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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 [17] had the largest ratio of [1.37500000000000000]

# 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 C 15 15 1.27 14 1.071
2 C 11 11 1.31 14 0.786
3 C 9 9 1.24 14 0.643
4 C 5 5 1.32 12 0.417
5 C 8 8 1.20 14 0.571
6 C 10 10 1.18 14 0.714
7 C 14 14 1.16 14 1.000
8 A 14 14 1.03 16 0.875
9 A 9 9 0.96 16 0.562
10 A 9 9 1.02 16 0.562
11 A 4 4 1.00 14 0.286
12 A 4 4 1.00 16 0.250
13 C 12 12 1.16 16 0.750
14 A 9 9 1.31 16 0.562
15 C 17 17 1.05 16 1.062
16 F 0 0 N/A 0.000 N/A
17 C 22 22 1.41 16 1.375
18 C 16 15 1.22 16 0.938
19 C 9 9 1.17 14 0.643
20 C 4 4 1.10 16 0.250
21 C 4 4 1.08 16 0.250
22 C 14 14 1.43 16 0.875
23 C 8 7 1.16 14 0.500
24 C 7 6 1.16 14 0.429
25 C 6 5 1.22 12 0.417
26 N/A 3 0 1.00 14 0.000
27 N/A 3 0 1.00 14 0.000
28 C 12 11 1.42 16 0.688
29 C 11 10 1.43 16 0.625
30 C 7 7 1.14 14 0.500
31 N/A 3 0 1.00 16 0.000
32 N/A 3 0 1.00 16 0.000
33 C 14 13 1.15 16 0.812
34 C 12 11 1.19 16 0.688
35 C 10 9 1.17 14 0.643
36 N/A 3 0 1.00 16 0.000
37 N/A 3 0 1.00 16 0.000
38 C 16 15 1.19 16 0.938
39 C 13 12 1.20 16 0.750
40 C 10 9 1.15 16 0.562
41 C 7 6 1.08 16 0.375
42 C 10 9 1.18 16 0.562
43 C 13 12 1.18 16 0.750
44 C 16 15 1.19 16 0.938
45 A 9 9 1.03 18 0.500
46 A 9 9 1.03 18 0.500
47 A 4 4 1.00 18 0.222
48 A 4 4 1.00 18 0.222
49 C 11 10 1.13 18 0.556
50 A 9 9 1.27 18 0.500
51 C 16 15 1.10 18 0.833
52 A 14 14 1.21 18 0.778
53 C 22 21 1.48 18 1.167
54 C 19 18 1.49 18 1.000
55 C 4 4 1.06 18 0.222
56 C 4 4 1.05 18 0.222
57 C 4 4 1.08 18 0.222
58 C 13 12 1.52 18 0.667
59 C 16 15 1.45 18 0.833
60 C 13 12 1.26 12 1.000
61 C 10 9 1.20 12 0.750
62 C 7 6 1.10 12 0.500
63 C 10 9 1.24 12 0.750
64 C 13 12 1.24 12 1.000
65 N/A 3 0 1.00 16 0.000
66 N/A 3 0 1.00 16 0.000
67 N/A 4 0 1.00 10 0.000
68 A 1 1 1.00 18 0.056
69 A 1 1 1.00 20 0.050
70 A 1 1 1.00 20 0.050
71 A 1 1 1.00 22 0.045
72 N/A 2 0 1.00 18 0.000
73 C 4 4 1.05 16 0.250
74 A 4 4 1.00 16 0.250
75 C 4 4 1.07 14 0.286
76 N/A 3 0 1.00 14 0.000
77 N/A 3 0 1.00 16 0.000
78 C 4 4 1.14 12 0.333
79 C 4 4 1.14 12 0.333
80 C 4 4 1.14 12 0.333
