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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 [233] had the largest ratio of [1.15385000000000004]

# 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 22 0.227
2 A 6 6 1.10 22 0.273
3 A 6 5 1.00 22 0.227
4 A 4 4 1.03 20 0.200
5 A 6 5 1.03 19 0.263
6 C 12 11 1.38 22 0.500
7 A 8 7 1.03 22 0.318
8 C 12 11 1.20 22 0.500
9 A 7 6 0.99 22 0.273
10 A 6 5 0.93 24 0.208
11 A 8 8 1.04 24 0.333
12 A 6 5 0.95 24 0.208
13 A 5 5 0.98 22 0.227
14 A 6 5 0.97 21 0.238
15 C 17 16 1.41 24 0.667
16 A 8 7 0.95 24 0.292
17 C 17 16 1.34 24 0.667
18 A 11 10 1.06 24 0.417
19 A 6 5 0.93 24 0.208
20 A 8 8 0.96 24 0.333
21 A 6 5 0.94 24 0.208
22 A 6 6 0.97 22 0.273
23 A 6 5 0.95 21 0.238
24 C 22 21 1.57 24 0.875
25 A 6 5 0.91 24 0.208
26 C 22 21 1.43 24 0.875
27 A 10 9 0.90 24 0.375
28 A 13 12 1.09 24 0.500
29 C 12 11 1.04 24 0.458
30 A 9 8 0.92 24 0.333
31 C 8 7 1.03 22 0.318
32 A 6 5 0.84 21 0.238
33 C 8 7 1.07 24 0.292
34 A 11 10 0.95 24 0.417
35 C 11 10 0.99 24 0.417
36 A 16 15 1.03 24 0.625
37 A 13 12 1.06 24 0.500
38 C 12 11 1.01 24 0.458
39 A 9 8 0.92 24 0.333
40 A 2 2 1.00 22 0.091
41 A 9 8 0.92 21 0.381
42 C 11 10 1.05 24 0.417
43 A 14 13 1.16 24 0.542
44 C 14 13 1.39 24 0.542
45 A 20 19 1.30 24 0.792
46 A 13 12 1.08 24 0.500
47 A 4 4 0.98 24 0.167
48 A 11 10 0.92 24 0.417
49 A 3 3 0.98 22 0.136
50 A 11 10 0.92 21 0.476
51 C 14 13 1.15 24 0.542
52 A 17 16 1.18 24 0.667
53 C 18 17 1.30 24 0.708
54 A 24 23 1.34 24 0.958
55 A 3 3 0.92 26 0.115
56 A 3 3 0.94 26 0.115
57 A 2 2 0.95 24 0.083
58 C 9 8 1.02 26 0.308
59 C 9 8 0.94 26 0.308
60 A 5 5 0.99 26 0.192
61 A 3 3 1.00 23 0.130
62 A 3 3 1.00 26 0.115
63 A 3 3 0.94 26 0.115
64 A 4 4 0.92 26 0.154
65 A 4 4 0.89 26 0.154
66 A 4 4 0.90 26 0.154
67 A 3 3 0.88 24 0.125
68 C 11 10 1.07 26 0.385
69 C 12 11 0.97 26 0.423
70 A 8 8 1.10 26 0.308
71 A 6 6 1.08 23 0.261
72 A 6 6 1.13 26 0.231
73 A 6 6 1.05 26 0.231
74 A 5 4 0.87 26 0.154
75 A 6 5 0.87 26 0.192
76 A 6 5 0.88 26 0.192
77 A 4 4 0.87 26 0.154
78 A 4 4 0.85 26 0.154
79 A 3 3 0.81 24 0.125
80 C 14 13 1.15 26 0.500
81 C 14 13 1.04 26 0.500
82 A 13 12 1.19 26 0.462
83 A 8 8 1.08 23 0.348
84 A 11 10 1.10 26 0.385
85 A 11 10 1.16 26 0.385
86 A 11 10 1.15 26 0.385
87 A 5 4 0.83 26 0.154
88 A 7 6 0.88 26 0.231
89 A 6 5 0.86 26 0.192
90 A 6 6 1.07 26 0.231
91 A 5 5 1.06 26 0.192
92 A 4 4 1.03 26 0.154
93 A 3 3 1.00 26 0.115
94 A 2 2 1.00 24 0.083
95 A 1 1 1.00 23 0.043
