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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 [34] had the largest ratio of [.636399999999999966]

# 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 2 1 1.00 17 0.059
2 A 2 1 1.00 17 0.059
3 A 2 1 1.00 17 0.059
4 A 2 1 1.00 15 0.067
5 A 7 7 1.00 17 0.412
6 A 7 7 1.00 17 0.412
7 A 8 8 1.00 17 0.471
8 A 2 1 1.00 19 0.053
9 A 2 1 1.00 19 0.053
10 A 2 1 1.00 17 0.059
11 A 8 7 1.00 19 0.368
12 A 9 8 1.00 19 0.421
13 A 8 8 1.00 19 0.421
14 A 8 7 1.00 19 0.368
15 A 8 7 1.00 19 0.368
16 A 8 7 1.00 19 0.368
17 A 7 7 1.00 17 0.412
18 A 13 7 1.00 19 0.368
19 A 14 8 1.00 19 0.421
20 A 9 8 1.00 19 0.421
21 A 9 8 1.00 19 0.421
22 A 9 8 1.00 19 0.421
23 A 9 8 1.00 19 0.421
24 A 7 7 1.00 17 0.412
25 A 14 8 1.00 19 0.421
26 A 15 9 1.00 19 0.474
27 A 3 3 1.00 20 0.150
28 A 2 2 1.00 20 0.100
29 A 2 2 1.00 20 0.100
30 A 2 2 1.00 20 0.100
31 A 3 3 1.00 20 0.150
32 A 4 3 1.00 20 0.150
33 A 5 3 1.00 20 0.150
34 A 22 14 1.00 22 0.636
35 A 21 13 1.00 22 0.591
36 A 14 8 1.00 22 0.364
37 A 17 11 1.00 22 0.500
38 A 21 13 1.00 22 0.591
39 A 22 14 1.00 22 0.636
40 A 4 4 1.00 22 0.182
41 A 3 3 1.00 22 0.136
42 A 3 3 1.00 22 0.136
43 A 3 3 1.00 22 0.136
44 A 3 2 1.00 22 0.091
45 A 4 3 1.00 22 0.136
46 A 5 4 1.00 22 0.182
47 A 6 4 1.00 22 0.182
48 A 4 4 1.00 22 0.182
49 A 4 4 1.00 22 0.182
50 A 4 4 1.00 22 0.182
51 A 4 4 1.00 22 0.182
52 A 4 4 1.00 22 0.182
53 A 4 4 1.00 22 0.182
54 A 4 4 1.00 22 0.182
55 A 4 4 1.00 22 0.182
56 A 4 3 1.00 19 0.158
57 A 3 3 1.00 19 0.158
58 A 2 2 1.00 19 0.105
59 A 2 2 1.00 19 0.105
60 A 2 2 1.00 19 0.105
61 A 3 3 1.00 19 0.158
62 A 4 3 1.00 19 0.158
63 A 5 3 1.00 19 0.158
64 A 3 3 1.00 19 0.158
65 A 3 3 1.00 19 0.158
66 A 3 3 1.00 19 0.158
67 A 3 3 1.00 19 0.158
68 A 3 3 1.00 19 0.158
69 A 3 3 1.00 19 0.158
70 A 5 4 1.00 21 0.190
71 A 4 4 1.00 21 0.190
72 A 3 3 1.00 21 0.143
73 A 3 3 1.00 21 0.143
74 A 3 3 1.00 21 0.143
75 A 3 2 1.00 21 0.095
76 A 4 3 1.00 21 0.143
77 A 5 4 1.00 21 0.190
78 A 6 4 1.00 21 0.190
79 A 4 4 1.00 21 0.190
80 A 4 4 1.00 21 0.190
81 A 4 4 1.00 21 0.190
82 A 4 4 1.00 21 0.190
83 A 4 4 1.00 21 0.190
84 A 4 4 1.00 21 0.190
85 A 4 2 1.00 21 0.095
86 A 5 5 1.00 21 0.238
87 A 4 4 1.00 21 0.190
88 A 3 3 1.00 21 0.143
