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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 [176] had the largest ratio of [1.11111000000000004]

# 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 6 5 0.98 23 0.217
2 A 6 6 1.10 23 0.261
3 A 6 5 1.00 23 0.217
4 A 4 4 1.03 21 0.190
5 A 6 5 1.03 20 0.250
6 A 12 11 1.12 23 0.478
7 A 8 7 1.03 23 0.304
8 A 12 11 0.99 23 0.478
9 A 7 6 0.99 23 0.261
10 A 6 5 0.94 25 0.200
11 A 9 9 1.04 25 0.360
12 A 6 5 0.95 25 0.200
13 A 5 5 0.98 23 0.217
14 A 6 5 0.97 22 0.227
15 A 17 16 1.23 25 0.640
16 A 8 7 0.94 25 0.280
17 A 17 16 1.16 25 0.640
18 A 11 10 1.07 25 0.400
19 A 6 5 0.93 25 0.200
20 A 8 8 0.97 25 0.320
21 A 6 5 0.94 25 0.200
22 A 6 6 0.97 23 0.261
23 A 6 5 0.95 22 0.227
24 A 22 21 1.43 25 0.840
25 A 6 5 0.91 25 0.200
26 A 22 21 1.30 25 0.840
27 A 10 9 0.90 25 0.360
28 A 13 12 1.08 25 0.480
29 A 11 10 1.01 25 0.400
30 A 9 8 0.92 25 0.320
31 A 7 6 0.95 23 0.261
32 A 6 5 0.87 22 0.227
33 A 7 6 0.94 25 0.240
34 A 11 10 0.95 25 0.400
35 A 10 9 0.93 25 0.360
36 A 16 15 1.02 25 0.600
37 A 13 12 1.06 25 0.480
38 A 11 10 0.99 25 0.400
39 A 9 8 0.92 25 0.320
40 A 2 2 1.00 23 0.087
41 A 9 8 0.92 22 0.364
42 A 10 9 0.98 25 0.360
43 A 14 13 1.16 25 0.520
44 A 13 12 1.32 25 0.480
45 A 20 19 1.30 25 0.760
46 A 13 12 1.08 25 0.480
47 A 4 4 0.99 25 0.160
48 A 11 10 0.93 25 0.400
49 A 3 3 0.98 23 0.130
50 A 11 10 0.93 22 0.455
51 A 13 12 1.10 25 0.480
52 A 17 16 1.18 25 0.640
53 A 17 16 1.26 25 0.640
54 A 24 23 1.34 25 0.920
55 A 7 7 0.82 27 0.259
56 A 5 5 0.87 27 0.185
57 A 3 3 1.00 24 0.125
58 A 3 3 1.00 27 0.111
59 A 3 3 0.76 27 0.111
60 A 4 4 0.70 27 0.148
61 A 4 4 0.66 27 0.148
62 A 3 3 0.67 27 0.111
63 A 3 3 0.70 27 0.111
64 A 2 2 0.75 25 0.080
65 A 8 7 0.72 27 0.259
66 A 8 7 0.72 27 0.259
67 A 10 9 0.69 27 0.333
68 A 10 10 0.90 27 0.370
69 A 8 8 0.96 27 0.296
70 A 6 6 1.10 24 0.250
71 A 6 6 1.06 27 0.222
72 A 6 6 1.04 27 0.222
73 A 5 4 0.61 27 0.148
74 A 6 5 0.60 27 0.185
75 A 6 5 0.61 27 0.185
76 A 6 5 0.59 27 0.185
77 A 4 4 0.60 27 0.148
78 A 4 4 0.60 27 0.148
79 A 4 4 0.61 27 0.148
80 A 3 3 0.61 25 0.120
81 A 10 9 0.80 27 0.333
82 A 11 10 0.79 27 0.370
83 A 11 10 0.82 27 0.370
84 A 15 14 0.95 27 0.519
85 A 13 12 1.01 27 0.444
86 A 8 8 1.06 24 0.333
87 A 11 10 0.98 27 0.370
88 A 11 10 1.07 27 0.370
89 A 11 10 1.07 27 0.370
90 A 5 4 0.53 27 0.148
91 A 7 6 0.60 27 0.222
92 A 6 5 0.55 27 0.185
93 A 4 4 0.55 27 0.148
94 A 4 4 0.54 27 0.148
95 A 3 3 0.51 25 0.120
96 A 13 12 0.86 27 0.444
97 A 13 12 0.84 27 0.444
98 A 14 13 0.85 27 0.481
