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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 [119] had the largest ratio of [.875000000000000000]

# 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 7 6 0.73 24 0.250
2 A 7 6 0.80 24 0.250
3 A 7 6 0.93 24 0.250
4 A 6 5 1.00 22 0.227
5 A 8 7 0.79 22 0.318
6 A 8 7 1.02 24 0.292
7 A 10 9 1.10 24 0.375
8 A 9 8 1.19 24 0.333
9 A 8 7 1.18 24 0.292
10 A 8 7 1.00 24 0.292
11 A 6 5 1.00 15 0.333
12 A 7 6 0.79 24 0.250
13 A 7 6 0.74 24 0.250
14 A 7 6 0.71 24 0.250
15 A 7 6 0.75 24 0.250
16 A 7 6 0.74 24 0.250
17 A 6 5 0.85 24 0.208
18 A 6 5 1.00 22 0.227
19 A 8 7 0.74 22 0.318
20 A 8 7 0.92 24 0.292
21 A 8 7 1.02 24 0.292
22 A 7 7 0.84 24 0.292
23 A 6 5 1.00 24 0.208
24 A 6 5 0.91 15 0.333
25 A 7 6 0.77 24 0.250
26 A 7 6 0.74 24 0.250
27 A 5 4 0.90 21 0.190
28 A 4 3 0.94 19 0.158
29 A 4 4 1.00 19 0.211
30 A 4 4 1.00 21 0.190
31 A 7 7 0.96 21 0.333
32 A 5 5 0.97 21 0.238
33 A 1 1 1.00 12 0.083
34 A 3 3 1.00 21 0.143
35 A 6 5 1.00 21 0.238
36 A 6 5 0.86 21 0.238
37 A 5 4 0.93 23 0.174
38 A 5 4 0.95 23 0.174
39 A 5 4 0.98 23 0.174
40 A 4 3 1.00 21 0.143
41 A 6 5 0.98 21 0.238
42 A 7 6 1.11 23 0.261
43 A 8 7 1.17 23 0.304
44 A 10 9 1.24 23 0.391
45 A 8 7 1.23 23 0.304
46 A 7 6 1.22 23 0.261
47 A 6 5 1.00 23 0.217
48 A 4 3 1.00 14 0.214
49 A 5 4 0.96 23 0.174
50 A 5 4 0.94 23 0.174
51 A 5 4 0.93 23 0.174
52 A 5 4 0.92 23 0.174
53 A 5 4 0.95 23 0.174
54 A 5 4 0.95 23 0.174
55 A 5 4 0.99 23 0.174
56 A 5 4 0.99 21 0.190
57 A 8 7 1.10 21 0.333
58 A 9 8 1.08 23 0.348
59 A 9 8 1.14 23 0.348
60 A 7 6 1.19 23 0.261
61 A 7 6 1.00 23 0.261
62 A 8 7 1.00 14 0.500
63 A 7 6 1.28 23 0.261
64 A 7 6 1.24 23 0.261
65 A 8 7 1.20 23 0.304
66 A 6 5 1.05 23 0.217
67 A 9 8 1.08 23 0.348
68 A 10 9 1.09 14 0.643
69 A 9 8 1.33 23 0.348
70 A 4 3 1.00 13 0.231
71 A 5 4 1.00 13 0.308
72 A 4 3 1.00 21 0.143
73 A 7 6 0.97 25 0.240
74 A 6 5 0.99 23 0.217
75 A 8 7 0.96 23 0.304
76 A 6 5 1.08 25 0.200
77 A 7 6 1.09 25 0.240
78 A 10 9 1.01 25 0.360
79 A 11 11 0.99 25 0.440
80 A 4 4 0.98 16 0.250
81 A 10 9 1.01 25 0.360
82 A 12 11 1.04 25 0.440
83 A 8 7 0.93 25 0.280
84 A 7 6 0.99 23 0.261
85 A 10 9 0.98 23 0.391