81 C 4 4 1.14 10 0.400
82 C 4 4 1.16 12 0.333
83 C 4 4 1.15 12 0.333
84 C 4 4 1.14 12 0.333
85 A 4 4 1.00 14 0.286
86 A 4 4 1.00 14 0.286
87 A 4 4 1.00 14 0.286
88 A 4 4 1.00 12 0.333
89 A 4 4 1.00 14 0.286
90 A 4 4 1.00 14 0.286
91 A 4 4 1.00 14 0.286
92 A 1 1 1.00 20 0.050
93 A 1 1 1.00 20 0.050
94 A 1 1 1.00 20 0.050
95 A 1 1 1.00 24 0.042
96 A 3 3 1.00 21 0.143
97 A 3 3 1.00 21 0.143
98 A 3 3 1.00 19 0.158
99 A 3 3 1.00 21 0.143
100 A 3 3 1.00 21 0.143
101 A 3 3 1.00 21 0.143
102 A 3 3 0.95 23 0.130
103 A 3 3 1.00 23 0.130
104 A 3 3 0.84 21 0.143
105 A 5 5 0.96 23 0.217
106 A 5 5 1.02 23 0.217
107 A 7 7 1.39 23 0.304
108 A 16 15 1.11 23 0.652
109 A 15 14 1.14 23 0.609
110 A 10 10 1.03 21 0.476
111 N/A 2 0 1.00 23 0.000
112 N/A 2 0 1.00 23 0.000
113 A 17 16 1.01 23 0.696
114 A 17 16 1.00 23 0.696
115 A 10 10 0.97 21 0.476
116 N/A 2 0 1.00 23 0.000
117 N/A 2 0 1.00 23 0.000
118 A 16 16 1.13 21 0.762
119 A 14 14 1.21 21 0.667
120 A 10 10 1.17 21 0.476
121 A 8 8 1.36 19 0.421
122 A 9 9 0.71 21 0.429
123 A 13 13 0.82 21 0.619
124 A 15 15 0.78 21 0.714
125 A 23 23 1.06 21 1.095
126 A 15 14 0.93 21 0.667
127 A 10 10 0.95 19 0.526
128 A 5 5 0.57 21 0.238
129 A 5 5 0.61 21 0.238
130 F 0 0 N/A 0.000 N/A
131 A 19 18 0.91 21 0.857
132 A 12 12 0.84 19 0.632
133 A 5 5 0.51 21 0.238
134 A 5 5 0.54 21 0.238
135 A 7 7 0.76 21 0.333
136 A 9 8 0.58 21 0.381
137 A 8 7 0.60 21 0.333
138 A 7 6 0.65 19 0.316
139 N/A 2 0 1.00 21 0.000
140 N/A 2 0 1.00 21 0.000
141 A 13 12 0.59 21 0.571
142 A 11 10 0.63 21 0.476
143 A 9 8 0.75 19 0.421
144 N/A 2 0 1.00 21 0.000
145 N/A 2 0 1.00 21 0.000
146 A 20 19 0.73 21 0.905
147 A 16 15 0.70 21 0.714
148 A 11 10 0.72 19 0.526
149 N/A 2 0 1.00 21 0.000
150 N/A 2 0 1.00 21 0.000
151 N/A 2 0 1.00 23 0.000
152 A 7 7 0.96 23 0.304
153 A 5 5 0.98 23 0.217
154 A 3 3 1.00 21 0.143
155 N/A 2 0 1.00 23 0.000
156 N/A 2 0 1.00 23 0.000
157 A 3 3 1.00 18 0.167
158 A 3 3 1.00 18 0.167
159 A 3 3 1.00 16 0.188
160 A 3 3 1.00 18 0.167
161 A 3 3 1.00 18 0.167
162 A 3 3 1.00 18 0.167
163 A 3 3 0.95 20 0.150
164 A 3 3 1.00 20 0.150
165 A 3 3 0.97 18 0.167
166 A 3 3 1.00 20 0.150
167 A 3 3 1.00 20 0.150
