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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 [137] had the largest ratio of [1.41667000000000010]

# 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 1.15 16 0.500
2 A 5 5 1.22 16 0.312
3 A 5 5 1.08 14 0.357
4 A 1 1 1.00 8 0.125
5 A 6 5 1.00 16 0.312
6 A 4 3 1.00 16 0.188
7 A 5 4 0.99 16 0.250
8 A 7 6 1.09 16 0.375
9 A 3 3 1.05 18 0.167
10 A 3 3 1.10 18 0.167
11 A 3 3 1.15 16 0.188
12 A 3 3 1.09 10 0.300
13 A 7 6 0.99 18 0.333
14 A 10 9 0.93 18 0.500
15 A 14 13 0.96 18 0.722
16 A 4 3 0.96 18 0.167
17 A 4 3 0.95 18 0.167
18 A 4 3 0.95 16 0.188
19 A 8 7 0.91 10 0.700
20 N/A 1 0 1.00 18 0.000
21 N/A 1 0 1.00 18 0.000
22 A 2 2 1.00 18 0.111
23 A 2 2 1.00 16 0.125
24 A 10 9 0.97 10 0.900
25 N/A 1 0 1.00 18 0.000
26 N/A 1 0 1.00 18 0.000
27 N/A 2 0 1.00 18 0.000
28 A 4 4 0.81 16 0.250
29 N/A 1 0 1.00 18 0.000
30 N/A 1 0 1.00 18 0.000
31 A 3 3 0.55 31 0.097
32 A 3 3 0.58 31 0.097
33 A 3 3 0.59 29 0.103
34 A 7 7 0.70 31 0.226
35 A 7 7 0.73 31 0.226
36 A 3 3 0.52 31 0.097
37 A 3 3 0.54 31 0.097
38 A 3 3 0.52 29 0.103
39 A 3 3 0.66 31 0.097
40 A 3 3 0.49 31 0.097
41 A 3 3 0.51 31 0.097
42 A 3 3 0.50 29 0.103
43 A 3 3 0.62 31 0.097
44 A 3 3 0.58 31 0.097
45 A 3 3 0.60 31 0.097
46 A 3 3 0.69 29 0.103
47 A 10 9 0.76 31 0.290
48 A 14 13 0.76 31 0.419
49 A 3 3 0.68 31 0.097
50 A 3 3 0.67 31 0.097
51 A 6 6 0.69 29 0.207
52 A 3 3 0.66 31 0.097
53 A 3 3 0.86 31 0.097
54 A 3 3 0.68 31 0.097
55 A 3 3 0.71 31 0.097
56 A 3 3 0.70 29 0.103
57 A 3 3 0.63 31 0.097
58 A 3 3 0.65 33 0.091
59 A 3 3 0.65 33 0.091
60 A 3 3 0.65 31 0.097
61 A 7 7 0.71 33 0.212
62 A 3 3 0.63 33 0.091
63 A 3 3 0.63 33 0.091
64 A 3 3 0.62 31 0.097
65 A 3 3 0.69 33 0.091
66 A 3 3 0.60 33 0.091
67 A 3 3 0.60 33 0.091
68 A 3 3 0.58 31 0.097
69 A 3 3 0.66 33 0.091
70 A 6 5 0.60 33 0.152
71 A 6 5 0.59 33 0.152
72 A 3 3 0.75 31 0.097
73 A 11 10 0.68 33 0.303
74 A 17 16 0.65 33 0.485
75 A 3 3 0.61 33 0.091
76 A 3 3 0.61 33 0.091
77 A 3 3 0.59 31 0.097
78 A 3 3 0.64 33 0.091
79 A 3 3 0.58 33 0.091
80 A 3 3 0.60 33 0.091
81 A 3 3 0.62 31 0.097
82 N/A 1 0 1.00 35 0.000
83 A 10 9 0.99 35 0.257
84 A 9 8 0.98 35 0.229
85 A 8 7 0.99 33 0.212
86 A 8 7 1.00 25 0.280
87 N/A 1 0 1.00 35 0.000
88 A 13 13 1.08 21 0.619
89 A 10 10 1.11 21 0.476
90 A 8 8 1.14 19 0.421
91 A 4 4 1.00 21 0.190
92 A 6 6 0.99 21 0.286