86 A 10 9 1.05 25 0.360
87 A 7 6 1.10 25 0.240
88 A 8 7 1.02 25 0.280
89 A 13 12 1.04 25 0.480
90 A 13 13 1.01 25 0.520
91 A 11 11 0.99 16 0.688
92 A 10 9 1.01 25 0.360
93 A 12 11 1.03 25 0.440
94 A 6 5 0.99 25 0.200
95 A 5 4 1.00 23 0.174
96 A 5 4 1.00 23 0.174
97 A 6 5 1.08 25 0.200
98 A 9 8 0.95 25 0.320
99 A 9 9 0.98 25 0.360
100 A 4 4 0.98 16 0.250
101 A 11 10 1.02 25 0.400
102 A 12 11 1.03 25 0.440
103 A 6 5 0.99 25 0.200
104 A 4 3 1.00 23 0.130
105 A 6 5 0.99 23 0.217
106 A 9 8 1.04 25 0.320
107 A 11 10 1.00 25 0.400
108 A 9 8 0.99 25 0.320
109 A 11 11 1.05 25 0.440
110 A 7 7 0.99 16 0.438
111 A 12 11 1.06 25 0.440
112 A 8 7 1.15 25 0.280
113 A 5 4 0.99 25 0.160
114 A 5 4 0.99 23 0.174
115 A 9 8 1.08 23 0.348
116 A 10 9 0.84 25 0.360
117 A 11 10 0.99 25 0.400
118 A 13 13 1.02 25 0.520
119 A 14 14 1.01 16 0.875
120 A 14 13 1.07 25 0.520
121 A 5 4 1.00 25 0.160
122 A 7 6 1.01 23 0.261
123 A 6 5 0.99 23 0.217
124 A 5 4 1.00 21 0.190
125 A 5 4 1.00 21 0.190
126 A 5 4 1.00 23 0.174
127 A 5 4 1.00 23 0.174
128 A 5 4 1.00 23 0.174
129 A 5 4 1.00 23 0.174
130 A 5 4 1.00 23 0.174
131 A 3 3 1.00 23 0.130
132 A 3 3 1.00 23 0.130
133 A 3 3 1.00 23 0.130
134 A 3 3 1.00 21 0.143
135 A 3 3 1.00 21 0.143
136 A 3 3 1.00 23 0.130
137 A 3 3 1.00 23 0.130
138 A 3 3 1.00 23 0.130
139 A 3 3 1.00 23 0.130
140 A 3 3 1.00 23 0.130
141 A 3 3 1.00 14 0.214
142 A 3 3 1.00 23 0.130
143 A 3 3 1.00 23 0.130
144 A 5 4 0.95 24 0.167
145 A 5 4 0.96 24 0.167
146 A 5 4 0.98 24 0.167
147 A 6 5 0.99 24 0.208
148 A 6 5 0.99 22 0.227
149 A 5 4 0.96 22 0.182
150 A 5 4 1.06 24 0.167
151 A 5 4 1.12 24 0.167
152 A 5 4 1.09 24 0.167
153 A 5 4 1.05 24 0.167
154 A 5 4 1.03 24 0.167
155 A 5 4 1.34 24 0.167
156 A 5 4 1.46 15 0.267
157 A 5 4 0.96 24 0.167
158 A 5 4 0.95 24 0.167
159 A 5 4 0.94 24 0.167
160 A 5 4 0.93 24 0.167
161 A 7 6 1.10 24 0.250
162 A 8 7 1.09 24 0.292
163 A 8 7 1.05 24 0.292
164 A 8 7 1.13 24 0.292
165 A 8 7 1.05 22 0.318
166 A 5 4 1.35 22 0.182
167 A 13 12 1.70 24 0.500
168 A 8 7 1.23 24 0.292
169 A 9 8 1.28 24 0.333
170 A 7 6 1.17 24 0.250
171 A 7 6 1.24 15 0.400
172 A 7 6 1.00 24 0.250
173 A 10 9 1.18 24 0.375
174 A 10 9 1.05 24 0.375