168 A 3 3 1.00 20 0.150
169 A 11 10 0.93 20 0.500
170 A 10 9 0.96 20 0.450
171 A 9 8 1.01 18 0.444
172 N/A 2 0 1.00 20 0.000
173 N/A 2 0 1.00 20 0.000
174 A 16 15 0.95 20 0.750
175 A 13 12 1.04 18 0.667
176 N/A 2 0 1.00 20 0.000
177 N/A 2 0 1.00 20 0.000
178 A 20 19 1.53 18 1.056
179 N/A 2 0 1.00 20 0.000
180 N/A 2 0 1.00 20 0.000
181 N/A 2 0 1.00 20 0.000
182 A 3 3 1.00 20 0.150
183 A 3 3 1.00 20 0.150
184 A 3 3 1.00 18 0.167
185 N/A 2 0 1.00 20 0.000
186 N/A 2 0 1.00 20 0.000
187 A 18 17 1.03 29 0.586
188 A 17 16 1.05 29 0.552
189 A 12 12 0.97 27 0.444
190 A 5 5 1.09 22 0.227
191 N/A 1 0 1.00 29 0.000
192 N/A 1 0 1.00 29 0.000
193 A 30 29 1.10 31 0.935
194 A 27 26 1.11 31 0.839
195 A 18 18 1.09 29 0.621
196 A 9 9 0.96 24 0.375
197 N/A 1 0 1.00 31 0.000
198 N/A 1 0 1.00 31 0.000
199 F 0 0 N/A 0.000 N/A
200 F 0 0 N/A 0.000 N/A
201 A 23 23 1.13 29 0.793
202 A 7 7 1.05 24 0.292
203 N/A 1 0 1.00 31 0.000
204 N/A 1 0 1.00 31 0.000
205 A 23 22 1.04 29 0.759
206 A 21 20 1.05 29 0.690
207 A 16 15 1.05 27 0.556
208 A 8 8 1.22 22 0.364
209 N/A 1 0 1.00 29 0.000
210 N/A 1 0 1.00 29 0.000
211 F 0 0 N/A 0.000 N/A
212 F 0 0 N/A 0.000 N/A
213 A 24 23 1.07 29 0.793
214 A 15 14 1.04 24 0.583
215 N/A 1 0 1.00 31 0.000
216 N/A 1 0 1.00 31 0.000
217 F 0 0 N/A 0.000 N/A
218 F 0 0 N/A 0.000 N/A
219 F 0 0 N/A 0.000 N/A
220 A 20 19 1.11 24 0.792
221 N/A 1 0 1.00 31 0.000
222 N/A 1 0 1.00 31 0.000
223 A 13 12 0.88 26 0.462
224 A 12 11 0.91 26 0.423
225 A 11 10 0.96 24 0.417
226 C 8 7 1.13 19 0.368
227 N/A 1 0 1.00 26 0.000
228 C 25 24 0.91 28 0.857
229 C 22 21 0.92 28 0.750
230 C 17 16 0.98 26 0.615
231 C 13 12 1.11 21 0.571
232 N/A 1 0 1.00 28 0.000
233 F 0 0 N/A 0.000 N/A
234 F 0 0 N/A 0.000 N/A
235 C 22 21 0.97 26 0.808
236 C 13 12 1.16 21 0.571
237 N/A 1 0 1.00 28 0.000
238 C 15 14 0.92 26 0.538
239 C 15 14 0.94 26 0.538
240 C 14 13 0.99 24 0.542
241 C 11 10 1.09 19 0.526
242 N/A 1 0 1.00 26 0.000
243 C 27 26 0.96 28 0.929
244 C 26 25 0.98 28 0.893
245 C 22 21 0.99 26 0.808
246 C 15 14 1.11 21 0.667
247 N/A 1 0 1.00 28 0.000
248 F 0 0 N/A 0.000 N/A
249 F 0 0 N/A 0.000 N/A
250 F 0 0 N/A 0.000 N/A
251 C 19 18 1.22 21 0.857
