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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 [96] had the largest ratio of [1.19999999999999996]

# 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 9 9 0.96 21 0.429
2 A 6 5 0.91 21 0.238
3 A 8 8 0.97 21 0.381
4 A 5 4 0.94 19 0.211
5 A 1 1 1.00 12 0.083
6 C 7 7 1.36 19 0.368
7 A 4 4 1.00 21 0.190
8 C 7 7 1.20 21 0.333
9 A 8 7 1.00 21 0.333
10 A 11 10 1.27 23 0.435
11 A 6 5 0.91 23 0.217
12 A 5 5 1.11 23 0.217
13 A 6 5 0.91 21 0.238
14 A 2 2 1.00 14 0.143
15 A 6 5 0.92 21 0.238
16 A 7 6 1.64 23 0.261
17 A 6 5 1.05 23 0.217
18 A 5 4 1.10 23 0.174
19 A 11 10 1.18 23 0.435
20 A 6 5 0.90 23 0.217
21 A 7 7 1.06 23 0.304
22 A 6 5 0.90 21 0.238
23 A 4 4 1.04 14 0.286
24 A 6 5 0.92 21 0.238
25 A 8 7 1.14 23 0.304
26 A 6 5 1.00 23 0.217
27 A 6 5 1.05 23 0.217
28 A 6 5 0.94 23 0.217
29 A 10 9 1.25 23 0.391
30 A 6 5 0.94 23 0.217
31 A 7 6 1.23 23 0.261
32 A 6 5 0.98 23 0.217
33 A 7 6 1.00 23 0.261
34 A 5 4 1.00 21 0.190
35 A 4 3 1.00 14 0.214
36 A 7 6 0.95 21 0.286
37 A 6 5 0.96 23 0.217
38 A 8 7 1.10 23 0.304
39 A 5 4 0.94 23 0.174
40 A 9 8 1.15 23 0.348
41 A 6 5 0.93 23 0.217
42 A 7 6 1.23 23 0.261
43 A 6 5 0.99 23 0.217
44 A 8 7 1.00 23 0.304
45 A 6 5 0.98 21 0.238
46 A 8 7 1.00 14 0.500
47 A 9 8 1.12 21 0.381
48 A 7 6 1.00 23 0.261
49 A 10 9 1.11 23 0.391
50 A 6 5 0.97 23 0.217
51 A 6 5 1.06 23 0.217
52 A 7 6 1.02 23 0.261
53 A 10 9 1.09 23 0.391
54 A 7 6 1.06 21 0.286
55 A 10 9 1.10 14 0.643
56 A 11 10 1.16 21 0.476
57 A 8 7 1.08 23 0.304
58 A 12 11 1.17 23 0.478
59 A 7 6 1.05 23 0.261
60 A 6 5 1.00 8 0.625
61 C 6 5 1.91 8 0.625
62 C 6 5 1.63 8 0.625
63 A 4 3 1.00 10 0.300
64 A 7 6 1.00 10 0.600
65 A 10 9 1.09 10 0.900
66 A 8 7 0.97 25 0.280
67 A 7 6 0.98 23 0.261
68 A 9 8 0.99 23 0.348
69 A 7 6 1.07 25 0.240
70 A 8 7 1.07 25 0.280
71 A 10 9 1.17 25 0.360
72 A 12 12 1.01 25 0.480
73 A 4 4 1.00 16 0.250
74 A 10 9 1.35 25 0.360
75 A 12 11 1.21 25 0.440
76 A 9 8 0.93 25 0.320
77 A 8 7 0.98 23 0.304
78 A 11 10 0.99 23 0.435
79 A 11 10 1.05 25 0.400
80 A 8 7 1.10 25 0.280
81 A 9 8 1.04 25 0.320
82 A 12 11 1.16 25 0.440
83 A 14 14 1.03 25 0.560
84 A 11 11 1.01 16 0.688
