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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 [54] had the largest ratio of [1.08000000000000007]

# 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 1.08 23 0.348
2 A 7 7 1.09 23 0.304
3 A 6 6 1.05 23 0.261
4 A 4 4 1.03 21 0.190
5 A 4 4 1.03 20 0.200
6 C 12 11 1.20 23 0.478
7 A 7 6 0.97 23 0.261
8 C 13 12 1.04 23 0.522
9 A 6 5 1.03 23 0.217
10 A 7 6 0.97 25 0.240
11 A 11 10 1.16 25 0.400
12 A 7 6 1.02 25 0.240
13 A 5 5 0.98 23 0.217
14 A 7 6 1.08 22 0.273
15 C 17 16 1.31 25 0.640
16 A 8 7 1.04 25 0.280
17 C 18 17 1.24 25 0.680
18 A 12 11 1.15 25 0.440
19 A 7 6 0.94 25 0.240
20 A 10 10 0.97 25 0.400
21 A 7 6 0.97 25 0.240
22 A 6 6 0.97 23 0.261
23 A 7 6 1.02 22 0.273
24 C 22 21 1.51 25 0.840
25 A 7 6 0.93 25 0.240
26 C 23 22 1.39 25 0.880
27 A 10 9 0.94 25 0.360
28 C 14 13 1.18 25 0.520
29 C 13 12 1.04 25 0.480
30 C 10 9 1.00 25 0.360
31 C 9 8 1.01 23 0.348
32 C 7 6 0.98 22 0.273
33 C 8 7 1.07 25 0.280
34 C 11 10 1.04 25 0.400
35 C 11 10 0.99 25 0.400
36 C 16 15 1.13 25 0.600
37 C 14 13 1.12 25 0.520
38 C 15 14 1.19 25 0.560
39 C 10 9 0.98 25 0.360
40 A 2 2 1.00 23 0.087
41 C 10 9 0.98 22 0.409
42 C 11 10 1.04 25 0.400
43 C 15 14 1.24 25 0.560
44 C 15 14 1.45 25 0.560
45 C 22 21 1.41 25 0.840
46 C 15 14 1.32 25 0.560
47 A 7 7 1.23 25 0.280
48 C 12 11 0.97 25 0.440
49 A 3 3 0.98 23 0.130
50 C 12 11 0.97 22 0.500
51 C 14 13 1.17 25 0.520
52 C 19 18 1.24 25 0.720
53 C 19 18 1.13 25 0.720
54 C 28 27 1.43 25 1.080
55 A 7 7 0.83 27 0.259
56 A 5 5 0.88 27 0.185
57 A 3 3 1.00 24 0.125
58 A 3 3 1.00 27 0.111
59 A 5 5 0.74 27 0.185
60 A 4 4 0.67 27 0.148
61 A 4 4 0.64 27 0.148
62 A 3 3 0.64 27 0.111
63 A 3 3 0.68 27 0.111
64 A 4 4 0.74 25 0.160
65 A 8 7 0.70 27 0.259
66 A 8 7 0.70 27 0.259
67 A 10 9 0.68 27 0.333
68 A 12 12 0.90 27 0.444
69 A 10 10 0.96 27 0.370
70 A 8 8 1.10 24 0.333
71 A 8 8 1.06 27 0.296
72 A 8 8 1.03 27 0.296
73 A 6 5 0.59 27 0.185
74 A 6 5 0.58 27 0.185
75 A 6 5 0.58 27 0.185
76 A 6 5 0.56 27 0.185
77 A 4 4 0.57 27 0.148
78 A 4 4 0.58 27 0.148
79 A 4 4 0.59 27 0.148
80 A 4 4 0.59 25 0.160
