 7 1.00 21 0.333
54 A 9 6 1.00 21 0.286
55 A 5 3 1.00 21 0.143
56 A 3 2 1.00 21 0.095
57 A 4 4 1.00 19 0.210
58 A 3 2 1.00 18 0.111
59 A 13 7 1.00 21 0.333
60 A 13 8 1.00 21 0.381
61 A 14 8 1.00 21 0.381
62 A 13 7 1.00 21 0.333
63 A 12 6 1.00 21 0.286
64 A 8 3 1.00 21 0.143
65 A 3 2 1.00 21 0.095
66 A 5 6 1.00 21 0.286
67 A 4 4 1.00 21 0.190
68 A 4 4 1.00 21 0.190
69 A 4 4 1.00 19 0.210
70 A 3 2 1.00 18 0.111
71 A 25 7 1.00 21 0.333
72 A 22 8 1.00 21 0.381
73 A 23 8 1.00 21 0.381
74 A 1 1 1.00 13 0.077
75 A 1 1 1.00 14 0.071
76 A 6 3 1.00 21 0.143
77 A 6 3 1.00 19 0.158
78 A 7 5 1.00 18 0.278
79 A 6 5 1.00 21 0.238
80 A 6 5 1.00 21 0.238
81 A 6 3 1.00 21 0.143
82 A 6 3 1.00 21 0.143
83 A 6 3 1.00 21 0.143
84 A 8 3 1.00 23 0.130
85 A 8 3 1.00 21 0.143
86 A 5 4 1.00 20 0.200
87 A 14 8 1.00 23 0.348
88 A 9 7 1.00 23 0.304
89 A 8 5 1.00 23 0.217
90 A 8 3 1.00 23 0.130
91 A 8 3 1.00 23 0.130
92 A 12 8 1.00 23 0.348
93 A 10 8 1.00 23 0.348
94 A 8 6 1.00 21 0.286
95 A 3 3 1.00 20 0.150
96 A 3 3 1.00 23 0.130
97 A 6 6 1.00 23 0.261
98 A 9 6 1.00 23 0.261
99 A 12 6 1.00 23 0.261
100 A 13 10 1.00 23 0.435
101 A 11 8 1.00 23 0.348
102 A 8 6 1.00 21 0.286
103 A 3 3 1.00 20 0.150
104 A 7 7 1.00 23 0.304
105 A 10 9 1.00 23 0.391
106 A 12 9 1.00 23 0.391
107 A 17 13 1.10 23 0.565
108 A 14 11 1.13 23 0.478
109 A 4 4 1.00 21 0.190
110 A 6 6 1.00 20 0.300
111 A 14 10 1.04 23 0.435
112 A 16 13 1.04 23 0.565
113 A 27 14 1.08 23 0.609
114 A 24 12 1.09 23 0.522
115 A 5 4 1.00 23 0.174
116 A 8 7 1.06 21 0.333
117 A 10 7 1.00 20 0.350
118 A 25 11 1.03 23 0.478
119 A 26 14 1.03 23 0.609
120 A 8 7 1.47 13 0.538
121 A 4 4 1.00 23 0.174
122 A 9 7 1.00 23 0.304
123 A 18 9 1.13 23 0.391
124 A 10 7 1.00 20 0.350
125 A 14 7 1.00 22 0.318
126 A 18 7 1.00 22 0.318
127 A 0 0 0.00 0 0.000
128 A 0 0 0.00 0 0.000
129 A 0 0 0.00 0 0.000
130 A 8 7 1.00 23 0.304
131 A 6 6 1.00 23 0.261
132 A 7 7 1.00 21 0.333
133 A 5 4 1.00 20 0.200
134 A 12 11 1.00 23 0.478
135 A 11 9 1.00 23 0.391
136 A 16 11 1.00 23 0.478
137 A 9 7 1.00 23 0.304
138 A 6 6 1.00 23 0.261
139 A 8 7 1.00 21 0.333
140 A 6 4 1.00 20 0.200
141 A 18 11 1.00 23 0.478
142 A 14 10 1.00 23 0.435
143 A 16 11 1.00 23 0.478
144 A 7 7 1.00 23 0.304
145 A 6 6 1.00 23 0.261
146 A 6 7 1.00 21 0.333
147 A 4 4 1.00 20 0.200
148 A 7 8 1.00 23 0.348
149 A 11 10 1.00 23 0.435
150 A 16 11 1.00 23 0.478
151 A 6 6 1.00 23 0.261
152 A 6 6 1.00 23 0.261
153 A 5 6 1.00 21 0.286
154 A 3 3 1.00 20 0.150