85 A 10 9 1.34 25 0.360
86 A 12 11 1.26 25 0.440
87 A 13 13 1.03 16 0.812
88 A 6 6 1.00 10 0.600
89 A 6 6 1.00 12 0.500
90 A 2 2 1.00 12 0.167
91 A 4 4 1.00 10 0.400
92 A 4 4 1.00 12 0.333
93 A 8 8 1.00 10 0.800
94 A 8 8 1.00 12 0.667
95 A 8 8 1.07 12 0.667
96 A 12 12 1.03 10 1.200
97 A 11 11 1.01 12 0.917
98 A 7 6 0.99 25 0.240
99 A 6 5 1.00 23 0.217
100 A 6 5 1.00 23 0.217
101 A 7 6 1.07 25 0.240
102 A 8 7 1.23 25 0.280
103 A 10 10 1.00 25 0.400
104 A 4 4 1.00 16 0.250
105 A 8 7 1.44 25 0.280
106 A 12 11 1.25 25 0.440
107 A 7 6 0.99 25 0.240
108 A 5 4 1.00 23 0.174
109 A 7 6 0.96 23 0.261
110 A 10 9 1.04 25 0.360
111 A 10 9 1.09 25 0.360
112 A 8 7 1.15 25 0.280
113 A 12 12 1.08 25 0.480
114 A 7 7 1.00 16 0.438
115 A 11 10 1.20 25 0.400
116 A 9 8 1.12 25 0.320
117 A 6 5 1.03 25 0.200
118 A 6 5 0.97 23 0.217
119 A 10 9 1.10 23 0.391
120 A 11 10 1.12 25 0.400
121 A 7 6 1.21 25 0.240
122 A 14 14 1.04 25 0.560
123 A 14 14 1.03 16 0.875
124 A 12 11 1.16 25 0.440
125 A 6 6 1.00 10 0.600
126 A 2 2 1.00 12 0.167
127 A 4 4 1.00 10 0.400
128 A 6 6 1.00 12 0.500
129 A 4 4 1.00 12 0.333
130 A 5 4 1.00 25 0.160
131 A 8 7 0.99 23 0.304
132 A 7 6 0.99 23 0.261
133 A 6 5 1.00 21 0.238
134 A 6 5 1.00 21 0.238
135 A 6 5 1.00 23 0.217
136 A 6 5 1.00 23 0.217
137 A 5 4 1.00 23 0.174
138 A 7 6 1.00 23 0.261
139 A 6 5 1.00 23 0.217
140 A 5 4 1.00 23 0.174
141 A 3 3 1.00 21 0.143
142 C 4 4 1.16 21 0.190
143 A 4 4 1.00 21 0.190
144 C 4 4 1.22 19 0.211
145 A 1 1 1.00 12 0.083
146 C 4 4 1.25 19 0.211
147 A 4 4 1.00 21 0.190
148 C 4 4 1.28 21 0.190
149 A 3 3 1.00 21 0.143
150 C 4 4 1.14 23 0.174
151 A 4 4 1.00 23 0.174
152 C 4 4 1.17 21 0.190
153 A 3 3 1.00 14 0.214
154 C 4 4 1.20 21 0.190
155 A 4 4 1.00 23 0.174
156 C 4 4 1.18 23 0.174
157 A 3 3 1.00 23 0.130
158 C 4 4 1.17 23 0.174
159 A 4 4 1.00 23 0.174
160 C 4 4 1.14 23 0.174
161 A 4 4 1.00 23 0.174
162 C 4 4 1.12 21 0.190
163 A 3 3 1.00 14 0.214
164 C 4 4 1.13 21 0.190
165 A 4 4 1.00 23 0.174
166 C 4 4 1.15 23 0.174
167 A 3 3 1.00 23 0.130
168 C 4 4 1.14 23 0.174
169 A 4 4 1.00 23 0.174
170 C 4 4 1.13 23 0.174
171 A 4 4 1.00 23 0.174
172 A 4 4 1.05 23 0.174
173 A 3 3 1.00 23 0.130
