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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 [102] had the largest ratio of [1.05882000000000009]

# 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 5 4 1.00 15 0.267
2 A 4 3 0.94 15 0.200
3 A 6 5 0.95 13 0.385
4 A 3 2 1.00 11 0.182
5 A 7 6 0.97 15 0.400
6 A 5 4 1.18 15 0.267
7 A 6 5 1.11 15 0.333
8 A 5 4 1.10 15 0.267
9 A 4 3 1.10 13 0.231
10 A 6 5 0.94 19 0.263
11 A 6 5 0.95 17 0.294
12 A 13 12 1.07 19 0.632
13 A 10 9 0.93 19 0.474
14 A 10 9 0.93 17 0.529
15 A 6 5 1.02 15 0.333
16 A 9 8 1.00 19 0.421
17 A 7 6 1.10 19 0.316
18 A 10 9 1.09 19 0.474
19 A 10 9 1.06 19 0.474
20 A 15 14 1.12 19 0.737
21 A 11 10 0.93 19 0.526
22 A 11 10 0.95 17 0.588
23 A 7 6 1.00 15 0.400
24 A 11 10 1.07 19 0.526
25 A 8 7 1.08 19 0.368
26 A 11 10 1.11 19 0.526
27 A 11 10 1.08 19 0.526
28 A 8 7 1.07 19 0.368
29 A 7 6 1.00 17 0.353
30 A 6 5 1.05 15 0.333
31 A 5 4 1.14 19 0.211
32 A 5 4 0.81 19 0.211
33 A 8 7 0.70 19 0.368
34 A 7 6 0.69 19 0.316
35 A 8 7 0.67 19 0.368
36 A 12 11 0.87 19 0.579
37 A 10 9 0.91 19 0.474
38 A 10 9 0.91 17 0.529
39 A 6 5 0.98 15 0.333
40 A 9 8 1.00 19 0.421
41 A 7 6 1.07 19 0.316
42 A 10 9 1.07 19 0.474
43 A 10 9 1.05 19 0.474
44 A 13 12 0.96 19 0.632
45 A 11 10 0.92 19 0.526
46 A 11 10 0.93 17 0.588
47 A 7 6 1.05 15 0.400
48 A 11 10 1.18 19 0.526
49 A 8 7 1.15 19 0.368
50 A 11 10 1.13 19 0.526
51 A 11 10 1.18 19 0.526
52 A 13 12 1.01 19 0.632
53 A 10 9 0.92 17 0.529
54 A 8 7 1.03 17 0.412
55 A 8 7 1.00 15 0.467
56 A 4 3 1.00 13 0.231
57 A 9 8 1.00 17 0.471
58 A 5 4 1.00 17 0.235
59 A 8 7 1.04 17 0.412
60 A 7 6 1.10 17 0.353
61 F 0 0 N/A 0.000 N/A
62 F 0 0 N/A 0.000 N/A
63 A 17 16 0.98 19 0.842
64 A 14 13 0.97 19 0.684
65 A 14 13 0.99 17 0.765
66 A 6 5 0.98 15 0.333
67 A 16 15 1.01 19 0.789
68 A 10 9 1.06 19 0.474
69 A 13 12 1.00 19 0.632
70 A 13 12 1.02 19 0.632
71 A 19 18 0.94 19 0.947
72 A 14 13 1.06 19 0.684
73 A 16 15 0.94 17 0.882
74 A 7 6 1.00 15 0.400
75 A 19 18 1.13 19 0.947
76 A 11 10 0.96 19 0.526
77 A 15 14 0.74 19 0.737
78 A 14 13 0.99 19 0.684
79 A 14 13 0.99 19 0.684
80 A 11 10 0.98 19 0.526
81 A 11 10 0.98 17 0.588
82 A 3 2 1.00 15 0.133
83 A 8 7 1.00 19 0.368
84 A 7 6 1.02 19 0.316
85 A 10 9 1.04 19 0.474
86 A 11 10 1.08 19 0.526
87 A 17 16 1.00 19 0.842
88 A 13 12 0.98 19 0.632
89 A 13 12 1.01 17 0.706
90 A 5 4 1.04 15 0.267
91 A 8 7 1.17 19 0.368
92 A 10 9 1.08 19 0.474