81 A 12 11 0.79 27 0.407
82 A 13 12 0.77 27 0.444
83 A 13 12 0.81 27 0.444
84 A 18 17 0.95 27 0.630
85 A 16 15 1.01 27 0.556
86 A 11 11 1.10 24 0.458
87 A 14 13 0.97 27 0.481
88 A 14 13 1.06 27 0.481
89 A 14 13 1.07 27 0.481
90 A 7 6 0.51 27 0.222
91 A 7 6 0.57 27 0.222
92 A 6 5 0.53 27 0.185
93 A 4 4 0.53 27 0.148
94 A 4 4 0.52 27 0.148
95 A 4 4 0.51 27 0.148
96 A 5 5 0.50 25 0.200
97 A 16 15 0.86 27 0.556
98 A 16 15 0.83 27 0.556
99 A 17 16 0.84 27 0.593
100 A 5 5 1.00 27 0.185
101 A 4 4 0.99 27 0.148
102 A 3 3 0.96 27 0.111
103 A 2 2 0.97 25 0.080
104 A 1 1 0.95 24 0.042
105 A 6 5 0.54 27 0.185
106 A 2 2 0.97 27 0.074
107 A 8 7 0.67 27 0.259
108 A 4 4 0.96 27 0.148
109 A 4 4 0.70 27 0.148
110 A 10 9 1.08 27 0.333
111 A 4 4 0.76 27 0.148
112 A 5 5 1.00 27 0.185
113 A 4 4 1.00 25 0.160
114 A 2 2 1.00 24 0.083
115 A 10 9 0.69 27 0.333
116 A 7 6 0.78 27 0.222
117 A 15 14 0.77 27 0.519
118 A 6 5 0.72 27 0.185
119 A 6 6 0.75 27 0.222
120 A 11 10 1.18 27 0.370
121 A 4 4 0.87 27 0.148
122 A 6 5 0.81 27 0.185
123 A 4 4 0.84 25 0.160
124 A 5 5 1.10 24 0.208
125 A 14 13 0.87 27 0.481
126 A 6 5 0.73 27 0.185
127 A 19 18 0.94 27 0.667
128 A 6 5 0.70 27 0.185
129 A 5 5 1.06 22 0.227
130 A 4 4 1.04 22 0.182
131 A 3 3 1.00 22 0.136
132 A 2 2 1.02 20 0.100
133 A 1 1 1.00 19 0.053
134 A 6 5 0.64 22 0.227
135 A 2 2 1.02 22 0.091
136 A 8 7 0.74 22 0.318
137 A 4 4 0.99 22 0.182
138 A 1 1 1.00 30 0.033
139 A 1 1 1.00 31 0.032
140 A 9 9 1.10 27 0.333
141 A 8 8 1.12 27 0.296
142 A 6 6 1.14 25 0.240
143 N/A 1 0 1.00 27 0.000
144 N/A 6 0 1.00 27 0.000
145 N/A 10 0 1.00 27 0.000
146 A 12 12 0.76 29 0.414
147 A 8 8 0.87 29 0.276
148 A 3 3 0.97 29 0.103
149 A 1 1 1.00 29 0.034
150 A 5 5 0.99 29 0.172
151 A 8 8 0.96 29 0.276
152 A 12 12 0.69 35 0.343
153 A 8 8 0.78 35 0.229
154 A 3 3 0.92 35 0.086
155 A 1 1 1.00 35 0.029
156 A 5 5 0.96 35 0.143
157 A 8 8 0.92 35 0.229
158 A 1 1 0.99 24 0.042
159 A 14 14 1.29 29 0.483
160 A 11 11 1.03 29 0.379
161 A 7 7 0.88 27 0.259
162 A 5 5 0.89 26 0.192
163 A 9 8 0.59 29 0.276
164 C 11 10 0.79 29 0.345
165 A 11 10 0.59 29 0.345
166 C 16 15 0.65 29 0.517