252 N/A 1 0 1.00 28 0.000
253 A 7 6 1.00 29 0.207
254 A 6 5 1.01 29 0.172
255 A 5 4 1.04 27 0.148
256 A 4 3 1.04 22 0.136
257 N/A 1 0 1.00 29 0.000
258 N/A 1 0 1.00 29 0.000
259 A 13 13 1.03 31 0.419
260 A 11 11 0.98 31 0.355
261 A 7 7 1.00 29 0.241
262 A 3 3 1.00 24 0.125
263 A 10 10 1.00 31 0.323
264 A 12 12 0.98 31 0.387
265 A 23 23 0.97 31 0.742
266 A 14 14 0.90 31 0.452
267 A 12 12 0.96 29 0.414
268 A 4 3 0.79 24 0.125
269 A 18 18 0.98 31 0.581
270 A 24 24 1.04 31 0.774
271 A 22 21 0.95 29 0.724
272 A 17 16 0.94 29 0.552
273 A 12 11 0.94 27 0.407
274 A 5 4 1.12 22 0.182
275 N/A 1 0 1.00 29 0.000
276 N/A 1 0 1.00 29 0.000
277 A 23 22 0.98 31 0.710
278 A 22 21 0.95 31 0.677
279 A 14 14 0.96 29 0.483
280 A 6 5 1.00 24 0.208
281 N/A 1 0 1.00 31 0.000
282 N/A 1 0 1.00 31 0.000
283 F 0 0 N/A 0.000 N/A
284 A 24 23 0.95 31 0.742
285 A 14 13 0.94 29 0.448
286 A 5 4 1.02 24 0.167
287 N/A 1 0 1.00 31 0.000
288 N/A 1 0 1.00 31 0.000
289 A 7 6 1.01 26 0.231
290 A 6 5 1.00 26 0.192
291 A 5 4 1.00 24 0.167
292 A 4 3 1.00 19 0.158
293 N/A 1 0 1.00 26 0.000
294 C 23 22 0.95 28 0.786
295 C 20 19 0.97 28 0.679
296 C 15 14 1.02 26 0.538
297 A 10 9 1.04 21 0.429
298 N/A 1 0 1.00 28 0.000
299 C 30 29 0.92 28 1.036
300 C 20 19 0.90 28 0.679
301 A 17 16 0.92 26 0.615
302 A 6 5 0.90 21 0.238
303 N/A 1 0 1.00 28 0.000
304 A 10 9 0.88 26 0.346
305 A 9 8 0.90 26 0.308
306 A 8 7 0.95 24 0.292
307 A 8 7 1.07 19 0.368
308 N/A 1 0 1.00 26 0.000
309 A 14 13 0.84 28 0.464
310 A 13 12 0.86 28 0.429
311 A 12 11 0.93 26 0.423
312 A 9 8 0.97 21 0.381
313 N/A 1 0 1.00 28 0.000
314 A 10 9 0.82 28 0.321
315 A 9 8 0.87 26 0.308
316 A 7 6 1.33 21 0.286
317 N/A 1 0 1.00 28 0.000
318 N/A 1 0 1.00 24 0.000
319 N/A 1 0 1.00 24 0.000
320 N/A 1 0 1.00 22 0.000
321 A 6 5 0.97 24 0.208
322 A 10 9 0.96 26 0.346
323 A 11 10 0.91 26 0.385
324 A 6 5 0.97 24 0.208
325 A 10 9 0.96 26 0.346
326 A 11 10 0.91 26 0.385
327 A 10 9 1.04 24 0.375
328 A 14 13 0.98 26 0.500
329 A 17 16 0.89 26 0.615
330 A 10 9 1.04 24 0.375
331 A 14 13 0.98 26 0.500
332 A 17 16 0.89 26 0.615
333 C 20 19 1.01 32 0.594
334 C 15 14 1.01 32 0.438
335 A 12 11 0.99 30 0.367