93 A 8 7 1.18 21 0.333
94 A 8 7 1.05 21 0.333
95 A 11 10 1.06 21 0.476
96 A 13 12 1.09 21 0.571
97 A 14 14 1.09 26 0.538
98 A 13 13 1.08 26 0.500
99 A 10 10 1.12 24 0.417
100 A 4 4 1.04 26 0.154
101 A 4 4 0.99 26 0.154
102 A 4 4 0.98 26 0.154
103 A 8 7 1.02 26 0.269
104 A 10 9 1.05 26 0.346
105 A 13 12 1.06 26 0.462
106 A 17 17 1.07 31 0.548
107 A 14 14 1.09 31 0.452
108 A 13 13 1.09 29 0.448
109 A 4 4 1.02 31 0.129
110 A 4 4 0.99 31 0.129
111 A 4 4 0.95 31 0.129
112 A 4 4 0.97 31 0.129
113 A 4 4 1.02 23 0.174
114 A 2 2 1.00 25 0.080
115 A 2 2 1.00 28 0.071
116 A 2 2 1.00 28 0.071
117 A 2 2 1.00 26 0.077
118 A 2 2 1.02 28 0.071
119 A 2 2 1.00 28 0.071
120 A 3 3 0.98 33 0.091
121 A 4 4 0.97 35 0.114
122 A 11 10 1.21 10 1.000
123 A 8 7 1.31 10 0.700
124 A 9 8 1.06 8 1.000
125 A 4 3 0.91 6 0.500
126 A 9 8 1.04 10 0.800
127 A 6 5 1.03 10 0.500
128 A 8 7 1.06 10 0.700
129 A 9 8 1.13 10 0.800
130 A 11 10 1.19 10 1.000
131 A 7 6 0.92 12 0.500
132 A 6 5 0.96 12 0.417
133 A 7 6 0.95 10 0.600
134 A 5 4 1.04 8 0.500
135 A 10 9 1.10 12 0.750
136 A 13 12 0.90 12 1.000
137 A 18 17 1.03 12 1.417
138 A 8 7 0.90 12 0.583
139 A 9 8 0.94 10 0.800
140 A 6 5 0.94 8 0.625
141 A 11 10 1.09 12 0.833
142 A 14 13 0.94 12 1.083
143 A 6 5 0.87 12 0.417
144 A 7 6 0.93 10 0.600
145 A 5 4 1.00 8 0.500
146 N/A 5 0 1.00 12 0.000
147 A 5 4 1.71 12 0.333
148 A 6 5 1.49 10 0.500
149 A 6 5 0.95 8 0.625
150 N/A 5 0 1.00 12 0.000
151 A 5 4 1.31 12 0.333
152 A 6 5 1.24 10 0.500
153 A 7 6 0.92 8 0.750
154 N/A 5 0 1.00 12 0.000
155 A 8 7 1.06 18 0.389
156 A 9 8 1.11 16 0.500
157 A 13 12 0.97 14 0.857
158 A 9 8 1.13 16 0.500
159 A 13 12 0.94 14 0.857
160 A 9 8 1.17 16 0.500
161 A 15 14 0.94 14 1.000
162 A 15 14 0.94 14 1.000
163 A 8 7 0.98 18 0.389
164 A 9 8 0.99 16 0.500
165 A 11 10 1.01 14 0.714
166 A 6 5 0.95 16 0.312
167 A 13 12 1.00 14 0.857
168 A 6 5 0.94 16 0.312
169 A 13 12 0.99 14 0.857
170 A 6 5 0.94 16 0.312
171 A 15 14 1.02 14 1.000
172 N/A 3 0 1.00 16 0.000
173 A 6 5 0.97 16 0.312
174 A 7 6 0.97 14 0.429
175 A 7 6 1.02 12 0.500
176 N/A 5 0 1.00 16 0.000
177 A 7 6 0.79 21 0.286
178 A 7 6 0.92 21 0.286
179 A 7 6 0.84 21 0.286
180 A 6 5 0.96 19 0.263
181 A 1 1 1.00 10 0.100
182 A 11 10 0.97 21 0.476
183 A 7 6 0.86 21 0.286
184 A 5 4 0.92 21 0.190
185 A 8 7 0.83 21 0.333
186 A 6 5 0.93 21 0.238
187 A 9 8 0.84 21 0.381
188 A 10 9 0.87 23 0.391
189 A 9 8 0.88 23 0.348