96 C 7 6 1.02 26 0.231
97 A 2 2 1.00 26 0.077
98 C 9 8 0.95 26 0.308
99 A 4 4 0.98 26 0.154
100 A 4 4 0.94 26 0.154
101 A 8 7 1.17 26 0.269
102 A 4 4 0.93 26 0.154
103 A 3 3 1.00 26 0.115
104 A 2 2 1.00 24 0.083
105 A 2 2 1.00 23 0.087
106 C 9 8 1.02 26 0.308
107 A 7 6 0.97 26 0.231
108 C 12 11 0.99 26 0.423
109 A 6 5 0.95 26 0.192
110 A 12 11 1.31 26 0.423
111 A 6 6 0.95 26 0.231
112 A 8 7 1.19 26 0.269
113 A 4 4 0.99 26 0.154
114 A 5 4 0.92 26 0.154
115 A 3 3 0.99 24 0.125
116 A 4 4 1.05 23 0.174
117 C 12 11 1.14 26 0.423
118 A 6 5 0.93 26 0.192
119 C 16 15 1.15 26 0.577
120 A 6 5 0.91 26 0.192
121 A 5 5 1.09 21 0.238
122 A 4 4 1.04 21 0.190
123 A 3 3 1.00 21 0.143
124 A 2 2 1.00 19 0.105
125 A 1 1 1.00 18 0.056
126 C 7 6 1.35 21 0.286
127 A 2 2 1.00 21 0.095
128 C 9 8 1.05 21 0.381
129 A 3 3 0.71 26 0.115
130 A 5 5 0.87 26 0.192
131 A 2 2 0.76 24 0.083
132 A 3 3 1.00 23 0.130
133 C 9 8 0.76 26 0.308
134 A 3 3 1.00 26 0.115
135 C 9 8 0.75 26 0.308
136 A 3 3 0.75 26 0.115
137 A 4 4 0.62 26 0.154
138 A 8 8 0.96 26 0.308
139 A 3 3 0.62 24 0.125
140 A 6 6 1.11 23 0.261
141 C 11 10 0.84 26 0.385
142 A 6 6 1.07 26 0.231
143 C 12 11 0.81 26 0.423
144 A 6 6 1.02 26 0.231
145 A 4 4 0.55 26 0.154
146 A 13 12 1.02 26 0.462
147 A 3 3 0.52 24 0.125
148 A 8 8 1.06 23 0.348
149 C 14 13 0.89 26 0.500
150 A 11 10 0.99 26 0.385
151 C 14 13 0.86 26 0.500
152 A 11 10 1.07 26 0.385
153 A 6 6 1.05 26 0.231
154 A 5 5 1.04 26 0.192
155 A 4 4 1.02 26 0.154
156 A 3 3 1.00 26 0.115
157 A 2 2 1.00 24 0.083
158 A 1 1 1.00 23 0.043
159 C 7 6 0.65 26 0.231
160 A 2 2 1.00 26 0.077
161 C 9 8 0.75 26 0.308
162 A 4 4 0.99 26 0.154
163 A 4 4 0.73 26 0.154
164 A 8 7 1.08 26 0.269
165 A 4 4 0.77 26 0.154
166 A 3 3 1.00 26 0.115
167 A 2 2 1.00 24 0.083
168 A 2 2 1.00 23 0.087
169 C 9 8 0.74 26 0.308
170 A 7 6 0.80 26 0.231
171 C 12 11 0.82 26 0.423
172 A 6 5 0.75 26 0.192
173 A 12 11 1.23 26 0.423
174 A 6 6 0.78 26 0.231
175 A 8 7 1.19 26 0.269
176 A 4 4 0.90 26 0.154
177 A 5 4 0.83 26 0.154
178 A 3 3 0.87 24 0.125
179 A 4 4 1.03 23 0.174
180 C 12 11 0.92 26 0.423
181 A 6 5 0.77 26 0.192
182 C 16 15 0.99 26 0.577
183 A 6 5 0.72 26 0.192
184 A 5 5 1.09 21 0.238
185 A 4 4 1.04 21 0.190
186 A 3 3 1.00 21 0.143
187 A 2 2 1.00 19 0.105
188 A 1 1 1.00 18 0.056
189 C 7 6 1.35 21 0.286
190 A 2 2 1.00 21 0.095
191 C 9 8 1.05 21 0.381
192 B 25 24 101.60 25 0.960
193 N/A 8 0 1.00 25 0.000
194 B 9 8 36.35 23 0.348
195 N/A 9 0 1.00 25 0.000