93 A 13 12 1.03 19 0.632
94 A 14 13 1.04 19 0.684
95 A 17 16 1.05 19 0.842
96 A 13 12 0.99 17 0.706
97 A 11 10 0.98 17 0.588
98 A 11 10 0.98 15 0.667
99 A 5 4 1.00 13 0.308
100 A 13 12 1.00 17 0.706
101 A 6 5 0.99 17 0.294
102 A 19 18 0.95 17 1.059
103 N/A 1 0 1.00 19 0.000
104 A 6 5 1.51 19 0.263
105 A 5 4 1.40 19 0.211
106 A 6 5 0.96 17 0.294
107 A 5 4 1.15 15 0.267
108 A 8 7 1.25 19 0.368
109 A 8 7 1.22 19 0.368
110 A 8 7 1.14 19 0.368
111 A 6 5 0.94 19 0.263
112 A 5 4 0.95 19 0.211
113 A 6 5 0.98 17 0.294
114 A 5 4 0.95 15 0.267
115 A 9 8 0.96 19 0.421
116 A 7 6 1.16 19 0.316
117 A 10 9 1.20 19 0.474
118 A 6 5 0.95 19 0.263
119 A 5 4 0.95 19 0.211
120 A 6 5 1.00 17 0.294
121 A 5 4 0.94 15 0.267
122 A 8 7 1.18 19 0.368
123 A 7 6 1.12 19 0.316
124 A 10 9 1.12 19 0.474
125 A 6 5 0.94 21 0.238
126 A 5 4 0.94 21 0.190
127 A 6 5 0.95 19 0.263
128 A 5 4 0.98 17 0.235
129 A 11 10 1.16 21 0.476
130 A 10 9 1.36 21 0.429
131 A 12 11 1.50 21 0.524
132 A 6 5 0.94 21 0.238
133 A 5 4 0.94 21 0.190
134 A 6 5 0.95 19 0.263
135 A 5 4 0.98 17 0.235
136 A 8 7 1.15 21 0.333
137 A 10 9 1.44 21 0.429
138 A 12 11 1.45 21 0.524
139 A 6 5 0.94 19 0.263
140 A 5 4 0.94 19 0.211
141 A 6 5 0.94 17 0.294
142 A 5 4 0.97 15 0.267
143 A 6 5 1.04 19 0.263
144 A 2 2 1.21 17 0.118
145 A 2 2 1.21 17 0.118
146 A 2 2 1.22 17 0.118
147 A 2 2 1.22 17 0.118
148 A 2 2 1.22 17 0.118
149 A 2 2 1.20 13 0.154
150 A 2 2 1.21 17 0.118
151 A 2 2 1.23 15 0.133
152 A 2 2 1.37 15 0.133
153 A 2 2 1.22 15 0.133
154 A 2 2 1.37 11 0.182
155 A 2 2 1.22 15 0.133
156 B 2 2 3.59 20 0.100
157 B 2 2 2.78 20 0.100
158 A 14 13 1.37 16 0.812
159 B 2 2 4.37 20 0.100
160 A 2 2 0.88 19 0.105
161 A 14 13 0.52 15 0.867
162 A 2 2 1.53 19 0.105
163 A 11 10 1.12 21 0.476
164 A 9 8 1.23 21 0.381
165 A 6 5 0.96 19 0.263
166 A 9 8 1.30 21 0.381
167 A 6 5 1.24 21 0.238
168 A 10 9 1.23 21 0.429
169 A 11 10 1.16 21 0.476
170 A 10 10 1.23 21 0.476
171 A 7 7 1.32 21 0.333
172 A 6 6 1.49 17 0.353
173 A 8 8 1.64 21 0.381
174 A 12 12 1.44 21 0.571
175 A 14 14 1.38 21 0.667
176 A 11 10 1.14 21 0.476
177 A 12 11 1.25 21 0.524
178 A 7 6 0.97 19 0.316
179 A 10 9 1.37 21 0.429
180 A 7 6 1.04 21 0.286
181 A 11 10 1.23 21 0.476
182 A 12 11 1.19 21 0.524
183 A 12 12 1.22 21 0.571
184 A 9 9 1.27 21 0.429
185 A 8 8 1.66 17 0.471
186 A 12 12 1.67 21 0.571
187 A 14 14 1.48 21 0.667
188 A 16 16 1.38 21 0.762
189 A 3 3 1.00 21 0.143