99 A 5 5 1.09 22 0.227
100 A 4 4 1.04 22 0.182
101 A 3 3 1.00 22 0.136
102 A 2 2 1.00 20 0.100
103 A 1 1 1.00 19 0.053
104 A 6 5 1.00 22 0.227
105 A 2 2 1.00 22 0.091
106 A 8 7 0.95 22 0.318
107 A 6 6 1.05 27 0.222
108 A 5 5 1.04 27 0.185
109 A 4 4 1.02 27 0.148
110 A 3 3 1.00 27 0.111
111 A 2 2 1.00 25 0.080
112 A 1 1 1.00 24 0.042
113 A 6 5 0.61 27 0.185
114 A 2 2 1.00 27 0.074
115 A 8 7 0.72 27 0.259
116 A 4 4 0.99 27 0.148
117 A 4 4 0.71 27 0.148
118 A 8 7 1.08 27 0.259
119 A 4 4 0.77 27 0.148
120 A 3 3 1.00 27 0.111
121 A 2 2 1.00 25 0.080
122 A 2 2 1.00 24 0.083
123 A 8 7 0.71 27 0.259
124 A 7 6 0.80 27 0.222
125 A 11 10 0.79 27 0.370
126 A 6 5 0.74 27 0.185
127 A 12 11 1.22 27 0.407
128 A 6 6 0.78 27 0.222
129 A 8 7 1.19 27 0.259
130 A 4 4 0.89 27 0.148
131 A 5 4 0.83 27 0.148
132 A 3 3 0.87 25 0.120
133 A 4 4 1.03 24 0.167
134 A 11 10 0.88 27 0.370
135 A 6 5 0.75 27 0.185
136 A 15 14 0.96 27 0.519
137 A 6 5 0.72 27 0.185
138 A 1 1 1.00 30 0.033
139 A 1 1 1.00 31 0.032
140 A 9 9 1.03 25 0.360
141 A 7 7 1.00 25 0.280
142 A 4 4 0.98 23 0.174
143 N/A 1 0 1.00 25 0.000
144 N/A 4 0 1.00 25 0.000
145 N/A 6 0 1.00 25 0.000
146 A 9 9 0.71 27 0.333
147 A 6 6 0.82 27 0.222
148 A 3 3 0.89 27 0.111
149 A 1 1 1.00 27 0.037
150 A 3 3 1.00 27 0.111
151 A 5 5 0.96 27 0.185
152 A 1 1 1.00 22 0.045
153 A 11 11 1.14 25 0.440
154 A 9 9 1.65 25 0.360
155 A 9 9 1.14 25 0.360
156 A 7 7 1.04 23 0.304
157 A 5 5 1.09 22 0.227
158 A 14 13 1.10 25 0.520
159 A 12 11 1.17 25 0.440
160 A 14 13 1.01 25 0.520
161 A 10 9 1.28 25 0.360
162 A 17 17 1.31 27 0.630
163 A 13 13 1.97 27 0.481
164 A 15 15 1.25 27 0.556
165 A 9 9 0.96 25 0.360
166 A 8 8 1.11 24 0.333
167 A 22 21 1.25 27 0.778
168 A 17 16 1.26 27 0.593
169 A 22 21 1.20 27 0.778
170 A 16 15 1.36 27 0.556
171 A 22 22 1.49 27 0.815
172 B 18 17 2.39 27 0.630
173 A 20 20 1.37 27 0.741
174 A 11 11 0.94 25 0.440
175 A 9 9 1.17 24 0.375
176 A 31 30 1.51 27 1.111
177 A 22 21 1.41 27 0.778
178 F 0 0 N/A 0.000 N/A
179 A 20 19 1.58 27 0.704
180 A 13 12 1.06 27 0.444
181 A 13 12 0.99 27 0.444
182 A 11 10 0.91 27 0.370
183 A 8 7 0.97 25 0.280
184 A 7 6 0.87 24 0.250
185 A 8 7 0.96 27 0.259
186 A 14 13 0.91 27 0.481
187 A 12 11 0.90 27 0.407
188 A 16 15 1.05 27 0.556
189 A 16 15 1.04 27 0.556
190 A 13 12 1.00 27 0.444
191 A 11 10 0.94 27 0.370
192 A 3 3 0.97 25 0.120
193 A 11 10 0.93 24 0.417
194 A 12 11 0.98 27 0.407
195 A 19 18 1.04 27 0.667
196 A 18 17 1.24 27 0.630
197 A 22 21 1.19 27 0.778
198 A 16 15 1.05 27 0.556
199 A 9 8 1.09 27 0.296
200 A 13 12 0.96 27 0.444