196 N/A 15 0 1.00 25 0.000
197 A 7 7 1.02 24 0.292
198 A 6 6 0.99 24 0.250
199 A 4 4 0.98 22 0.182
200 N/A 1 0 1.00 24 0.000
201 N/A 4 0 1.00 24 0.000
202 N/A 6 0 1.00 24 0.000
203 A 9 9 0.72 26 0.346
204 A 6 6 0.82 26 0.231
205 A 3 3 0.90 26 0.115
206 A 1 1 1.00 26 0.038
207 A 3 3 1.00 26 0.115
208 A 5 5 0.96 26 0.192
209 A 1 1 1.00 21 0.048
210 A 11 11 1.14 24 0.458
211 A 9 9 1.66 24 0.375
212 A 9 9 1.15 24 0.375
213 A 7 7 1.05 22 0.318
214 A 5 5 1.10 21 0.238
215 C 14 13 1.38 24 0.542
216 C 13 12 1.27 24 0.500
217 C 14 13 1.27 24 0.542
218 C 11 10 1.32 24 0.417
219 A 17 17 1.31 26 0.654
220 A 13 13 1.97 26 0.500
221 A 15 15 1.25 26 0.577
222 A 9 9 0.96 24 0.375
223 A 8 8 1.12 23 0.348
224 C 22 21 1.45 26 0.808
225 C 18 17 1.32 26 0.654
226 C 22 21 1.38 26 0.808
227 C 17 16 1.40 26 0.615
228 A 22 22 1.49 26 0.846
229 B 18 17 2.39 26 0.654
230 A 20 20 1.38 26 0.769
231 A 11 11 0.94 24 0.458
232 A 9 9 1.18 23 0.391
233 C 31 30 1.67 26 1.154
234 C 23 22 1.47 26 0.846
235 F 0 0 N/A 0.000 N/A
236 C 21 20 1.62 26 0.769
237 A 13 12 1.05 26 0.462
238 C 14 13 1.00 26 0.500
239 A 11 10 0.87 26 0.385
240 C 9 8 1.00 24 0.333
241 A 7 6 0.80 23 0.261
242 C 9 8 1.04 26 0.308
243 A 15 14 0.91 26 0.538
244 C 13 12 0.94 26 0.462
245 A 17 16 1.04 26 0.615
246 A 16 15 1.02 26 0.577
247 C 14 13 1.00 26 0.500
248 A 11 10 0.90 26 0.385
249 A 3 3 0.96 24 0.125
250 A 11 10 0.89 23 0.435
251 C 13 12 1.03 26 0.462
252 A 20 19 1.06 26 0.731
253 C 19 18 1.27 26 0.692
254 A 23 22 1.21 26 0.846
255 A 16 15 1.03 26 0.577
256 A 9 8 1.08 26 0.308
257 A 13 12 0.93 26 0.462
258 A 5 5 0.93 24 0.208
259 A 13 12 0.94 23 0.522
260 C 18 17 1.18 26 0.654
261 A 25 24 1.20 26 0.923
262 C 24 23 1.31 26 0.885
263 A 29 28 1.45 26 1.077
264 A 13 12 1.14 28 0.429
265 A 10 10 1.01 28 0.357
266 A 7 6 0.83 26 0.231
267 A 5 5 0.89 25 0.200
268 C 10 9 0.63 28 0.321
269 C 11 10 0.92 28 0.357
270 C 13 12 0.63 28 0.429
271 C 13 12 0.74 28 0.429
272 A 19 18 1.29 28 0.643
273 A 17 17 1.22 28 0.607
274 A 7 6 0.74 26 0.231
275 A 10 10 1.13 25 0.400
276 C 16 15 0.72 28 0.536
277 C 18 17 0.96 28 0.607
278 C 17 16 0.64 28 0.571
279 C 23 22 1.10 28 0.786
280 A 25 24 1.43 28 0.857
281 A 26 26 1.39 28 0.929
282 A 7 6 0.67 26 0.231
283 A 12 12 1.27 25 0.480
284 C 22 21 0.87 28 0.750
285 C 27 26 1.20 28 0.929
286 C 24 23 0.78 28 0.821
287 F 0 0 N/A 0.000 N/A
288 A 10 10 1.44 23 0.435
289 A 9 8 1.26 23 0.348
290 A 5 5 1.10 23 0.217
291 A 3 3 1.04 21 0.143