155 A 11 10 1.00 23 0.435
156 A 15 13 1.00 23 0.565
157 A 0 0 0.00 0 0.000
158 A 0 0 0.00 0 0.000
159 A 0 0 0.00 0 0.000
160 A 0 0 0.00 0 0.000
161 A 0 0 0.00 0 0.000
162 A 3 3 1.00 23 0.130
163 A 4 4 1.00 23 0.174
164 A 3 2 1.00 21 0.095
165 A 1 1 1.00 16 0.062
166 A 0 0 0.00 0 0.000
167 A 0 0 0.00 0 0.000
168 A 0 0 0.00 0 0.000
169 A 2 2 1.00 14 0.143
170 A 0 0 0.00 0 0.000
171 A 2 2 1.00 21 0.095
172 A 2 2 1.00 21 0.095
173 A 4 3 1.00 19 0.158
174 A 4 4 1.00 21 0.190
175 A 3 3 1.04 21 0.143
176 A 4 3 1.00 21 0.143
177 A 2 2 1.00 21 0.095
178 A 2 2 1.00 21 0.095
179 A 2 1 1.00 18 0.056
180 A 2 2 1.00 21 0.095
181 A 4 3 1.00 21 0.143
182 A 4 3 1.00 21 0.143
183 A 4 5 1.00 23 0.217
184 A 4 5 1.00 23 0.217
185 A 5 5 1.00 21 0.238
186 A 3 4 1.00 23 0.174
187 A 7 6 1.00 23 0.261
188 A 5 5 1.00 23 0.217
189 A 2 2 1.00 23 0.087
190 A 2 2 1.00 23 0.087
191 A 2 2 1.00 20 0.100
192 A 2 2 1.00 23 0.087
193 A 2 2 1.00 23 0.087
194 A 4 4 1.00 23 0.174
195 A 4 4 1.00 23 0.174
196 A 4 5 1.00 23 0.217
197 A 6 6 1.00 23 0.261
198 A 5 5 1.00 21 0.238
199 A 5 5 1.00 23 0.217
200 A 7 6 1.00 23 0.261
201 A 7 6 1.00 23 0.261
202 A 2 2 1.00 23 0.087
203 A 2 2 1.00 23 0.087
204 A 2 2 1.00 20 0.100
205 A 2 2 1.00 23 0.087
206 A 3 3 1.00 23 0.130
207 A 2 2 1.00 23 0.087
208 A 4 4 1.00 23 0.174
209 A 4 4 1.00 23 0.174
210 A 6 6 1.00 23 0.261
211 A 5 6 1.00 23 0.261
212 A 2 2 1.00 21 0.095
213 A 2 2 1.00 23 0.087
214 A 4 4 1.00 23 0.174
215 A 6 4 1.00 23 0.174
216 A 10 9 1.00 23 0.391
217 A 9 8 1.00 23 0.348
218 A 5 5 1.00 20 0.250
219 A 7 7 1.00 23 0.304
220 A 9 7 1.00 23 0.304
221 A 7 8 1.00 23 0.348
222 A 6 7 1.00 23 0.304
223 A 2 2 1.00 21 0.095
224 A 3 3 1.00 23 0.130
225 A 5 5 1.00 23 0.217
226 A 16 10 1.00 23 0.435
227 A 14 8 1.00 23 0.348
228 A 7 6 1.00 20 0.300
229 A 8 8 1.00 23 0.348
230 A 10 8 1.00 23 0.348
231 A 10 9 1.00 23 0.391
232 A 4 3 1.00 23 0.130
233 A 4 3 1.00 21 0.143
234 A 4 3 1.00 23 0.130
235 A 6 5 1.00 23 0.217
236 A 24 9 1.00 23 0.391
237 A 19 9 1.00 23 0.391
238 A 10 7 1.00 20 0.350
239 A 9 8 1.00 23 0.348
240 A 11 8 1.00 23 0.348
241 A 2 2 1.00 18 0.111
242 A 2 2 1.00 19 0.105
243 A 2 3 1.00 12 0.250
244 A 4 4 1.00 10 0.400
245 A 3 4 1.00 19 0.210
246 A 3 4 1.00 21 0.190
247 A 16 6 1.00 22 0.273
248 A 20 6 1.00 22 0.273
249 A 0 0 0.00 0 0.000
250 A 0 0 0.00 0 0.000
251 A 7 8 1.00 25 0.320
252 A 8 9 1.00 25 0.360
253 A 6 5 1.00 23 0.217
254 A 12 9 1.00 25 0.360
255 A 14 11 1.00 25 0.440
256 A 19 13 1.00 25 0.520