89 A 1 1 1.00 21 0.048
90 A 2 2 1.00 21 0.095
91 A 4 4 1.00 21 0.190
92 A 5 4 1.00 21 0.190
93 A 2 2 1.00 21 0.095
94 A 2 2 1.00 21 0.095
95 A 2 2 1.00 21 0.095
96 A 2 2 1.00 21 0.095
97 A 2 2 1.00 21 0.095
98 A 5 5 1.00 21 0.238
99 A 4 4 1.00 21 0.190
100 A 2 2 1.00 21 0.095
101 A 2 2 1.00 21 0.095
102 A 4 4 1.00 21 0.190
103 A 5 4 1.00 21 0.190
104 A 2 2 1.00 21 0.095
105 A 2 2 1.00 21 0.095
106 A 2 2 1.00 21 0.095
107 A 2 2 1.00 21 0.095
108 A 2 2 1.00 21 0.095
109 A 7 6 1.00 21 0.286
110 A 6 6 1.00 21 0.286
111 A 5 5 1.00 21 0.238
112 A 3 2 1.00 21 0.095
113 A 3 3 1.00 21 0.143
114 A 4 4 1.00 21 0.190
115 A 5 4 1.00 21 0.190
116 A 6 4 1.00 21 0.190
117 A 2 2 1.00 21 0.095
118 A 2 2 1.00 21 0.095
119 A 2 2 1.00 21 0.095
120 A 2 2 1.00 21 0.095
121 A 2 2 1.00 21 0.095
122 A 3 2 1.00 23 0.087
123 A 3 2 1.00 23 0.087
124 A 2 2 1.00 23 0.087
125 A 2 2 1.00 23 0.087
126 A 1 1 1.00 23 0.043
127 A 1 1 1.00 23 0.043
128 A 1 1 1.00 23 0.043
129 A 2 2 1.00 23 0.087
130 A 2 2 1.00 23 0.087
131 A 3 2 1.00 23 0.087
132 A 3 2 1.00 23 0.087
133 A 3 2 1.00 19 0.105
134 A 4 4 1.05 19 0.210
135 A 3 3 1.01 17 0.176
136 A 2 2 1.00 19 0.105
137 A 2 2 1.00 19 0.105
138 A 5 5 1.00 19 0.263
139 A 4 4 1.00 19 0.210
140 A 3 3 0.91 17 0.176
141 A 2 2 1.00 9 0.222
142 A 2 2 1.00 19 0.105
143 A 2 2 1.00 19 0.105
144 A 2 2 1.00 19 0.105
145 A 1 1 1.00 50 0.020
146 A 2 1 1.00 17 0.059
147 A 2 1 1.00 17 0.059
148 A 2 1 1.00 17 0.059
149 A 2 1 1.00 15 0.067
150 A 10 7 1.00 17 0.412
151 A 10 7 1.00 17 0.412
152 A 11 8 1.00 17 0.471
153 A 2 1 1.00 19 0.053
154 A 2 1 1.00 19 0.053
155 A 2 1 1.00 19 0.053
156 A 2 1 1.00 17 0.059
157 A 11 7 1.00 19 0.368
158 A 12 8 1.00 19 0.421
159 A 11 8 1.00 19 0.421
160 A 11 7 1.00 19 0.368
161 A 11 7 1.00 19 0.368
162 A 11 7 1.00 19 0.368
163 A 10 7 1.00 17 0.412
164 A 19 7 1.00 19 0.368
165 A 20 8 1.00 19 0.421
166 A 12 8 1.00 19 0.421
167 A 12 8 1.00 19 0.421
168 A 12 8 1.00 19 0.421
169 A 12 8 1.00 19 0.421
170 A 10 7 1.00 17 0.412
171 A 20 8 1.00 19 0.421
172 A 21 9 1.00 19 0.474
173 A 10 8 1.00 23 0.348
174 A 9 7 1.00 23 0.304
175 A 8 6 1.00 23 0.261
176 A 5 3 1.00 23 0.130
177 A 9 7 1.00 23 0.304
178 A 10 8 1.00 23 0.348
179 A 10 6 1.00 21 0.286
180 A 9 5 1.00 21 0.238
181 A 7 4 1.00 21 0.190