336 A 8 7 0.88 25 0.280
337 N/A 1 0 1.00 32 0.000
338 C 30 29 0.92 34 0.853
339 C 27 26 0.95 34 0.765
340 C 19 18 0.99 32 0.562
341 C 11 10 1.13 27 0.370
342 N/A 1 0 1.00 34 0.000
343 F 0 0 N/A 0.000 N/A
344 F 0 0 N/A 0.000 N/A
345 A 26 25 0.90 32 0.781
346 A 8 7 0.88 27 0.259
347 N/A 1 0 1.00 34 0.000
348 A 14 13 0.87 26 0.500
349 A 14 13 0.88 26 0.500
350 A 13 12 0.93 24 0.500
351 A 10 9 1.03 19 0.474
352 N/A 1 0 1.00 26 0.000
353 A 25 24 0.86 32 0.750
354 A 23 22 0.88 32 0.688
355 A 19 18 0.93 30 0.600
356 C 10 9 1.08 25 0.360
357 N/A 1 0 1.00 32 0.000
358 A 18 17 0.81 34 0.500
359 A 16 15 0.84 32 0.469
360 A 10 9 1.19 27 0.333
361 N/A 1 0 1.00 34 0.000
362 C 31 30 0.98 34 0.882
363 C 21 20 0.95 34 0.588
364 A 18 17 0.99 32 0.531
365 A 8 7 0.87 27 0.259
366 N/A 1 0 1.00 34 0.000
367 F 0 0 N/A 0.000 N/A
368 F 0 0 N/A 0.000 N/A
369 C 24 23 0.97 34 0.676
370 C 22 21 1.16 29 0.724
371 N/A 1 0 1.00 36 0.000
372 F 0 0 N/A 0.000 N/A
373 F 0 0 N/A 0.000 N/A
374 F 0 0 N/A 0.000 N/A
375 A 7 6 0.88 29 0.207
376 N/A 1 0 1.00 36 0.000
377 A 20 19 0.85 32 0.594
378 A 21 20 0.87 32 0.625
379 A 20 19 0.91 30 0.633
380 A 7 6 1.15 25 0.240
381 N/A 1 0 1.00 32 0.000
382 A 31 30 0.85 28 1.071
383 A 29 28 0.87 28 1.000
384 A 23 22 0.92 26 0.846
385 A 14 13 0.98 21 0.619
386 N/A 1 0 1.00 28 0.000
387 A 26 25 0.82 34 0.735
388 A 21 20 0.85 32 0.625
389 A 11 10 1.21 27 0.370
390 N/A 1 0 1.00 34 0.000
391 F 0 0 N/A 0.000 N/A
392 F 0 0 N/A 0.000 N/A
393 A 24 23 0.96 32 0.719
394 A 8 7 0.87 27 0.259
395 N/A 1 0 1.00 34 0.000
396 F 0 0 N/A 0.000 N/A
397 F 0 0 N/A 0.000 N/A
398 C 27 26 0.96 34 0.765
399 C 25 24 1.21 29 0.828
400 N/A 1 0 1.00 36 0.000
401 F 0 0 N/A 0.000 N/A
402 F 0 0 N/A 0.000 N/A
403 F 0 0 N/A 0.000 N/A
404 A 8 7 0.89 29 0.241
405 N/A 1 0 1.00 36 0.000
406 F 0 0 N/A 0.000 N/A
407 F 0 0 N/A 0.000 N/A
408 A 31 30 0.90 32 0.938
409 A 10 9 1.09 27 0.333
410 N/A 1 0 1.00 34 0.000
411 F 0 0 N/A 0.000 N/A
412 F 0 0 N/A 0.000 N/A
413 F 0 0 N/A 0.000 N/A
414 C 18 17 1.05 27 0.630
415 N/A 1 0 1.00 34 0.000
416 F 0 0 N/A 0.000 N/A
417 F 0 0 N/A 0.000 N/A
418 A 9 8 1.22 21 0.381
419 N/A 1 0 1.00 28 0.000