190 A 2 2 1.00 21 0.095
191 A 10 9 1.19 21 0.429
192 A 9 8 1.18 21 0.381
193 A 6 5 0.94 19 0.263
194 A 9 8 1.30 21 0.381
195 A 6 5 1.23 21 0.238
196 A 9 8 1.23 21 0.381
197 A 9 9 1.02 21 0.429
198 A 7 7 1.04 21 0.333
199 A 6 6 1.28 17 0.353
200 A 8 8 1.42 21 0.381
201 A 10 10 1.20 21 0.476
202 A 10 9 1.14 21 0.429
203 A 13 12 1.10 21 0.571
204 A 7 6 1.02 19 0.316
205 A 10 9 1.25 21 0.429
206 A 7 6 0.93 21 0.286
207 A 12 11 1.11 21 0.524
208 A 13 13 1.04 21 0.619
209 A 10 10 1.36 21 0.476
210 A 8 8 1.44 17 0.471
211 A 10 10 1.61 21 0.476
212 A 13 13 1.20 21 0.619
213 F 0 0 N/A 0.000 N/A
214 A 4 3 1.00 17 0.176
215 F 0 0 N/A 0.000 N/A
216 F 0 0 N/A 0.000 N/A
217 F 0 0 N/A 0.000 N/A
218 A 5 5 1.09 19 0.263
219 A 5 5 1.10 15 0.333
220 A 5 5 1.09 19 0.263
221 A 5 5 1.09 19 0.263
222 A 5 5 1.08 21 0.238
223 A 2 2 1.00 17 0.118
224 A 2 2 1.00 17 0.118
225 A 2 2 1.00 15 0.133
226 A 2 2 1.00 17 0.118
227 A 2 2 1.00 17 0.118
228 A 2 2 1.00 17 0.118
229 A 2 2 1.00 17 0.118
230 A 2 2 1.00 17 0.118
231 A 1 1 1.00 13 0.077
232 A 2 2 1.00 17 0.118
233 A 2 2 1.00 17 0.118
234 A 8 7 0.78 19 0.368
235 A 7 6 0.81 19 0.316
236 A 5 4 1.06 17 0.235
237 A 2 2 1.11 19 0.105
238 A 2 2 1.09 19 0.105
239 A 2 2 1.41 19 0.105
240 A 2 2 1.47 19 0.105
241 A 2 2 1.31 19 0.105
242 A 2 2 0.43 15 0.133
243 A 2 2 1.32 19 0.105
244 A 6 5 0.94 23 0.217
245 A 7 6 0.95 23 0.261
246 A 5 4 0.97 21 0.190
247 A 14 13 1.14 23 0.565
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 F 0 0 N/A 0.000 N/A
252 F 0 0 N/A 0.000 N/A
253 F 0 0 N/A 0.000 N/A
254 F 0 0 N/A 0.000 N/A
255 A 6 5 0.94 23 0.217
256 A 7 6 0.95 23 0.261
257 A 5 4 0.97 21 0.190
258 A 17 16 1.03 23 0.696
259 F 0 0 N/A 0.000 N/A
260 F 0 0 N/A 0.000 N/A
261 F 0 0 N/A 0.000 N/A
262 F 0 0 N/A 0.000 N/A
263 F 0 0 N/A 0.000 N/A
264 F 0 0 N/A 0.000 N/A
265 F 0 0 N/A 0.000 N/A
266 A 1 1 1.00 17 0.059
267 A 1 1 1.00 15 0.067
268 A 1 1 1.00 15 0.067
269 A 1 1 1.06 25 0.040
270 A 6 5 0.94 23 0.217
271 A 7 6 0.95 23 0.261
272 A 5 4 0.97 21 0.190
273 A 10 9 1.15 23 0.391
274 F 0 0 N/A 0.000 N/A
275 F 0 0 N/A 0.000 N/A
276 F 0 0 N/A 0.000 N/A
277 F 0 0 N/A 0.000 N/A
278 F 0 0 N/A 0.000 N/A
279 F 0 0 N/A 0.000 N/A
280 A 6 5 0.94 23 0.217
281 A 7 6 0.95 23 0.261
282 A 5 4 0.96 21 0.190
283 A 12 11 1.27 23 0.478
284 F 0 0 N/A 0.000 N/A
285 F 0 0 N/A 0.000 N/A
286 F 0 0 N/A 0.000 N/A
287 F 0 0 N/A 0.000 N/A
288 F 0 0 N/A 0.000 N/A
289 F 0 0 N/A 0.000 N/A