167 A 25 25 1.46 29 0.862
168 A 21 21 1.25 29 0.724
169 A 9 8 0.75 27 0.296
170 A 12 12 1.10 26 0.462
171 A 16 15 0.69 29 0.517
172 C 20 19 0.89 29 0.655
173 A 17 16 0.61 29 0.552
174 C 26 25 0.97 29 0.862
175 F 0 0 N/A 0.000 N/A
176 F 0 0 N/A 0.000 N/A
177 A 10 9 0.64 27 0.333
178 A 14 14 1.21 26 0.538
179 A 24 23 0.81 29 0.793
180 C 29 28 1.13 29 0.966
181 A 25 24 0.78 29 0.828
182 F 0 0 N/A 0.000 N/A
183 A 14 14 1.29 29 0.483
184 A 11 11 1.06 29 0.379
185 A 7 7 1.12 29 0.241
186 A 5 5 0.83 29 0.172
187 A 2 2 0.97 27 0.074
188 A 1 1 0.95 26 0.038
189 A 7 6 0.48 29 0.207
190 C 10 9 0.71 29 0.310
191 A 11 10 0.56 29 0.345
192 C 13 12 0.79 29 0.414
193 C 19 18 0.94 29 0.621
194 C 14 13 0.83 29 0.448
195 C 13 12 0.77 29 0.414
196 C 10 9 0.64 27 0.333
197 C 10 9 0.71 26 0.346
198 A 16 15 0.55 29 0.517
199 C 20 19 0.82 29 0.655
200 A 28 27 0.67 29 0.931
201 C 19 18 1.05 29 0.621
202 C 20 19 1.02 29 0.655
203 C 16 15 0.72 29 0.517
204 C 11 10 0.66 27 0.370
205 C 14 13 0.87 26 0.500
206 A 26 25 0.77 29 0.862
207 C 24 23 1.01 29 0.793
208 A 11 11 1.21 24 0.458
209 A 8 8 1.09 24 0.333
210 A 5 5 0.93 24 0.208
211 A 3 3 1.08 22 0.136
212 A 1 1 1.00 21 0.048
213 A 7 6 0.58 24 0.250
214 C 9 8 0.83 24 0.333
215 A 11 10 0.65 24 0.417
216 N/A 25 0 1.00 31 0.000
217 N/A 15 0 1.00 31 0.000
218 N/A 6 0 1.00 31 0.000
219 N/A 1 0 1.00 31 0.000
220 N/A 1 0 1.00 31 0.000
221 N/A 1 0 1.00 26 0.000
222 A 11 11 1.10 24 0.458
223 A 10 10 1.07 24 0.417
224 A 6 6 0.84 24 0.250
225 A 4 4 0.90 22 0.182
226 A 1 1 1.00 21 0.048
227 A 8 7 0.58 24 0.292
228 C 10 9 0.75 24 0.375
229 A 15 14 0.59 24 0.583
230 N/A 1 0 1.00 30 0.000
231 A 4 3 0.56 28 0.107
232 A 4 3 0.58 28 0.107
233 A 4 3 0.65 28 0.107
234 A 4 3 0.62 26 0.115
235 A 6 5 0.65 25 0.200
236 N/A 2 0 1.00 28 0.000
237 N/A 2 0 1.00 28 0.000
238 A 4 3 0.56 28 0.107
239 A 4 3 0.56 28 0.107
240 A 4 3 0.59 26 0.115
241 A 5 4 0.59 25 0.160
242 N/A 2 0 1.00 28 0.000
243 N/A 2 0 1.00 28 0.000
244 A 4 3 0.56 28 0.107
245 A 4 3 0.55 28 0.107
246 A 4 3 0.56 26 0.115
247 A 6 5 0.56 25 0.200
248 N/A 2 0 1.00 28 0.000
249 N/A 2 0 1.00 28 0.000
250 A 5 4 0.56 24 0.167