174 A 4 4 1.03 23 0.174
175 A 4 4 1.00 23 0.174
176 A 4 4 1.03 21 0.190
177 A 3 3 1.00 14 0.214
178 A 4 4 1.04 21 0.190
179 A 4 4 1.00 23 0.174
180 A 4 4 1.03 23 0.174
181 A 3 3 1.00 23 0.130
182 A 3 3 1.06 8 0.375
183 A 3 3 1.00 10 0.300
184 A 9 8 1.35 21 0.381
185 A 6 5 0.88 21 0.238
186 A 10 9 1.37 21 0.429
187 A 5 4 0.89 19 0.211
188 A 1 1 1.00 12 0.083
189 A 6 5 0.86 19 0.263
190 A 8 7 1.38 21 0.333
191 A 8 7 1.13 21 0.333
192 A 5 4 1.13 21 0.190
193 A 8 7 1.23 21 0.333
194 A 6 5 0.89 21 0.238
195 A 9 8 1.16 21 0.381
196 A 6 5 0.88 23 0.217
197 A 13 12 1.29 23 0.522
198 A 6 5 0.88 21 0.238
199 A 11 10 1.31 14 0.714
200 A 6 5 0.87 21 0.238
201 A 12 11 1.30 23 0.478
202 A 8 7 1.00 23 0.304
203 A 8 7 1.22 23 0.304
204 A 10 9 1.11 23 0.391
205 A 8 7 1.11 23 0.304
206 A 12 11 1.20 23 0.478
207 A 6 5 0.90 23 0.217
208 A 6 5 0.89 23 0.217
209 A 6 5 0.88 21 0.238
210 A 6 5 0.89 21 0.238
211 A 8 7 0.96 23 0.304
212 A 10 9 1.05 23 0.391
213 A 12 11 1.10 23 0.478
214 A 14 13 1.16 23 0.565
215 A 16 15 1.21 23 0.652
216 A 16 15 1.21 23 0.652
217 A 17 16 1.25 23 0.696
218 A 15 14 1.26 14 1.000
219 A 16 15 1.26 23 0.652
220 A 12 11 1.22 23 0.478
221 A 12 11 1.17 23 0.478
222 A 8 7 1.11 23 0.304
223 A 8 7 1.02 23 0.304
224 A 5 4 0.95 23 0.174
225 A 6 5 0.88 23 0.217
226 A 5 4 0.89 23 0.174
227 A 6 5 0.90 23 0.217
228 A 5 4 0.90 23 0.174
229 A 6 5 0.96 24 0.208
230 A 6 5 0.96 24 0.208
231 A 7 6 0.99 24 0.250
232 A 7 6 0.98 22 0.273
233 A 6 5 0.96 22 0.227
234 A 6 5 0.94 24 0.208
235 A 6 5 0.99 24 0.208
236 A 5 4 1.03 24 0.167
237 A 6 5 1.34 24 0.208
238 A 5 4 1.46 15 0.267
239 A 6 5 0.96 24 0.208
240 A 5 4 0.95 24 0.167
241 A 8 7 1.10 24 0.292
242 A 9 8 1.09 24 0.333
243 A 9 8 1.05 24 0.333
244 A 9 8 1.13 24 0.333
245 A 9 8 1.05 22 0.364
246 A 6 5 0.96 22 0.227
247 A 13 12 1.22 24 0.500
248 A 10 9 1.17 24 0.375
249 A 9 8 1.29 24 0.333
250 A 8 7 1.17 24 0.292
251 A 7 6 1.24 15 0.400
252 A 8 7 1.00 24 0.292
253 A 11 10 1.17 24 0.417
254 A 11 10 1.05 24 0.417
255 A 11 10 1.15 24 0.417
256 A 11 10 1.10 24 0.417
257 A 11 10 1.16 22 0.455
258 A 6 5 0.96 22 0.227
259 A 14 13 1.14 24 0.542
260 A 10 9 1.11 24 0.375
261 A 9 8 1.18 24 0.333
262 A 10 9 1.12 24 0.375