201 A 5 5 0.93 25 0.200
202 A 13 12 0.96 24 0.500
203 A 17 16 1.14 27 0.593
204 A 24 23 1.17 27 0.852
205 A 23 22 1.24 27 0.815
206 A 28 27 1.42 27 1.000
207 A 13 12 1.13 29 0.414
208 A 10 10 1.00 29 0.345
209 A 7 6 0.82 27 0.222
210 A 5 5 0.88 26 0.192
211 A 9 8 0.62 29 0.276
212 A 11 10 0.80 29 0.345
213 A 12 11 0.62 29 0.379
214 A 13 12 0.66 29 0.414
215 A 19 18 1.29 29 0.621
216 A 17 17 1.21 29 0.586
217 A 7 6 0.73 27 0.222
218 A 10 10 1.12 26 0.385
219 A 15 14 0.71 29 0.483
220 A 18 17 0.87 29 0.586
221 A 16 15 0.64 29 0.517
222 A 23 22 0.98 29 0.759
223 A 25 24 1.43 29 0.828
224 A 27 27 1.37 29 0.931
225 A 7 6 0.66 27 0.222
226 A 12 12 1.27 26 0.462
227 A 21 20 0.85 29 0.690
228 A 27 26 1.13 29 0.897
229 A 23 22 0.77 29 0.759
230 F 0 0 N/A 0.000 N/A
231 A 13 12 1.22 29 0.414
232 A 10 10 1.07 29 0.345
233 A 8 7 1.09 29 0.241
234 A 5 5 0.85 29 0.172
235 A 2 2 0.95 27 0.074
236 A 1 1 1.00 26 0.038
237 A 7 6 0.56 29 0.207
238 A 10 9 0.75 29 0.310
239 A 12 11 0.62 29 0.379
240 A 13 12 0.82 29 0.414
241 A 19 18 1.15 29 0.621
242 A 15 14 0.95 29 0.483
243 A 11 10 0.90 29 0.345
244 A 9 8 0.78 29 0.276
245 A 7 6 0.66 27 0.222
246 A 8 7 0.72 26 0.269
247 A 13 12 0.60 29 0.414
248 A 15 14 0.83 29 0.483
249 A 23 22 0.72 29 0.759
250 A 17 16 0.98 29 0.552
251 A 15 14 1.26 29 0.483
252 A 12 11 1.01 29 0.379
253 A 15 14 1.05 29 0.483
254 A 11 10 0.66 29 0.345
255 A 9 8 0.67 27 0.296
256 A 11 10 0.87 26 0.385
257 A 21 20 0.82 29 0.690
258 A 20 19 1.01 29 0.655
259 F 0 0 N/A 0.000 N/A
260 A 23 22 1.34 29 0.759
261 A 10 10 1.43 24 0.417
262 A 9 8 1.26 24 0.333
263 A 5 5 1.09 24 0.208
264 A 3 3 1.02 22 0.136
265 A 1 1 1.00 21 0.048
266 A 7 6 1.07 24 0.250
267 A 10 9 1.16 24 0.375
268 A 12 11 1.00 24 0.458
269 A 12 12 0.79 27 0.444
270 A 9 9 0.86 27 0.333
271 A 5 5 0.95 25 0.200
272 N/A 1 0 1.00 27 0.000
273 N/A 6 0 1.00 27 0.000
274 N/A 8 0 1.00 27 0.000
275 N/A 15 0 1.00 29 0.000
276 N/A 8 0 1.00 29 0.000
277 N/A 4 0 1.00 29 0.000
278 N/A 1 0 1.00 29 0.000
279 N/A 1 0 1.00 29 0.000
280 N/A 1 0 1.00 29 0.000
281 N/A 1 0 1.00 24 0.000
282 A 9 9 1.45 24 0.375
283 A 10 10 1.32 24 0.417
284 A 6 6 1.08 24 0.250
285 A 4 4 1.07 22 0.182
286 A 1 1 1.00 21 0.048
287 A 8 7 1.09 24 0.292
288 A 11 10 1.18 24 0.417
289 A 12 11 0.97 24 0.458
290 A 4 3 0.83 28 0.107
291 A 5 4 0.84 28 0.143
292 A 4 3 0.87 28 0.107
293 A 5 4 0.86 26 0.154
294 A 5 4 0.87 25 0.160
295 N/A 2 0 1.00 28 0.000
296 N/A 2 0 1.00 28 0.000
297 N/A 1 0 1.00 28 0.000
298 A 5 4 0.83 28 0.143
299 A 4 3 0.83 28 0.107
300 A 5 4 0.84 26 0.154