257 A 11 12 1.00 25 0.480
258 A 11 11 1.00 22 0.500
259 A 11 10 1.00 25 0.400
260 A 5 4 1.00 25 0.160
261 A 7 8 1.00 25 0.320
262 A 8 9 1.00 25 0.360
263 A 7 8 1.00 25 0.320
264 A 9 9 1.00 25 0.360
265 A 7 5 1.00 23 0.217
266 A 17 9 1.00 25 0.360
267 A 18 12 1.00 25 0.480
268 A 19 13 1.00 25 0.520
269 A 16 11 1.00 22 0.500
270 A 14 12 1.00 25 0.480
271 A 11 10 1.00 25 0.400
272 A 6 4 1.00 25 0.160
273 A 8 8 1.00 25 0.320
274 A 9 9 1.00 25 0.360
275 A 6 5 1.00 13 0.385
276 A 7 8 1.00 25 0.320
277 A 7 9 1.00 25 0.360
278 A 5 5 1.00 23 0.217
279 A 8 9 1.00 25 0.360
280 A 14 12 1.00 25 0.480
281 A 12 12 1.00 25 0.480
282 A 7 7 1.00 22 0.318
283 A 4 4 1.00 25 0.160
284 A 6 8 1.00 25 0.320
285 A 7 9 1.00 25 0.360
286 A 7 8 1.00 25 0.320
287 A 7 8 1.00 25 0.320
288 A 6 8 1.00 25 0.320
289 A 4 4 1.00 23 0.174
290 A 11 9 1.00 25 0.360
291 A 12 12 1.00 25 0.480
292 A 11 11 1.00 25 0.440
293 A 3 3 1.00 22 0.136
294 A 5 7 1.00 25 0.280
295 A 6 8 1.00 25 0.320
296 A 8 10 1.00 25 0.400
297 A 9 8 1.00 25 0.320
298 A 7 8 1.00 25 0.320
299 A 6 8 1.00 25 0.320
300 A 5 5 1.00 23 0.217
301 A 15 9 1.00 25 0.360
302 A 13 14 1.00 25 0.560
303 A 12 13 1.00 25 0.520
304 A 11 11 1.00 25 0.440
305 A 4 4 1.00 25 0.160
306 A 5 5 1.00 22 0.227
307 A 6 9 1.00 25 0.360
308 A 7 10 1.00 25 0.400
309 A 8 10 1.00 33 0.303
310 A 6 6 1.00 31 0.194
311 A 8 9 1.00 33 0.273
312 A 13 11 1.00 33 0.333
313 A 12 12 1.00 33 0.364
314 A 7 7 1.00 30 0.233
315 A 4 4 1.00 33 0.121
316 A 6 8 1.00 33 0.242
317 A 5 5 1.00 13 0.385
318 A 3 3 1.00 25 0.120
319 A 4 4 1.00 25 0.160
320 A 3 2 1.00 23 0.087
321 A 1 1 1.00 16 0.062
322 A 0 0 0.00 0 0.000
323 A 0 0 0.00 0 0.000
324 A 26 6 1.00 22 0.273
325 A 20 6 1.00 22 0.273
326 A 14 11 1.00 20 0.550
327 A 0 0 0.00 0 0.000
328 A 0 0 0.00 0 0.000
329 A 9 7 1.00 23 0.304
330 A 8 7 1.00 23 0.304
331 A 7 7 1.00 21 0.333
332 A 6 6 1.00 20 0.300
333 A 3 3 1.00 23 0.130
334 A 2 2 1.00 23 0.087
335 A 6 7 1.00 23 0.304
336 A 7 7 1.00 23 0.304
337 A 9 7 1.00 21 0.333
338 A 8 7 1.00 21 0.333
339 A 7 7 1.00 19 0.368
340 A 6 6 1.00 18 0.333
341 A 3 3 1.00 21 0.143
342 A 2 2 1.00 21 0.095
343 A 6 7 1.00 21 0.333
344 A 7 7 1.00 21 0.333
345 A 2 2 1.00 22 0.091
346 A 2 2 1.00 23 0.087
347 A 2 2 1.00 25 0.080
348 A 4 4 1.00 18 0.222
349 A 4 4 1.00 18 0.222
350 A 3 3 1.00 22 0.136
351 A 5 4 1.00 27 0.148
352 A 5 4 1.00 27 0.148
353 A 5 4 1.26 25 0.160
354 A 1 1 1.00 18 0.056
355 A 3 3 1.00 27 0.111
356 A 3 3 1.00 27 0.111