190 A 8 7 0.89 23 0.304
191 A 7 6 0.93 21 0.286
192 A 5 4 1.03 12 0.333
193 A 12 11 0.98 23 0.478
194 A 9 8 0.79 23 0.348
195 A 6 5 0.87 23 0.217
196 A 11 10 0.80 23 0.435
197 A 16 15 1.01 23 0.652
198 A 14 13 1.03 23 0.565
199 A 11 10 0.91 23 0.435
200 A 9 8 0.93 21 0.381
201 A 5 4 0.93 12 0.333
202 A 13 12 0.97 23 0.522
203 A 10 9 0.82 23 0.391
204 A 13 12 0.93 23 0.522
205 A 15 14 0.82 23 0.609
206 A 13 12 1.08 23 0.522
207 A 14 13 1.00 23 0.565
208 A 10 9 0.94 21 0.429
209 A 7 6 0.97 12 0.500
210 A 14 13 1.00 23 0.565
211 A 11 10 0.84 23 0.435
212 A 14 13 0.96 23 0.565
213 A 15 14 0.83 23 0.609
214 A 7 6 0.93 12 0.500
215 A 6 5 0.79 23 0.217
216 A 7 6 0.82 23 0.261
217 A 6 5 0.82 23 0.217
218 A 13 12 0.88 21 0.571
219 A 9 8 0.91 12 0.667
220 N/A 4 0 1.00 23 0.000
221 A 5 4 0.81 23 0.174
222 A 5 4 0.84 23 0.174
223 A 5 4 0.84 23 0.174
224 A 10 9 0.92 21 0.429
225 A 11 10 0.95 12 0.833
226 N/A 4 0 1.00 23 0.000
227 A 8 7 1.20 23 0.304
228 A 16 15 1.12 23 0.652
229 A 15 14 1.08 23 0.609
230 A 16 15 0.94 21 0.714
231 A 11 10 0.93 12 0.833
232 N/A 4 0 1.00 23 0.000
233 A 7 6 1.16 23 0.261
234 A 13 12 1.06 23 0.522
235 A 16 15 1.07 23 0.652
236 A 13 12 0.93 21 0.571
237 A 13 12 0.99 12 1.000
238 N/A 4 0 1.00 23 0.000
239 A 13 12 1.01 12 1.000
240 A 8 7 0.92 25 0.280
241 A 9 8 0.93 25 0.320
242 A 8 7 0.95 23 0.304
243 A 13 12 0.97 14 0.857
244 N/A 4 0 1.00 25 0.000
245 A 23 22 1.19 25 0.880
246 A 18 17 1.22 25 0.680
247 A 18 17 0.96 23 0.739
248 A 13 12 0.94 14 0.857
249 N/A 4 0 1.00 25 0.000
250 A 13 12 1.16 25 0.480
251 A 20 19 1.17 25 0.760
252 A 11 10 0.95 23 0.435
253 A 15 14 0.94 14 1.000
254 N/A 4 0 1.00 25 0.000
255 F 0 0 N/A 0.000 N/A
256 A 21 20 0.96 23 0.870
257 A 15 14 0.94 14 1.000
258 N/A 4 0 1.00 25 0.000
259 A 6 5 0.93 25 0.200
260 A 7 6 0.94 25 0.240
261 A 6 5 0.94 25 0.200
262 A 15 14 0.98 23 0.609
263 A 11 10 1.01 14 0.714
264 N/A 4 0 1.00 25 0.000
265 A 5 4 0.93 25 0.160
266 A 5 4 0.97 25 0.160
267 A 5 4 0.98 25 0.160
268 A 12 11 0.98 23 0.478
269 A 13 12 1.00 14 0.857
270 N/A 4 0 1.00 25 0.000
271 A 18 17 1.24 25 0.680
272 A 17 16 1.30 25 0.640
273 A 18 17 0.96 23 0.739
274 A 13 12 0.99 14 0.857
275 N/A 4 0 1.00 25 0.000
276 A 15 14 1.20 25 0.560
277 A 18 17 1.22 25 0.680
278 A 15 14 0.98 23 0.609
279 A 15 14 1.02 14 1.000
280 N/A 4 0 1.00 25 0.000
281 A 8 7 1.03 23 0.304
282 A 7 6 1.04 23 0.261