420 C 13 12 1.18 26 0.462
421 C 13 12 1.22 26 0.462
422 C 12 11 1.28 24 0.458
423 A 7 6 1.00 19 0.316
424 N/A 1 0 1.00 26 0.000
425 F 0 0 N/A 0.000 N/A
426 F 0 0 N/A 0.000 N/A
427 C 25 24 1.29 30 0.800
428 C 15 14 1.13 25 0.560
429 N/A 1 0 1.00 32 0.000
430 F 0 0 N/A 0.000 N/A
431 F 0 0 N/A 0.000 N/A
432 C 30 29 1.31 32 0.906
433 A 8 7 0.96 27 0.259
434 N/A 1 0 1.00 34 0.000
435 A 16 15 0.87 32 0.469
436 A 16 15 0.89 32 0.469
437 A 15 14 0.92 30 0.467
438 A 8 7 1.16 25 0.280
439 N/A 1 0 1.00 32 0.000
440 A 19 18 0.85 34 0.529
441 A 18 17 0.87 34 0.500
442 A 15 14 0.88 32 0.438
443 C 4 4 1.12 27 0.148
444 N/A 1 0 1.00 34 0.000
445 A 15 14 0.84 34 0.412
446 A 12 11 0.84 32 0.344
447 A 8 7 1.13 27 0.259
448 N/A 1 0 1.00 34 0.000
449 C 21 20 1.13 32 0.625
450 C 20 19 1.17 32 0.594
451 C 17 16 1.25 30 0.533
452 A 8 7 0.98 25 0.280
453 N/A 1 0 1.00 32 0.000
454 F 0 0 N/A 0.000 N/A
455 F 0 0 N/A 0.000 N/A
456 F 0 0 N/A 0.000 N/A
457 C 18 17 1.14 21 0.810
458 N/A 1 0 1.00 28 0.000
459 F 0 0 N/A 0.000 N/A
460 F 0 0 N/A 0.000 N/A
461 F 0 0 N/A 0.000 N/A
462 A 7 6 1.00 27 0.222
463 N/A 1 0 1.00 34 0.000
464 A 21 20 0.88 34 0.588
465 A 21 20 0.91 34 0.588
466 A 18 17 0.90 32 0.531
467 A 7 6 1.13 27 0.222
468 N/A 1 0 1.00 34 0.000
469 A 30 29 0.89 36 0.806
470 C 24 23 0.89 34 0.676
471 A 4 4 1.00 29 0.138
472 N/A 1 0 1.00 36 0.000
473 A 15 14 0.82 34 0.412
474 A 8 7 1.15 29 0.241
475 N/A 1 0 1.00 36 0.000
476 F 0 0 N/A 0.000 N/A
477 C 29 28 1.13 34 0.824
478 C 23 22 1.17 32 0.688
479 A 8 7 0.94 27 0.259
480 N/A 1 0 1.00 34 0.000
481 F 0 0 N/A 0.000 N/A
482 F 0 0 N/A 0.000 N/A
483 F 0 0 N/A 0.000 N/A
484 C 22 21 1.23 27 0.778
485 N/A 1 0 1.00 34 0.000
486 F 0 0 N/A 0.000 N/A
487 F 0 0 N/A 0.000 N/A
488 F 0 0 N/A 0.000 N/A
489 A 7 6 0.95 21 0.286
490 N/A 1 0 1.00 28 0.000
491 A 24 23 0.89 34 0.676
492 A 24 23 0.92 34 0.676
493 A 21 20 0.88 32 0.625
494 A 8 7 1.11 27 0.259
495 N/A 1 0 1.00 34 0.000
496 F 0 0 N/A 0.000 N/A
497 C 27 26 0.87 34 0.765
498 C 4 4 1.12 29 0.138
499 N/A 1 0 1.00 36 0.000
500 A 26 25 0.84 34 0.735
501 A 8 7 1.11 29 0.241
502 N/A 1 0 1.00 36 0.000

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