263 A 9 8 1.13 15 0.533
264 A 10 9 1.04 24 0.375
265 A 5 4 1.00 10 0.400
266 A 9 8 1.11 8 1.000
267 A 3 3 1.00 10 0.300
268 A 6 5 1.00 10 0.500
269 A 6 5 1.05 10 0.500
270 A 3 3 1.01 8 0.375
271 A 10 9 1.00 8 1.125
272 A 6 5 1.00 8 0.625
273 A 3 3 1.02 10 0.300
274 A 6 5 1.00 10 0.500
275 A 10 9 1.00 10 0.900
276 C 6 5 1.33 15 0.333
277 A 5 5 0.90 15 0.333
278 A 4 4 1.00 15 0.267
279 A 3 3 1.00 15 0.200
280 A 4 4 1.00 13 0.308
281 A 6 6 0.91 13 0.462
282 A 8 8 1.00 15 0.533
283 A 7 6 1.19 21 0.286
284 A 5 4 0.89 21 0.190
285 A 6 5 1.26 21 0.238
286 A 4 3 0.93 19 0.158
287 A 5 4 0.93 19 0.211
288 A 5 4 1.37 21 0.190
289 A 5 4 1.10 21 0.190
290 A 4 3 0.94 21 0.143
291 A 6 5 1.07 21 0.238
292 A 5 4 0.91 21 0.190
293 A 9 8 1.06 23 0.348
294 A 5 4 0.89 23 0.174
295 A 8 7 1.15 23 0.304
296 A 5 4 0.90 21 0.190
297 A 5 4 0.91 21 0.190
298 A 5 4 1.23 23 0.174
299 A 5 4 1.02 23 0.174
300 A 5 4 1.09 23 0.174
301 A 6 5 1.10 23 0.217
302 A 5 4 0.91 23 0.174
303 A 7 6 1.02 23 0.261
304 A 10 9 1.00 23 0.391
305 A 5 4 0.89 23 0.174
306 A 9 8 1.04 23 0.348
307 A 5 4 0.88 21 0.190
308 A 5 4 0.91 21 0.190
309 A 5 4 1.16 23 0.174
310 A 5 4 0.98 23 0.174
311 A 5 4 1.11 23 0.174
312 A 5 4 1.02 23 0.174
313 A 5 4 1.01 23 0.174
314 A 8 7 1.10 23 0.304
315 A 5 4 0.90 23 0.174
316 A 5 4 0.93 23 0.174
317 A 10 9 1.23 23 0.391
318 A 5 4 0.94 23 0.174
319 A 8 7 1.22 23 0.304
320 A 5 4 0.96 23 0.174
321 A 6 5 1.14 23 0.217
322 A 4 3 1.00 21 0.143
323 A 6 5 0.97 21 0.238
324 A 5 4 0.97 23 0.174
325 A 8 7 1.12 23 0.304
326 A 5 4 0.94 23 0.174
327 A 10 9 1.17 23 0.391
328 A 5 4 0.94 23 0.174
329 A 10 9 1.12 23 0.391
330 A 5 4 0.95 23 0.174
331 A 8 7 1.15 23 0.304
332 A 5 4 0.97 23 0.174
333 A 5 4 0.97 23 0.174
334 A 5 4 0.97 21 0.190
335 A 7 6 1.09 21 0.286
336 A 5 4 0.96 23 0.174
337 A 10 9 1.09 23 0.391
338 A 5 4 0.94 23 0.174
339 A 10 9 1.13 23 0.391
340 A 6 5 1.08 23 0.217
341 A 6 5 1.03 23 0.217
342 A 6 5 0.98 23 0.217
343 A 6 5 0.97 23 0.217
344 A 6 5 1.03 21 0.238
345 A 8 7 1.15 21 0.333
346 A 5 4 0.95 23 0.174
347 A 11 10 1.16 23 0.435
348 A 5 4 0.95 23 0.174
349 A 5 4 1.11 15 0.267
350 A 5 4 1.00 15 0.267
351 A 7 6 1.43 15 0.400