357 A 5 4 1.00 27 0.148
358 A 5 4 1.00 27 0.148
359 A 7 7 1.00 29 0.241
360 A 7 8 1.00 29 0.276
361 A 7 8 1.00 27 0.296
362 A 2 2 1.00 20 0.100
363 A 4 4 1.00 29 0.138
364 A 4 4 1.00 29 0.138
365 A 7 7 1.00 29 0.241
366 A 12 9 1.00 29 0.310
367 A 4 3 1.00 21 0.143
368 A 4 3 1.00 21 0.143
369 A 4 3 1.00 19 0.158
370 A 4 4 1.00 21 0.190
371 A 2 2 1.00 21 0.095
372 A 2 2 1.00 21 0.095
373 A 4 3 1.00 21 0.143
374 A 4 3 1.00 21 0.143
375 A 3 2 1.00 18 0.111
376 A 4 3 1.00 21 0.143
377 A 2 2 1.00 21 0.095
378 A 2 2 1.00 21 0.095
379 A 4 4 1.00 23 0.174
380 A 4 4 1.00 23 0.174
381 A 4 4 1.00 21 0.190
382 A 5 6 1.00 23 0.261
383 A 4 4 1.00 23 0.174
384 A 4 4 1.00 23 0.174
385 A 4 4 1.00 23 0.174
386 A 4 4 1.00 23 0.174
387 A 2 2 1.00 20 0.100
388 A 3 3 1.00 23 0.130
389 A 4 4 1.00 23 0.174
390 A 4 4 1.00 23 0.174
391 A 4 4 1.00 23 0.174
392 A 4 4 1.00 23 0.174
393 A 4 4 1.00 23 0.174
394 A 4 4 1.00 21 0.190
395 A 5 6 1.00 23 0.261
396 A 4 4 1.00 23 0.174
397 A 4 4 1.00 23 0.174
398 A 4 4 1.00 23 0.174
399 A 4 4 1.00 23 0.174
400 A 2 2 1.00 20 0.100
401 A 3 3 1.00 23 0.130
402 A 4 4 1.00 23 0.174
403 A 4 4 1.00 23 0.174
404 A 4 4 1.00 23 0.174
405 A 4 4 1.00 23 0.174
406 A 0 0 0.00 0 0.000
407 A 0 0 0.00 0 0.000
408 A 2 2 1.00 23 0.087
409 A 0 0 0.00 0 0.000
410 A 0 0 0.00 0 0.000
411 A 0 0 0.00 0 0.000
412 A 0 0 0.00 0 0.000
413 A 0 0 0.00 0 0.000
414 A 0 0 0.00 0 0.000
415 A 5 5 1.00 23 0.217
416 A 0 0 0.00 0 0.000
417 A 0 0 0.00 0 0.000
418 A 0 0 0.00 0 0.000
419 A 0 0 0.00 0 0.000
420 A 4 4 1.00 25 0.160
421 A 5 6 1.00 23 0.261
422 A 5 6 1.00 23 0.261
423 A 4 4 1.00 21 0.190
424 A 2 2 1.00 23 0.087
425 A 5 5 1.00 23 0.217
426 A 10 8 1.00 23 0.348
427 A 10 5 1.00 25 0.200
428 A 8 5 1.00 25 0.200
429 A 6 5 1.00 23 0.217
430 A 3 3 1.00 25 0.120
431 A 7 6 1.00 25 0.240
432 A 14 8 1.00 25 0.320
433 A 23 9 1.00 25 0.360
434 A 17 9 1.00 25 0.360
435 A 12 9 1.00 25 0.360
436 A 8 9 1.00 25 0.360
437 A 11 9 1.00 25 0.360
438 A 15 9 1.00 25 0.360
439 A 20 9 1.00 25 0.360
440 A 9 5 1.00 25 0.200
441 A 7 5 1.00 25 0.200
442 A 5 4 1.00 23 0.174
443 A 1 1 1.00 16 0.062
444 A 0 0 0.00 0 0.000
445 A 0 0 0.00 0 0.000
446 A 3 3 1.00 26 0.115
447 A 3 3 1.00 32 0.094
448 A 13 4 1.00 27 0.148
449 A 10 4 1.00 27 0.148
450 A 7 4 1.00 25 0.160
451 A 2 2 1.00 18 0.111
452 A 0 0 0.00 0 0.000
453 A 0 0 0.00 0 0.000
454 A 3 2 1.00 23 0.087
455 A 8 7 1.00 25 0.280
456 A 11 9 1.00 25 0.360

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