292 A 1 1 1.00 20 0.050
293 C 8 7 1.18 23 0.304
294 C 10 9 1.26 23 0.391
295 C 13 12 1.04 23 0.522
296 C 13 12 1.07 23 0.522
297 A 13 12 1.22 28 0.429
298 A 10 10 1.08 28 0.357
299 A 8 7 1.09 28 0.250
300 A 5 5 0.86 28 0.179
301 A 2 2 0.96 26 0.077
302 A 1 1 1.00 25 0.040
303 C 8 7 0.56 28 0.250
304 C 10 9 0.90 28 0.321
305 C 13 12 0.63 28 0.429
306 C 13 12 0.90 28 0.429
307 A 19 18 1.16 28 0.643
308 C 16 15 0.98 28 0.536
309 A 11 10 0.90 28 0.357
310 C 10 9 0.80 28 0.321
311 A 7 6 0.64 26 0.231
312 C 9 8 0.74 25 0.320
313 A 14 13 0.59 28 0.464
314 C 17 16 0.87 28 0.571
315 A 24 23 0.71 28 0.821
316 C 19 18 1.01 28 0.643
317 A 15 14 1.25 28 0.500
318 C 13 12 1.03 28 0.429
319 A 15 14 1.03 28 0.500
320 C 12 11 0.67 28 0.393
321 A 9 8 0.66 26 0.308
322 C 12 11 0.88 25 0.440
323 A 22 21 0.81 28 0.750
324 C 22 21 1.04 28 0.750
325 F 0 0 N/A 0.000 N/A
326 C 25 24 1.37 28 0.857
327 A 12 12 0.78 26 0.462
328 A 9 9 0.86 26 0.346
329 A 5 5 0.95 24 0.208
330 N/A 1 0 1.00 26 0.000
331 N/A 6 0 1.00 26 0.000
332 N/A 8 0 1.00 26 0.000
333 N/A 14 0 1.00 28 0.000
334 N/A 8 0 1.00 28 0.000
335 N/A 4 0 1.00 28 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 23 0.000
340 N/A 1 0 1.00 23 0.000
341 A 9 9 1.45 23 0.391
342 A 10 10 1.33 23 0.435
343 A 6 6 1.09 23 0.261
344 A 4 4 1.08 21 0.190
345 A 1 1 1.00 20 0.050
346 C 9 8 1.20 23 0.348
347 C 11 10 1.17 23 0.435
348 C 13 12 1.04 23 0.522
349 A 4 3 0.83 27 0.111
350 A 5 4 0.84 27 0.148
351 A 4 3 0.87 27 0.111
352 A 5 4 0.86 25 0.160
353 A 5 4 0.87 24 0.167
354 N/A 2 0 1.00 27 0.000
355 N/A 2 0 1.00 27 0.000
356 N/A 1 0 1.00 27 0.000
357 A 5 4 0.83 27 0.148
358 A 4 3 0.83 27 0.111
359 A 5 4 0.84 25 0.160
360 A 5 4 0.84 24 0.167
361 N/A 2 0 1.00 27 0.000
362 N/A 2 0 1.00 27 0.000
363 N/A 1 0 1.00 27 0.000
364 A 5 4 0.83 27 0.148
365 A 4 3 0.82 27 0.111
366 A 5 4 0.83 25 0.160
367 A 5 4 0.83 24 0.167
368 N/A 2 0 1.00 27 0.000
369 N/A 2 0 1.00 27 0.000
370 N/A 1 0 1.00 27 0.000
371 A 5 4 0.88 23 0.174
372 C 6 5 1.19 23 0.217
373 A 6 5 0.93 23 0.217
374 A 6 5 0.93 23 0.217
375 A 5 4 1.00 21 0.190
376 A 1 1 1.00 20 0.050
377 N/A 1 0 1.00 23 0.000
378 N/A 1 0 1.00 23 0.000
379 C 7 6 0.92 27 0.222
380 A 5 4 0.84 27 0.148
381 C 7 6 0.95 27 0.222
382 A 6 5 0.87 27 0.185
383 C 11 10 1.06 25 0.400
384 A 1 1 1.00 24 0.042
385 N/A 1 0 1.00 27 0.000
386 N/A 1 0 1.00 27 0.000
387 N/A 1 0 1.00 27 0.000
388 N/A 1 0 1.00 25 0.000
389 N/A 1 0 1.00 24 0.000
390 N/A 1 0 1.00 27 0.000