352 A 7 6 0.96 25 0.240
353 A 6 5 0.97 23 0.217
354 A 8 7 0.98 23 0.304
355 A 6 5 1.05 25 0.200
356 A 7 6 1.02 25 0.240
357 A 10 9 1.16 25 0.360
358 A 9 8 1.24 25 0.320
359 A 4 4 1.00 16 0.250
360 A 4 3 1.43 25 0.120
361 A 8 7 1.21 25 0.280
362 A 8 7 0.92 25 0.280
363 A 7 6 0.98 23 0.261
364 A 9 8 0.98 23 0.348
365 A 9 8 1.09 25 0.320
366 A 7 6 1.06 25 0.240
367 A 8 7 0.97 25 0.280
368 A 12 11 1.16 25 0.440
369 A 10 9 1.16 25 0.360
370 A 11 11 1.01 16 0.688
371 A 9 8 1.32 25 0.320
372 A 7 6 1.23 25 0.240
373 A 6 5 0.97 25 0.200
374 A 5 4 1.00 23 0.174
375 A 5 4 1.00 23 0.174
376 A 6 5 1.04 25 0.200
377 A 9 8 1.21 25 0.320
378 A 7 6 1.29 25 0.240
379 A 4 4 1.00 16 0.250
380 A 9 8 1.77 25 0.320
381 A 8 7 1.23 25 0.280
382 A 6 5 0.97 25 0.200
383 A 4 3 1.00 23 0.130
384 A 6 5 0.98 23 0.217
385 A 9 8 1.05 25 0.320
386 A 10 9 1.12 25 0.360
387 A 8 7 1.19 25 0.280
388 A 4 3 1.31 25 0.120
389 A 7 7 1.00 16 0.438
390 A 8 7 1.28 25 0.280
391 A 7 6 1.02 25 0.240
392 A 5 4 1.00 25 0.160
393 A 5 4 0.97 23 0.174
394 A 8 7 1.07 23 0.304
395 A 10 9 1.12 25 0.360
396 A 7 6 1.21 25 0.240
397 A 8 7 1.20 25 0.280
398 A 14 14 1.03 16 0.875
399 A 9 8 1.25 25 0.320
400 A 5 4 1.00 25 0.160
401 A 8 7 0.98 23 0.304
402 A 6 5 0.94 23 0.217
403 A 5 4 1.00 21 0.190
404 A 5 4 1.00 21 0.190
405 A 5 4 1.00 23 0.174
406 A 5 4 1.00 23 0.174
407 A 5 4 1.00 23 0.174
408 A 5 4 1.00 14 0.286
409 A 5 4 1.00 23 0.174
410 A 5 4 1.00 23 0.174
411 A 6 5 0.91 25 0.200
412 A 6 5 0.91 25 0.200
413 A 6 5 0.95 23 0.217
414 A 6 5 1.00 23 0.217
415 A 6 5 0.92 25 0.200
416 A 6 5 0.91 25 0.200
417 A 6 5 0.94 23 0.217
418 A 6 5 0.99 23 0.217
419 A 5 4 0.96 23 0.174
420 A 5 4 0.98 23 0.174
421 A 4 3 1.00 21 0.143
422 A 5 4 0.96 23 0.174
423 A 5 4 0.98 23 0.174
424 A 4 3 1.00 21 0.143
425 A 7 6 1.24 13 0.462
426 A 11 10 1.11 25 0.400
427 A 11 10 1.29 25 0.400
428 A 10 9 1.00 23 0.391
429 A 11 10 1.04 23 0.435
430 A 13 12 1.03 25 0.480
431 A 17 16 0.82 25 0.640
432 A 10 9 0.76 25 0.360
433 A 15 14 0.72 25 0.560
434 C 14 13 0.86 25 0.520
435 C 9 8 0.68 25 0.320
436 C 14 13 0.60 25 0.520
437 A 11 10 1.09 25 0.400
438 A 11 10 1.21 25 0.400
439 A 10 9 1.00 23 0.391
440 A 10 9 1.00 23 0.391