175 A 10 9 1.15 24 0.375
176 A 10 9 1.10 24 0.375
177 A 10 9 1.16 22 0.409
178 A 5 4 1.85 22 0.182
179 A 13 12 1.15 24 0.500
180 A 9 8 1.11 24 0.333
181 A 9 8 1.14 24 0.333
182 A 9 8 1.12 24 0.333
183 A 9 8 1.13 15 0.533
184 A 9 8 1.06 24 0.333
185 A 8 7 1.02 23 0.304
186 A 8 7 1.07 23 0.304
187 A 8 7 1.03 25 0.280
188 A 6 5 1.03 25 0.200
189 A 4 3 1.00 23 0.130
190 A 6 5 1.08 23 0.217
191 A 12 11 1.05 25 0.440
192 A 7 6 1.08 25 0.240
193 A 4 3 1.00 16 0.188
194 A 9 8 1.21 25 0.320
195 A 6 5 0.79 16 0.312
196 A 6 5 0.90 16 0.312
197 A 6 5 1.00 16 0.312
198 A 4 4 1.00 16 0.250
199 A 4 4 1.00 14 0.286
200 A 8 8 1.00 16 0.500
201 A 7 7 1.00 16 0.438
202 A 5 5 0.90 16 0.312
203 A 3 3 1.00 16 0.188
204 A 6 6 0.91 14 0.429
205 A 6 5 1.00 16 0.312
206 A 6 5 0.90 16 0.312
207 A 6 5 0.90 16 0.312
208 A 6 5 1.00 16 0.312
209 A 4 4 1.00 16 0.250
210 A 4 4 1.00 16 0.250
211 A 6 6 0.91 14 0.429
212 A 8 8 1.00 14 0.571
213 A 7 7 1.00 16 0.438
214 A 5 5 0.90 16 0.312
215 A 3 3 1.00 16 0.188
216 A 6 5 1.00 16 0.312
217 A 6 5 0.90 16 0.312
218 A 6 5 0.86 16 0.312
219 A 8 7 1.15 21 0.333
220 A 7 6 1.18 21 0.286
221 A 6 5 1.25 21 0.238
222 A 1 1 1.00 12 0.083
223 A 5 4 1.39 21 0.190
224 A 4 3 0.93 21 0.143
225 A 5 4 0.90 21 0.190
226 A 5 4 0.89 21 0.190
227 A 8 7 1.09 23 0.304
228 A 7 6 1.23 23 0.261
229 A 2 2 1.00 14 0.143
230 A 5 4 1.20 23 0.174
231 A 5 4 1.09 23 0.174
232 A 5 4 0.91 23 0.174
233 A 5 4 0.90 23 0.174
234 A 5 4 0.90 23 0.174
235 A 5 4 1.00 15 0.267
236 A 8 7 1.31 15 0.467
237 A 5 4 1.00 15 0.267
238 A 7 6 1.25 15 0.400
239 A 5 4 1.00 15 0.267
240 A 6 5 1.05 15 0.333
241 A 4 3 1.00 13 0.231
242 A 6 5 1.00 13 0.385
243 A 5 4 1.00 15 0.267
244 A 7 6 1.26 15 0.400
245 A 5 4 1.00 15 0.267
246 A 8 7 1.34 15 0.467
247 A 5 4 1.00 15 0.267
248 A 9 8 1.16 15 0.533
249 A 5 4 1.00 15 0.267
250 A 7 6 1.16 15 0.400
251 A 5 4 1.00 15 0.267
252 A 5 4 1.00 15 0.267
253 A 5 4 1.00 13 0.308
254 A 7 6 1.18 13 0.462
255 A 5 4 1.00 15 0.267
256 A 9 8 1.19 15 0.533
257 A 5 4 1.00 15 0.267
258 A 7 6 0.96 25 0.240
259 A 6 5 0.97 23 0.217
260 A 8 7 0.98 23 0.304
261 A 6 5 1.07 25 0.200
262 A 7 6 1.09 25 0.240
263 A 11 10 1.17 25 0.400
264 A 10 9 1.16 25 0.360