301 A 5 4 0.84 25 0.160
302 N/A 2 0 1.00 28 0.000
303 N/A 2 0 1.00 28 0.000
304 N/A 1 0 1.00 28 0.000
305 A 5 4 0.83 28 0.143
306 A 4 3 0.82 28 0.107
307 A 5 4 0.83 26 0.154
308 A 5 4 0.83 25 0.160
309 N/A 2 0 1.00 28 0.000
310 N/A 2 0 1.00 28 0.000
311 N/A 1 0 1.00 28 0.000
312 A 5 4 0.88 24 0.167
313 A 5 4 0.93 24 0.167
314 A 5 4 0.93 24 0.167
315 A 5 4 0.93 24 0.167
316 A 4 3 1.00 22 0.136
317 A 1 1 1.00 21 0.048
318 N/A 1 0 1.00 24 0.000
319 N/A 1 0 1.00 24 0.000
320 A 6 5 0.84 28 0.179
321 A 5 4 0.84 28 0.143
322 A 6 5 0.86 28 0.179
323 A 5 4 0.87 28 0.143
324 A 9 8 0.91 26 0.308
325 A 1 1 1.00 25 0.040
326 N/A 1 0 1.00 28 0.000
327 N/A 1 0 1.00 28 0.000
328 N/A 1 0 1.00 28 0.000
329 N/A 1 0 1.00 26 0.000
330 N/A 1 0 1.00 25 0.000
331 N/A 1 0 1.00 28 0.000
332 N/A 1 0 1.00 28 0.000
333 N/A 1 0 1.00 28 0.000
334 N/A 1 0 1.00 26 0.000
335 N/A 1 0 1.00 25 0.000
336 N/A 1 0 1.00 28 0.000
337 N/A 1 0 1.00 28 0.000
338 N/A 1 0 1.00 28 0.000
339 N/A 1 0 1.00 28 0.000
340 N/A 1 0 1.00 28 0.000
341 N/A 1 0 1.00 28 0.000
342 N/A 1 0 1.00 28 0.000
343 N/A 1 0 1.00 28 0.000
344 N/A 1 0 1.00 24 0.000
345 N/A 1 0 1.00 28 0.000
346 N/A 1 0 1.00 28 0.000
347 N/A 1 0 1.00 28 0.000
348 N/A 2 0 1.00 28 0.000
349 N/A 1 0 1.00 28 0.000
350 N/A 1 0 1.00 28 0.000
351 A 5 4 1.36 28 0.143
352 B 13 12 2.06 28 0.429
353 A 12 11 1.22 26 0.423
354 A 12 11 0.97 25 0.440
355 N/A 10 0 1.00 28 0.000
356 N/A 2 0 1.00 28 0.000
357 N/A 1 0 1.00 28 0.000
358 A 5 4 1.42 28 0.143
359 A 6 5 1.15 28 0.179
360 A 9 8 1.36 26 0.308
361 A 6 5 0.93 25 0.200
362 N/A 7 0 1.00 28 0.000
363 N/A 2 0 1.00 28 0.000
364 N/A 1 0 1.00 28 0.000
365 A 5 4 1.78 28 0.143
366 A 6 5 1.43 28 0.179
367 A 9 8 1.42 26 0.308
368 A 6 5 0.88 25 0.200
369 N/A 7 0 1.00 28 0.000
370 N/A 2 0 1.00 28 0.000
371 N/A 1 0 1.00 28 0.000
372 A 5 4 0.87 28 0.143
373 A 6 5 0.93 28 0.179
374 A 5 4 0.89 28 0.143
375 A 12 11 0.95 28 0.393
376 A 9 8 0.94 26 0.308
377 A 1 1 1.00 25 0.040
378 N/A 2 0 1.00 28 0.000
379 N/A 2 0 1.00 28 0.000
380 N/A 1 0 1.00 28 0.000
381 N/A 2 0 1.00 28 0.000
382 N/A 1 0 1.00 26 0.000
383 N/A 2 0 1.00 25 0.000
384 N/A 1 0 1.00 28 0.000
385 N/A 1 0 1.00 28 0.000
386 A 1 1 1.00 33 0.030
387 B 5 4 2.02 27 0.148
388 A 6 5 0.99 27 0.185
389 A 9 8 1.18 25 0.320
390 A 6 5 1.01 24 0.208
391 N/A 8 0 1.00 27 0.000
392 N/A 4 0 1.00 27 0.000
393 A 5 4 1.25 29 0.138
394 A 6 5 1.57 29 0.172
395 A 9 8 1.62 27 0.296
396 A 6 5 0.94 26 0.192
397 N/A 8 0 1.00 29 0.000
398 N/A 4 0 1.00 29 0.000
399 A 1 1 1.00 38 0.026
400 A 5 4 1.00 19 0.211