391 N/A 1 0 1.00 27 0.000
392 N/A 1 0 1.00 30 0.000
393 N/A 1 0 1.00 30 0.000
394 N/A 1 0 1.00 30 0.000
395 N/A 1 0 1.00 30 0.000
396 A 5 4 1.37 27 0.148
397 C 15 14 2.16 27 0.519
398 A 13 12 1.23 25 0.480
399 C 14 13 1.05 24 0.542
400 N/A 11 0 1.00 27 0.000
401 N/A 2 0 1.00 27 0.000
402 N/A 1 0 1.00 27 0.000
403 N/A 1 0 1.00 27 0.000
404 A 5 4 1.42 27 0.148
405 A 6 5 1.15 27 0.185
406 A 9 8 1.36 25 0.320
407 A 6 5 0.93 24 0.208
408 N/A 7 0 1.00 27 0.000
409 N/A 2 0 1.00 27 0.000
410 N/A 1 0 1.00 27 0.000
411 N/A 2 0 1.00 27 0.000
412 A 5 4 1.78 27 0.148
413 A 6 5 1.43 27 0.185
414 A 9 8 1.42 25 0.320
415 A 6 5 0.88 24 0.208
416 N/A 7 0 1.00 27 0.000
417 N/A 2 0 1.00 27 0.000
418 N/A 1 0 1.00 27 0.000
419 N/A 1 0 1.00 27 0.000
420 A 5 4 0.87 27 0.148
421 A 6 5 0.93 27 0.185
422 A 5 4 0.89 27 0.148
423 C 14 13 1.05 27 0.481
424 A 10 9 0.95 25 0.360
425 A 1 1 1.00 24 0.042
426 N/A 2 0 1.00 27 0.000
427 N/A 2 0 1.00 27 0.000
428 N/A 1 0 1.00 27 0.000
429 N/A 2 0 1.00 27 0.000
430 N/A 1 0 1.00 25 0.000
431 N/A 2 0 1.00 24 0.000
432 N/A 1 0 1.00 27 0.000
433 N/A 1 0 1.00 27 0.000
434 N/A 1 0 1.00 27 0.000
435 N/A 1 0 1.00 27 0.000
436 N/A 1 0 1.00 25 0.000
437 N/A 2 0 1.00 24 0.000
438 N/A 1 0 1.00 27 0.000
439 N/A 1 0 1.00 27 0.000
440 N/A 1 0 1.00 27 0.000
441 N/A 1 0 1.00 27 0.000
442 N/A 1 0 1.00 27 0.000
443 N/A 2 0 1.00 27 0.000
444 N/A 1 0 1.00 27 0.000
445 N/A 1 0 1.00 27 0.000
446 A 5 4 1.80 26 0.154
447 A 6 5 1.55 26 0.192
448 A 9 8 1.14 24 0.333
449 A 6 5 0.99 23 0.217
450 N/A 8 0 1.00 26 0.000
451 N/A 4 0 1.00 26 0.000
452 N/A 2 0 1.00 26 0.000
453 A 5 4 1.19 28 0.143
454 A 6 5 1.57 28 0.179
455 A 9 8 1.57 26 0.308
456 A 6 5 0.94 25 0.200
457 N/A 8 0 1.00 28 0.000
458 N/A 4 0 1.00 28 0.000
459 N/A 1 0 1.00 28 0.000
460 C 8 7 1.24 17 0.412
461 A 4 3 0.76 28 0.107
462 A 5 4 0.77 26 0.154
463 A 5 4 0.76 25 0.160
464 N/A 2 0 1.00 28 0.000
465 N/A 2 0 1.00 28 0.000
466 A 4 3 0.71 28 0.107
467 A 5 4 0.73 26 0.154
468 A 5 4 0.72 25 0.160
469 N/A 2 0 1.00 28 0.000
470 N/A 2 0 1.00 28 0.000
471 A 4 3 0.69 28 0.107
472 A 5 4 0.71 26 0.154
473 A 5 4 0.70 25 0.160
474 N/A 2 0 1.00 28 0.000
475 N/A 2 0 1.00 28 0.000
476 N/A 1 0 1.00 23 0.000
477 C 6 5 1.03 23 0.217
478 A 6 5 0.94 23 0.217
479 C 6 5 1.10 21 0.238
480 A 1 1 1.00 20 0.050
481 N/A 1 0 1.00 23 0.000
482 N/A 1 0 1.00 23 0.000
483 C 8 7 1.28 15 0.467
484 A 2 2 1.00 15 0.133

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