265 A 4 4 0.98 16 0.250
266 A 10 9 1.31 25 0.360
267 A 12 11 1.23 25 0.440
268 A 8 7 0.92 25 0.280
269 A 7 6 0.98 23 0.261
270 A 10 9 0.99 23 0.391
271 A 10 9 1.05 25 0.360
272 A 7 6 1.10 25 0.240
273 A 8 7 1.01 25 0.280
274 A 13 12 1.02 25 0.480
275 A 12 11 0.99 25 0.440
276 A 11 11 0.99 16 0.688
277 A 10 9 0.87 25 0.360
278 A 12 11 1.07 25 0.440
279 A 6 5 0.97 25 0.200
280 A 5 4 1.00 23 0.174
281 A 5 4 1.00 23 0.174
282 A 6 5 1.07 25 0.200
283 A 9 8 1.16 25 0.320
284 A 8 7 1.15 25 0.280
285 A 4 4 0.98 16 0.250
286 A 10 9 1.30 25 0.360
287 A 11 10 1.21 25 0.400
288 A 6 5 0.97 25 0.200
289 A 4 3 1.00 23 0.130
290 A 6 5 0.97 23 0.217
291 A 9 8 1.06 25 0.320
292 A 11 10 0.99 25 0.400
293 A 10 9 0.97 25 0.360
294 A 10 9 0.95 25 0.360
295 A 7 7 0.99 16 0.438
296 A 12 11 1.06 25 0.440
297 A 8 7 1.10 25 0.280
298 A 5 4 0.95 25 0.160
299 A 5 4 0.97 23 0.174
300 A 8 7 1.06 23 0.304
301 A 11 10 1.15 25 0.400
302 A 11 10 1.20 25 0.400
303 A 12 11 1.16 25 0.440
304 A 14 14 1.01 16 0.875
305 A 14 13 1.21 25 0.520
306 A 5 4 1.00 25 0.160
307 A 7 6 1.02 23 0.261
308 A 6 5 0.94 23 0.217
309 A 5 4 1.00 21 0.190
310 A 5 4 1.00 21 0.190
311 A 5 4 1.00 23 0.174
312 A 5 4 1.00 23 0.174
313 A 5 4 1.00 23 0.174
314 A 5 4 1.00 14 0.286
315 A 5 4 1.00 23 0.174
316 A 5 4 0.95 23 0.174
317 A 13 12 0.93 23 0.522
318 A 11 10 0.94 21 0.476
319 A 5 4 0.95 21 0.190
320 A 5 4 0.95 23 0.174
321 A 3 3 1.00 23 0.130
322 A 3 3 1.00 23 0.130
323 A 3 3 1.00 14 0.214
324 F 0 0 N/A 0.000 N/A
325 F 0 0 N/A 0.000 N/A
326 A 7 6 1.00 23 0.261
327 A 13 12 1.03 23 0.522
328 A 13 12 0.88 23 0.522
329 A 12 11 0.97 21 0.524
330 A 5 4 0.91 21 0.190
331 A 5 4 0.92 23 0.174
332 N/A 2 0 1.00 23 0.000
333 N/A 2 0 1.00 23 0.000
334 N/A 2 0 1.00 14 0.000
335 N/A 2 0 1.00 23 0.000
336 N/A 2 0 1.00 23 0.000
337 A 5 4 0.94 24 0.167
338 A 5 4 0.96 24 0.167
339 A 6 5 1.01 24 0.208
340 A 6 5 0.97 22 0.227
341 A 5 4 0.96 22 0.182
342 A 5 4 1.09 24 0.167
343 A 5 4 1.10 24 0.167
344 A 5 4 1.05 24 0.167
345 A 5 4 1.03 24 0.167
346 A 5 4 1.29 24 0.167
347 A 5 4 0.96 24 0.167
348 A 5 4 0.95 24 0.167
349 A 5 4 0.95 24 0.167
350 N/A 2 0 1.00 23 0.000
351 A 7 6 1.01 23 0.261
352 A 5 4 0.99 23 0.174