401 A 4 3 0.76 29 0.103
402 A 5 4 0.77 27 0.148
403 A 5 4 0.76 26 0.154
404 N/A 2 0 1.00 29 0.000
405 N/A 2 0 1.00 29 0.000
406 A 4 3 0.72 29 0.103
407 A 5 4 0.74 27 0.148
408 A 5 4 0.73 26 0.154
409 N/A 2 0 1.00 29 0.000
410 N/A 2 0 1.00 29 0.000
411 A 4 3 0.70 29 0.103
412 A 5 4 0.71 27 0.148
413 A 5 4 0.71 26 0.154
414 N/A 2 0 1.00 29 0.000
415 N/A 2 0 1.00 29 0.000
416 N/A 1 0 1.00 24 0.000
417 A 5 4 0.95 24 0.167
418 A 5 4 0.95 24 0.167
419 A 5 4 0.97 22 0.182
420 A 1 1 1.00 21 0.048
421 N/A 1 0 1.00 24 0.000
422 N/A 1 0 1.00 24 0.000
423 A 6 5 1.01 19 0.263
424 A 6 6 0.97 19 0.316
425 A 6 5 1.02 19 0.263
426 A 5 5 1.13 17 0.294
427 A 6 5 1.04 16 0.312
428 A 4 4 1.08 19 0.211
429 A 7 6 1.08 19 0.316
430 A 4 4 1.07 19 0.211
431 A 7 6 0.99 19 0.316
432 A 6 5 1.00 21 0.238
433 A 8 8 0.93 21 0.381
434 A 6 5 1.01 21 0.238
435 A 7 7 1.16 19 0.368
436 A 6 5 1.01 18 0.278
437 A 4 4 1.01 21 0.190
438 A 8 7 0.90 21 0.333
439 A 4 4 1.05 21 0.190
440 A 9 8 1.13 21 0.381
441 A 6 5 1.00 21 0.238
442 A 12 12 1.20 21 0.571
443 A 6 5 1.00 21 0.238
444 A 9 9 1.15 19 0.474
445 A 6 5 1.00 18 0.278
446 A 4 4 1.00 21 0.190
447 A 6 5 1.00 21 0.238
448 A 4 4 1.02 21 0.190
449 A 10 9 0.92 21 0.429
450 A 2 2 1.00 21 0.095
451 A 2 2 1.00 21 0.095
452 A 2 2 1.00 21 0.095
453 A 2 2 1.00 19 0.105
454 A 2 2 1.00 18 0.111
455 A 2 2 1.00 21 0.095
456 A 2 2 1.00 21 0.095
457 A 2 2 1.00 21 0.095
458 A 2 2 1.00 21 0.095
459 A 2 2 1.00 21 0.095
460 A 4 3 0.97 19 0.158
461 A 2 2 1.00 21 0.095
462 A 2 2 1.00 21 0.095
463 A 2 2 1.00 21 0.095
464 A 2 2 1.00 21 0.095
465 A 2 2 1.00 18 0.111
466 A 2 2 1.00 21 0.095
467 A 2 2 1.00 21 0.095
468 A 8 7 1.16 21 0.333
469 A 5 4 1.03 19 0.211
470 A 2 2 1.00 21 0.095
471 A 2 2 1.00 21 0.095
472 A 2 2 1.00 21 0.095
473 A 2 2 1.00 21 0.095
474 A 2 2 1.00 18 0.111
475 A 7 6 1.17 15 0.400
476 A 2 2 1.00 15 0.133
477 A 8 8 1.02 23 0.348
478 A 6 6 1.01 23 0.261
479 A 4 4 1.06 21 0.190
480 N/A 1 0 1.00 23 0.000
481 N/A 1 0 1.00 23 0.000
482 A 11 11 0.80 35 0.314
483 A 8 7 0.68 33 0.212
484 A 6 6 0.66 32 0.188
485 A 10 9 0.48 35 0.257
486 A 12 11 0.62 35 0.314
487 A 18 18 0.90 35 0.514
488 A 8 7 0.57 33 0.212
489 A 11 11 0.77 32 0.344
490 A 16 15 0.50 35 0.429
491 A 19 18 0.63 35 0.514
492 A 6 6 0.60 35 0.171
493 A 3 3 0.75 33 0.091
494 A 2 2 1.00 32 0.062
495 A 8 7 0.52 35 0.200
496 A 11 10 0.66 35 0.286
497 A 10 9 0.57 35 0.257
498 A 8 7 0.59 33 0.212
499 A 9 8 0.61 32 0.250
500 A 14 13 0.46 35 0.371
501 A 16 15 0.62 35 0.429

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