290 A 6 5 0.94 21 0.238
291 A 7 6 0.96 21 0.286
292 A 5 4 0.97 19 0.211
293 A 7 6 1.00 21 0.286
294 A 8 7 1.53 21 0.333
295 F 0 0 N/A 0.000 N/A
296 F 0 0 N/A 0.000 N/A
297 F 0 0 N/A 0.000 N/A
298 F 0 0 N/A 0.000 N/A
299 F 0 0 N/A 0.000 N/A
300 A 9 8 1.52 19 0.421
301 A 6 5 1.55 17 0.294
302 A 5 4 1.06 21 0.190
303 A 5 4 0.97 21 0.190
304 A 5 4 0.94 21 0.190
305 A 4 3 0.94 21 0.143
306 A 13 12 1.13 19 0.632
307 A 8 7 1.49 17 0.412
308 A 8 7 1.03 21 0.333
309 A 5 4 1.00 21 0.190
310 A 9 8 1.04 21 0.381
311 A 10 9 1.04 21 0.429
312 A 7 6 0.73 17 0.353
313 A 8 7 0.75 17 0.412
314 A 5 5 1.08 19 0.263
315 A 5 5 1.09 17 0.294
316 A 9 8 1.24 21 0.381
317 A 5 5 1.08 21 0.238
318 A 5 5 1.08 21 0.238
319 A 5 5 1.07 19 0.263
320 A 5 5 1.08 17 0.294
321 A 10 9 1.27 21 0.429
322 A 5 5 1.07 21 0.238
323 A 5 5 1.07 21 0.238
324 A 5 5 1.08 19 0.263
325 A 5 5 1.09 17 0.294
326 A 9 8 1.24 21 0.381
327 A 5 5 1.08 21 0.238
328 A 5 5 1.08 21 0.238
329 A 5 5 1.07 19 0.263
330 A 5 5 1.08 17 0.294
331 A 10 9 1.19 21 0.429
332 A 5 5 1.07 21 0.238
333 A 5 5 1.07 21 0.238
334 A 5 5 1.09 17 0.294
335 A 5 5 1.10 15 0.333
336 F 0 0 N/A 0.000 N/A
337 A 5 5 1.09 19 0.263
338 A 5 5 1.08 19 0.263
339 A 5 5 1.08 21 0.238
340 A 8 7 0.89 25 0.280
341 A 6 5 0.92 25 0.200
342 A 5 4 1.00 23 0.174
343 A 6 5 1.00 22 0.227
344 A 6 5 0.99 25 0.200
345 A 6 5 0.99 25 0.200
346 A 6 5 0.77 23 0.217
347 A 6 5 0.82 23 0.217
348 A 3 3 1.00 21 0.143
349 A 5 4 1.00 20 0.200
350 A 5 4 1.00 23 0.174
351 A 5 4 1.00 23 0.174
352 F 0 0 N/A 0.000 N/A
353 F 0 0 N/A 0.000 N/A
354 A 7 6 1.42 23 0.261
355 F 0 0 N/A 0.000 N/A
356 F 0 0 N/A 0.000 N/A
357 F 0 0 N/A 0.000 N/A
358 A 12 11 1.26 25 0.440
359 A 9 8 1.37 25 0.320
360 A 8 7 1.45 23 0.304
361 F 0 0 N/A 0.000 N/A
362 F 0 0 N/A 0.000 N/A
363 F 0 0 N/A 0.000 N/A
364 F 0 0 N/A 0.000 N/A
365 F 0 0 N/A 0.000 N/A
366 N/A 8 0 1.00 24 0.000
367 N/A 1 0 1.00 27 0.000
368 N/A 1 0 1.00 27 0.000
369 F 0 0 N/A 0.000 N/A
370 F 0 0 N/A 0.000 N/A
371 F 0 0 N/A 0.000 N/A
372 A 8 7 1.00 24 0.292
373 F 0 0 N/A 0.000 N/A
374 F 0 0 N/A 0.000 N/A
375 F 0 0 N/A 0.000 N/A
376 F 0 0 N/A 0.000 N/A
377 F 0 0 N/A 0.000 N/A
378 A 10 9 0.98 24 0.375
379 F 0 0 N/A 0.000 N/A
380 F 0 0 N/A 0.000 N/A
381 F 0 0 N/A 0.000 N/A
382 F 0 0 N/A 0.000 N/A
383 F 0 0 N/A 0.000 N/A
384 N/A 6 0 1.00 22 0.000
385 N/A 1 0 1.00 25 0.000
386 N/A 1 0 1.00 25 0.000

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