353 A 5 4 1.00 21 0.190
354 A 5 4 0.99 21 0.190
355 A 5 4 0.98 23 0.174
356 N/A 2 0 1.00 23 0.000
357 N/A 2 0 1.00 23 0.000
358 N/A 2 0 1.00 14 0.000
359 N/A 2 0 1.00 23 0.000
360 N/A 2 0 1.00 23 0.000
361 N/A 2 0 1.00 23 0.000
362 A 5 4 0.98 23 0.174
363 A 5 4 0.99 23 0.174
364 A 5 4 1.00 21 0.190
365 N/A 2 0 1.00 21 0.000
366 N/A 2 0 1.00 23 0.000
367 N/A 2 0 1.00 23 0.000
368 N/A 2 0 1.00 23 0.000
369 N/A 2 0 1.00 14 0.000
370 N/A 2 0 1.00 23 0.000
371 N/A 2 0 1.00 23 0.000
372 A 5 4 1.09 23 0.174
373 A 5 4 1.09 23 0.174
374 A 5 4 1.08 23 0.174
375 A 5 4 1.09 21 0.190
376 A 6 5 1.03 21 0.238
377 A 5 4 0.92 23 0.174
378 A 5 4 0.91 23 0.174
379 A 5 4 0.91 23 0.174
380 A 5 4 0.91 23 0.174
381 A 5 4 0.92 23 0.174
382 A 5 4 0.93 23 0.174
383 A 5 4 0.96 23 0.174
384 A 5 4 0.96 23 0.174
385 A 6 5 1.04 23 0.217
386 A 7 6 1.02 23 0.261
387 A 8 7 1.04 23 0.304
388 A 9 8 1.09 26 0.308
389 A 9 8 1.29 26 0.308
390 A 8 7 1.00 24 0.292
391 A 9 8 1.04 24 0.333
392 A 11 10 1.03 26 0.385
393 A 11 10 0.78 26 0.385
394 A 10 9 0.76 26 0.346
395 A 9 8 0.70 26 0.308
396 A 9 8 0.67 26 0.308
397 A 9 8 0.59 26 0.308
398 A 9 8 0.50 26 0.308
399 A 9 8 1.11 26 0.308
400 A 9 8 1.21 26 0.308
401 A 8 7 1.00 24 0.292
402 A 8 7 1.00 24 0.292
403 A 10 9 1.03 26 0.346
404 A 10 10 0.89 26 0.385
405 A 8 8 0.89 26 0.308
406 A 9 8 1.00 26 0.308
407 A 9 8 0.77 26 0.308
408 A 10 9 0.58 26 0.346
409 A 9 8 1.09 26 0.308
410 A 9 8 1.20 26 0.308
411 A 8 7 1.00 24 0.292
412 A 9 8 1.04 24 0.333
413 A 10 9 1.06 26 0.346
414 A 10 10 0.79 26 0.385
415 A 10 9 0.70 26 0.346
416 A 9 8 1.00 26 0.308
417 A 11 10 0.69 26 0.385
418 A 10 9 0.57 26 0.346
419 A 9 8 1.00 25 0.320
420 A 7 6 0.96 25 0.240
421 A 6 5 1.03 23 0.217
422 A 6 5 1.04 23 0.217
423 A 7 6 0.91 25 0.240
424 A 9 8 0.92 25 0.320
425 A 11 10 1.03 25 0.400
426 A 9 8 0.96 25 0.320
427 A 4 4 0.98 16 0.250
428 A 10 9 0.96 25 0.360
429 A 12 11 1.03 25 0.440
430 A 10 9 0.92 25 0.360
431 A 8 7 0.93 25 0.280
432 A 7 6 1.01 23 0.261
433 A 7 6 1.01 23 0.261
434 A 8 7 0.88 25 0.280
435 A 10 9 0.85 25 0.360
436 A 14 13 1.03 25 0.520
437 A 11 10 1.00 25 0.400
438 A 11 11 0.99 16 0.688
439 A 12 11 1.00 25 0.440
440 A 14 13 1.02 25 0.520