283 A 7 6 1.04 23 0.261
284 A 6 5 1.03 23 0.217
285 A 6 5 0.98 23 0.217
286 A 5 4 0.97 23 0.174
287 A 7 6 0.98 23 0.261
288 A 6 5 1.02 23 0.217
289 A 8 7 1.01 23 0.304
290 A 7 6 1.04 23 0.261
291 A 4 3 1.01 25 0.120
292 A 4 3 1.01 25 0.120
293 A 4 3 1.01 25 0.120
294 A 4 3 1.01 25 0.120
295 A 4 3 0.99 25 0.120
296 A 4 3 0.99 25 0.120
297 A 4 3 0.98 25 0.120
298 A 4 3 1.01 25 0.120
299 A 4 3 1.01 25 0.120
300 N/A 4 0 1.00 25 0.000
301 N/A 4 0 1.00 25 0.000
302 N/A 4 0 1.00 25 0.000
303 N/A 4 0 1.00 25 0.000
304 N/A 4 0 1.00 25 0.000
305 N/A 4 0 1.00 25 0.000
306 N/A 4 0 1.00 25 0.000
307 N/A 4 0 1.00 25 0.000
308 N/A 4 0 1.00 23 0.000
309 N/A 4 0 1.00 23 0.000
310 A 4 3 0.96 23 0.130
311 A 4 3 0.98 21 0.143
312 N/A 3 0 1.00 23 0.000
313 A 8 7 0.93 33 0.212
314 A 7 6 0.95 33 0.182
315 A 5 4 0.92 31 0.129
316 A 6 5 0.94 33 0.152
317 A 8 7 0.95 33 0.212
318 A 6 5 0.96 33 0.152
319 A 11 10 0.90 33 0.303
320 A 16 15 1.28 33 0.455
321 A 12 11 1.20 33 0.333
322 A 8 7 1.09 31 0.226
323 A 6 5 0.89 33 0.152
324 A 6 5 1.00 33 0.152
325 A 11 10 1.27 33 0.303
326 A 17 16 1.12 33 0.485
327 A 3 2 1.00 33 0.061
328 A 3 2 1.00 33 0.061
329 A 3 2 1.00 31 0.065
330 A 3 2 1.00 33 0.061
331 A 3 2 1.00 33 0.061
332 A 3 2 1.00 33 0.061
333 A 10 9 1.03 33 0.273
334 A 9 8 1.00 33 0.242
335 A 4 3 0.96 31 0.097
336 N/A 3 0 1.00 33 0.000
337 N/A 4 0 1.00 33 0.000
338 A 3 2 1.00 23 0.087
339 A 3 2 1.00 36 0.056
340 A 6 5 1.02 14 0.357
341 A 7 6 1.15 14 0.429
342 A 6 5 1.05 14 0.357
343 A 6 5 1.09 14 0.357
344 A 3 2 0.89 12 0.167
345 A 2 2 1.00 14 0.143
346 A 6 5 1.00 14 0.357
347 A 3 3 1.00 14 0.214
348 A 7 6 1.00 14 0.429
349 A 4 4 1.06 14 0.286
350 A 8 7 1.04 14 0.500
351 A 5 5 1.09 14 0.357
352 A 5 5 1.14 14 0.357
353 A 7 7 1.08 14 0.500
354 A 4 4 1.08 14 0.286
355 A 1 1 1.00 10 0.100
356 A 3 3 1.00 14 0.214
357 A 7 7 1.02 14 0.500
358 A 4 4 1.07 14 0.286
359 A 8 8 1.06 14 0.571
360 A 9 8 1.15 10 0.800
361 A 9 8 1.17 10 0.800
362 A 8 7 1.13 8 0.875
363 A 7 6 1.05 6 1.000
364 A 9 8 1.23 10 0.800
365 A 3 3 1.00 10 0.300
366 A 4 4 1.10 10 0.400
367 A 5 5 1.15 10 0.500
368 A 6 6 1.17 10 0.600
369 A 9 8 1.04 14 0.571
370 A 5 5 1.06 14 0.357
371 A 8 7 1.00 14 0.500
372 A 4 4 1.00 12 0.333
373 A 1 1 1.00 10 0.100
374 A 2 2 1.00 14 0.143
375 A 3 2 1.00 14 0.143
376 A 7 6 1.09 14 0.429
377 A 7 6 1.05 14 0.429
378 A 8 7 1.15 14 0.500
379 A 3 3 1.00 14 0.214