251 A 5 4 0.68 24 0.167
252 A 5 4 0.68 24 0.167
253 A 4 3 1.00 22 0.136
254 A 1 1 0.97 21 0.048
255 N/A 1 0 1.00 24 0.000
256 N/A 1 0 1.00 24 0.000
257 A 5 4 0.62 28 0.143
258 A 5 4 0.65 28 0.143
259 A 9 8 0.74 26 0.308
260 A 1 1 0.97 25 0.040
261 N/A 1 0 1.00 28 0.000
262 N/A 1 0 1.00 28 0.000
263 N/A 1 0 1.00 28 0.000
264 N/A 1 0 1.00 26 0.000
265 N/A 1 0 1.00 25 0.000
266 N/A 1 0 1.00 28 0.000
267 N/A 1 0 1.00 28 0.000
268 N/A 1 0 1.00 28 0.000
269 N/A 1 0 1.00 28 0.000
270 N/A 1 0 1.00 28 0.000
271 N/A 1 0 1.00 28 0.000
272 N/A 1 0 1.00 28 0.000
273 A 6 5 1.01 28 0.179
274 C 15 14 1.70 28 0.500
275 C 16 15 1.02 26 0.577
276 C 14 13 0.90 25 0.520
277 N/A 13 0 1.00 28 0.000
278 N/A 2 0 1.00 28 0.000
279 A 8 7 0.88 28 0.250
280 C 15 14 1.03 26 0.538
281 A 8 7 0.73 25 0.280
282 N/A 12 0 1.00 28 0.000
283 N/A 4 0 1.00 28 0.000
284 A 7 6 1.01 28 0.214
285 C 14 13 1.04 26 0.500
286 A 7 6 0.65 25 0.240
287 N/A 11 0 1.00 28 0.000
288 N/A 3 0 1.00 28 0.000
289 A 6 5 0.64 28 0.179
290 A 6 5 0.72 28 0.179
291 A 6 5 0.70 28 0.179
292 C 14 13 0.89 28 0.464
293 C 12 11 0.88 26 0.423
294 A 1 1 1.03 25 0.040
295 N/A 2 0 1.00 28 0.000
296 N/A 2 0 1.00 28 0.000
297 N/A 3 0 1.00 28 0.000
298 N/A 1 0 1.00 26 0.000
299 N/A 3 0 1.00 25 0.000
300 N/A 1 0 1.00 28 0.000
301 N/A 1 0 1.00 28 0.000
302 N/A 1 0 1.00 30 0.000
303 N/A 1 0 1.00 30 0.000
304 N/A 2 0 1.00 30 0.000
305 N/A 1 0 1.00 30 0.000
306 N/A 1 0 1.00 30 0.000
307 A 5 4 1.79 27 0.148
308 A 5 4 1.54 27 0.148
309 A 10 9 1.14 25 0.360
310 A 5 4 0.99 24 0.167
311 N/A 9 0 1.00 27 0.000
312 A 5 4 1.19 29 0.138
313 A 5 4 1.56 29 0.138
314 A 9 8 1.56 27 0.296
315 A 5 4 0.94 26 0.154
316 N/A 8 0 1.00 29 0.000
317 A 8 7 0.77 19 0.368
318 A 4 3 0.73 29 0.103
319 A 4 3 0.74 27 0.111
320 A 6 5 0.73 26 0.192
321 N/A 2 0 1.00 29 0.000
322 N/A 2 0 1.00 29 0.000
323 A 4 3 0.67 29 0.103
324 A 4 3 0.70 27 0.111
325 A 5 4 0.68 26 0.154
326 N/A 2 0 1.00 29 0.000
327 N/A 2 0 1.00 29 0.000
328 A 4 3 0.65 29 0.103
329 A 4 3 0.67 27 0.111
330 A 6 5 0.66 26 0.192
331 N/A 2 0 1.00 29 0.000
332 N/A 2 0 1.00 29 0.000
333 A 5 4 0.82 28 0.143
334 A 5 4 0.81 28 0.143