441 A 8 7 1.11 25 0.280
442 A 6 5 1.02 25 0.200
443 A 5 4 1.00 23 0.174
444 A 5 4 1.00 23 0.174
445 A 6 5 0.95 25 0.200
446 A 8 7 1.01 25 0.280
447 A 11 10 1.01 25 0.400
448 A 6 5 1.13 25 0.200
449 A 4 4 0.98 16 0.250
450 A 7 6 1.13 25 0.240
451 A 11 10 1.01 25 0.400
452 A 9 8 1.03 25 0.320
453 A 7 6 1.00 25 0.240
454 A 6 5 1.03 23 0.217
455 A 6 5 1.04 23 0.217
456 A 7 6 0.94 25 0.240
457 A 9 8 0.95 25 0.320
458 A 14 13 1.07 25 0.520
459 A 12 11 1.04 25 0.440
460 A 7 7 0.99 16 0.438
461 A 11 10 1.06 25 0.400
462 A 13 12 1.05 25 0.480
463 A 10 9 0.97 25 0.360
464 A 8 7 0.98 25 0.280
465 A 7 6 1.07 23 0.261
466 A 7 6 1.05 23 0.261
467 A 8 7 0.92 25 0.280
468 A 10 9 0.89 25 0.360
469 A 17 16 1.09 25 0.640
470 A 14 13 1.06 25 0.520
471 A 14 14 1.01 16 0.875
472 A 13 12 1.09 25 0.480
473 A 15 14 1.09 25 0.560
474 A 6 5 1.22 25 0.200
475 A 5 4 1.02 23 0.174
476 A 4 3 1.00 21 0.143
477 A 4 3 1.00 21 0.143
478 A 5 4 0.96 23 0.174
479 A 5 4 1.00 23 0.174
480 A 5 4 1.00 23 0.174
481 A 5 4 1.00 23 0.174
482 A 5 4 1.00 23 0.174
483 A 5 4 1.00 15 0.267
484 A 7 6 1.00 15 0.400
485 A 6 5 1.00 15 0.333
486 A 7 6 0.95 23 0.261
487 A 6 5 1.04 25 0.200
488 A 5 4 1.06 23 0.174
489 A 6 5 1.00 23 0.217
490 A 7 6 0.94 25 0.240
491 A 8 7 1.01 25 0.280
492 A 7 6 1.11 25 0.240
493 A 4 3 1.00 16 0.188
494 A 9 8 1.07 25 0.320
495 N/A 2 0 1.00 23 0.000
496 A 12 11 0.95 23 0.478
497 A 8 7 0.99 21 0.333
498 A 5 4 1.00 21 0.190
499 A 8 7 0.99 23 0.304
500 N/A 2 0 1.00 23 0.000
501 N/A 2 0 1.00 23 0.000
502 N/A 2 0 1.00 14 0.000
503 N/A 2 0 1.00 23 0.000
504 N/A 2 0 1.00 23 0.000
505 A 3 3 1.00 23 0.130
506 A 3 3 1.00 23 0.130
507 A 3 3 1.00 21 0.143
508 N/A 2 0 1.00 23 0.000
509 N/A 2 0 1.00 23 0.000
510 A 7 6 0.96 15 0.400
511 A 6 5 1.00 15 0.333
512 N/A 2 0 1.00 23 0.000
513 N/A 2 0 1.00 23 0.000
514 N/A 2 0 1.00 21 0.000
515 A 5 4 1.00 21 0.190
516 A 5 4 0.99 23 0.174
517 N/A 2 0 1.00 23 0.000
518 N/A 2 0 1.00 23 0.000
519 N/A 2 0 1.00 14 0.000
520 N/A 2 0 1.00 23 0.000
521 N/A 2 0 1.00 23 0.000
522 A 9 8 1.38 37 0.216
523 A 5 4 1.00 35 0.114
524 A 6 6 1.00 25 0.240
525 A 6 6 1.00 25 0.240

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