380 A 3 3 1.00 14 0.214
381 A 3 3 1.00 12 0.250
382 A 1 1 1.00 10 0.100
383 A 2 2 1.00 14 0.143
384 A 3 3 1.00 14 0.214
385 A 3 3 1.01 14 0.214
386 A 9 8 1.19 16 0.500
387 A 9 8 1.18 16 0.500
388 A 3 2 0.91 14 0.143
389 A 2 2 1.00 16 0.125
390 A 6 5 1.00 16 0.312
391 A 7 6 0.99 16 0.375
392 A 10 9 1.05 16 0.562
393 A 10 10 0.86 16 0.625
394 A 7 7 0.81 16 0.438
395 A 1 1 1.00 12 0.083
396 A 4 4 1.00 16 0.250
397 A 9 9 0.85 16 0.562
398 A 11 11 0.85 16 0.688
399 A 5 4 0.74 12 0.333
400 A 5 4 0.79 14 0.286
401 A 3 3 1.00 14 0.214
402 A 2 2 0.97 14 0.143
403 A 2 2 1.00 14 0.143
404 A 1 1 1.00 12 0.083
405 A 1 1 1.00 14 0.071
406 A 1 1 1.00 14 0.071
407 A 2 2 1.04 14 0.143
408 A 3 3 1.00 16 0.188
409 A 2 2 0.98 16 0.125
410 A 2 2 1.00 16 0.125
411 A 1 1 1.00 14 0.071
412 A 1 1 1.00 16 0.062
413 A 1 1 1.00 16 0.062
414 A 2 2 1.03 16 0.125
415 A 2 2 1.00 8 0.250
416 A 2 2 1.00 10 0.200
417 A 2 2 1.00 16 0.125
418 A 2 2 1.02 16 0.125
419 A 1 1 1.00 16 0.062
420 A 1 1 1.00 16 0.062
421 A 1 1 1.00 16 0.062
422 A 2 2 1.02 16 0.125
423 A 2 2 1.00 16 0.125
424 A 2 2 1.00 18 0.111
425 A 2 2 1.02 18 0.111
426 A 1 1 1.00 18 0.056
427 A 1 1 1.00 18 0.056
428 A 1 1 1.00 18 0.056
429 A 2 2 1.01 18 0.111
430 A 2 2 1.00 18 0.111
431 N/A 1 0 1.00 40 0.000
432 A 12 11 1.03 40 0.275
433 A 11 10 1.03 40 0.250
434 A 10 9 1.02 38 0.237
435 N/A 1 0 1.00 40 0.000
436 N/A 1 0 1.00 40 0.000
437 A 4 3 1.00 8 0.375
438 A 10 9 1.01 10 0.900
439 A 5 4 0.90 10 0.400
440 A 5 4 0.91 10 0.400
441 A 6 5 1.02 8 0.625
442 A 3 2 1.05 6 0.333
443 A 5 4 1.00 10 0.400
444 A 5 4 1.00 10 0.400
445 A 5 4 0.92 12 0.333
446 A 5 4 0.94 12 0.333
447 A 5 4 0.96 10 0.400
448 A 4 3 0.97 8 0.375
449 N/A 4 0 1.00 12 0.000
450 N/A 4 0 1.00 12 0.000
451 A 7 6 0.90 12 0.500
452 A 6 5 0.90 12 0.417
453 A 7 6 0.93 10 0.600
454 A 3 2 0.96 8 0.250
455 N/A 6 0 1.00 12 0.000
456 N/A 5 0 1.00 12 0.000
457 A 7 6 0.92 14 0.429
458 A 6 5 0.92 14 0.357
459 A 7 6 0.94 12 0.500
460 A 4 3 0.97 10 0.300
461 N/A 6 0 1.00 14 0.000
462 N/A 5 0 1.00 14 0.000
463 A 8 7 1.03 21 0.333
464 A 7 6 1.02 21 0.286
465 A 6 5 0.98 21 0.238
466 A 5 4 1.00 21 0.190
467 A 5 4 1.00 21 0.190
468 A 6 5 0.99 21 0.238
469 A 7 6 1.02 10 0.600
470 F 0 0 N/A 0.000 N/A
471 A 3 2 1.00 26 0.077
472 A 3 2 1.00 26 0.077
473 A 1 1 1.00 28 0.036
474 F 0 0 N/A 0.000 N/A

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