441 A 12 11 1.03 25 0.440
442 A 12 12 0.89 25 0.480
443 A 13 13 0.90 25 0.520
444 A 12 11 1.00 25 0.440
445 C 9 8 0.85 25 0.320
446 C 13 12 0.69 25 0.480
447 A 11 10 1.09 25 0.400
448 A 11 10 1.20 25 0.400
449 A 10 9 1.00 23 0.391
450 A 11 10 1.04 23 0.435
451 A 12 11 1.06 25 0.440
452 A 15 15 0.80 25 0.600
453 C 15 14 0.81 25 0.560
454 A 9 8 1.00 25 0.320
455 C 14 13 0.77 25 0.520
456 C 10 9 0.63 25 0.360
457 A 10 9 0.99 25 0.360
458 A 8 7 0.94 25 0.280
459 A 7 6 1.03 23 0.261
460 A 7 6 1.04 23 0.261
461 A 8 7 0.92 25 0.280
462 A 10 9 0.92 25 0.360
463 A 9 8 1.20 25 0.320
464 A 9 8 1.59 25 0.320
465 A 4 4 1.00 16 0.250
466 A 10 9 1.35 25 0.360
467 A 10 9 1.25 25 0.360
468 A 11 10 0.92 25 0.400
469 A 9 8 0.94 25 0.320
470 A 8 7 1.01 23 0.304
471 A 8 7 1.01 23 0.304
472 A 9 8 0.88 25 0.320
473 A 11 10 0.86 25 0.400
474 A 12 11 1.24 25 0.440
475 A 10 9 1.25 25 0.360
476 A 11 11 1.01 16 0.688
477 A 11 10 1.27 25 0.400
478 A 12 11 1.24 25 0.440
479 A 9 8 1.09 25 0.320
480 A 7 6 1.00 25 0.240
481 A 6 5 1.00 23 0.217
482 A 6 5 1.00 23 0.217
483 A 7 6 0.96 25 0.240
484 A 9 8 1.02 25 0.320
485 A 7 6 1.23 25 0.240
486 A 9 8 1.81 25 0.320
487 A 4 4 1.00 16 0.250
488 A 9 8 1.32 25 0.320
489 A 10 9 1.22 25 0.360
490 A 10 9 1.03 25 0.360
491 A 8 7 1.02 25 0.280
492 A 7 6 1.03 23 0.261
493 A 7 6 1.04 23 0.261
494 A 8 7 0.94 25 0.280
495 A 10 9 0.94 25 0.360
496 A 9 8 1.25 25 0.320
497 A 8 7 1.27 25 0.280
498 A 7 7 1.00 16 0.438
499 A 12 11 1.35 25 0.440
500 A 12 11 1.22 25 0.440
501 A 11 10 0.99 25 0.400
502 A 9 8 0.99 25 0.320
503 A 8 7 1.08 23 0.304
504 A 8 7 1.05 23 0.304
505 A 9 8 0.92 25 0.320
506 A 11 10 0.89 25 0.400
507 A 11 10 1.25 25 0.400
508 A 10 9 1.26 25 0.360
509 A 14 14 1.03 16 0.875
510 A 13 12 1.17 25 0.480
511 A 14 13 1.22 25 0.520
512 A 6 5 1.22 25 0.200
513 A 6 5 1.00 23 0.217
514 A 5 4 1.00 21 0.190
515 A 5 4 1.00 21 0.190
516 A 6 5 0.97 23 0.217
517 A 5 4 1.00 23 0.174
518 A 6 5 1.00 23 0.217
519 A 6 5 1.00 23 0.217
520 A 5 4 1.00 23 0.174
521 A 6 5 1.00 15 0.333
522 A 7 6 1.00 15 0.400
523 A 8 7 1.00 15 0.467
524 A 7 6 1.00 15 0.400
525 A 8 7 0.96 15 0.467

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