335 A 6 5 0.90 26 0.192
336 A 1 1 0.98 25 0.040
337 N/A 1 0 1.00 28 0.000
338 N/A 1 0 1.00 28 0.000
339 A 5 4 0.74 29 0.138
340 A 5 4 0.73 29 0.138
341 A 6 5 0.84 27 0.185
342 A 1 1 0.93 26 0.038
343 N/A 1 0 1.00 29 0.000
344 N/A 1 0 1.00 29 0.000
345 N/A 1 0 1.00 29 0.000
346 N/A 1 0 1.00 27 0.000
347 N/A 1 0 1.00 26 0.000
348 N/A 1 0 1.00 29 0.000
349 N/A 1 0 1.00 29 0.000
350 N/A 1 0 1.00 30 0.000
351 N/A 1 0 1.00 29 0.000
352 N/A 1 0 1.00 27 0.000
353 N/A 1 0 1.00 16 0.000
354 N/A 1 0 1.00 29 0.000
355 N/A 1 0 1.00 29 0.000
356 N/A 1 0 1.00 31 0.000
357 N/A 1 0 1.00 31 0.000
358 N/A 1 0 1.00 31 0.000
359 N/A 1 0 1.00 31 0.000
360 A 7 7 0.98 19 0.368
361 A 7 7 0.98 19 0.368
362 A 5 5 0.99 19 0.263
363 A 5 5 0.99 17 0.294
364 A 4 4 1.05 16 0.250
365 A 4 4 1.04 19 0.211
366 A 5 4 1.01 19 0.211
367 A 4 4 1.03 19 0.211
368 A 6 5 1.03 19 0.263
369 A 7 6 1.02 21 0.286
370 A 10 9 0.88 21 0.429
371 A 7 6 1.06 21 0.286
372 A 8 7 1.06 19 0.368
373 A 7 6 1.11 18 0.333
374 A 4 4 1.09 21 0.190
375 A 8 7 1.02 21 0.333
376 A 4 4 1.02 21 0.190
377 A 10 9 1.20 21 0.429
378 A 7 6 1.00 21 0.286
379 A 12 11 1.11 21 0.524
380 A 7 6 1.02 21 0.286
381 A 9 8 1.05 19 0.421
382 A 7 6 1.05 18 0.333
383 A 4 4 1.00 21 0.190
384 A 7 6 1.01 21 0.286
385 A 4 4 1.19 21 0.190
386 A 10 9 0.95 21 0.429
387 A 2 2 1.00 21 0.095
388 A 2 2 1.00 21 0.095
389 A 2 2 1.00 21 0.095
390 A 2 2 1.00 19 0.105
391 A 2 2 1.00 18 0.111
392 A 2 2 1.04 21 0.095
393 A 2 2 1.00 21 0.095
394 A 2 2 1.04 21 0.095
395 A 2 2 1.00 21 0.095
396 A 2 2 1.00 21 0.095
397 A 5 4 1.00 19 0.211
398 A 2 2 1.03 21 0.095
399 A 2 2 1.03 21 0.095
400 A 2 2 1.00 21 0.095
401 A 2 2 1.00 21 0.095
402 A 2 2 1.00 18 0.111
403 A 2 2 1.00 21 0.095
404 A 2 2 1.01 21 0.095
405 A 11 10 0.95 21 0.476
406 A 6 5 0.99 19 0.263
407 A 2 2 1.04 21 0.095
408 A 2 2 1.04 21 0.095
409 A 2 2 1.00 21 0.095
410 A 2 2 1.00 21 0.095
411 A 2 2 1.00 18 0.111
412 A 8 8 1.05 23 0.348
413 A 7 7 1.09 23 0.304
414 A 5 5 1.11 21 0.238
415 N/A 1 0 1.00 23 0.000
416 N/A 1 0 1.00 23 0.000
417 N/A 1 0 1.00 23 0.000

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