182 A 10 6 1.00 21 0.286
183 A 11 7 1.00 21 0.333
184 A 11 8 1.00 23 0.348
185 A 10 8 1.00 23 0.348
186 A 9 7 1.00 23 0.304
187 A 9 7 1.00 23 0.304
188 A 9 7 1.00 23 0.304
189 A 10 8 1.00 23 0.348
190 A 11 8 1.00 23 0.348
191 A 4 4 1.00 25 0.160
192 A 1 1 1.00 25 0.040
193 A 10 9 1.00 21 0.429
194 A 9 8 1.00 21 0.381
195 A 4 4 1.00 21 0.190
196 A 5 5 1.00 21 0.238
197 A 7 7 1.00 21 0.333
198 A 8 7 1.00 21 0.333
199 A 11 10 1.00 21 0.476
200 A 10 9 1.00 21 0.429
201 A 4 3 1.00 21 0.143
202 A 9 8 1.00 21 0.381
203 A 10 9 1.00 21 0.429
204 A 11 10 1.00 21 0.476
205 A 11 10 1.00 21 0.476
206 A 10 9 1.00 21 0.429
207 A 5 5 1.00 21 0.238
208 A 5 5 1.00 21 0.238
209 A 7 7 1.00 21 0.333
210 A 8 7 1.00 21 0.333
211 A 11 10 1.00 21 0.476
212 A 10 9 1.00 21 0.429
213 A 10 9 1.00 21 0.429
214 A 10 9 1.00 21 0.429
215 A 11 10 1.00 21 0.476
216 A 4 4 1.00 17 0.235
217 A 4 4 1.00 26 0.154
218 A 3 2 1.00 19 0.105
219 A 4 4 1.00 19 0.210
220 A 3 3 0.91 17 0.176
221 A 2 2 1.00 19 0.105
222 A 2 2 1.00 19 0.105
223 A 7 7 1.00 21 0.333
224 A 6 6 1.00 21 0.286
225 A 6 6 1.00 21 0.286
226 A 5 5 1.00 19 0.263
227 A 4 4 1.00 11 0.364
228 A 7 6 1.00 21 0.286
229 A 8 7 1.00 21 0.333
230 A 9 7 1.00 21 0.333
231 A 7 7 1.00 21 0.333
232 A 7 6 1.00 21 0.286
233 A 6 5 1.00 19 0.263
234 A 5 5 1.00 11 0.454
235 A 7 6 1.00 21 0.286
236 A 8 7 1.00 21 0.333
237 A 9 7 1.00 21 0.333
238 A 8 7 1.00 21 0.333
239 A 8 6 1.00 21 0.286
240 A 7 5 1.00 19 0.263
241 A 6 5 1.00 11 0.454
242 A 8 7 1.00 21 0.333
243 A 8 7 1.00 21 0.333
244 A 9 8 1.00 21 0.381
245 A 5 5 1.00 21 0.238
246 A 5 5 1.00 21 0.238
247 A 4 4 1.00 19 0.210
248 A 4 4 1.00 11 0.364
249 A 7 6 1.00 21 0.286
250 A 8 7 1.00 21 0.333
251 A 9 7 1.00 21 0.333
252 A 5 5 1.00 21 0.238
253 A 5 5 0.99 21 0.238
254 A 5 5 1.00 19 0.263
255 A 5 5 1.00 11 0.454
256 A 8 7 1.00 21 0.333
257 A 9 8 1.00 21 0.381
258 A 10 8 1.00 21 0.381
259 A 5 5 1.00 21 0.238
260 A 6 6 0.99 21 0.286
261 A 6 5 1.00 19 0.263
262 A 6 5 1.00 11 0.454
263 A 9 7 1.00 21 0.333
264 A 10 8 1.00 21 0.381
265 A 11 8 1.00 21 0.381
266 A 8 8 1.00 23 0.348
267 A 4 4 1.00 23 0.174
268 A 5 5 1.00 23 0.217
269 A 3 3 1.00 19 0.158
270 A 3 3 1.00 17 0.176
271 A 6 6 1.00 23 0.261
272 A 7 7 1.00 23 0.304
273 A 7 7 1.00 23 0.304
274 A 4 3 1.00 19 0.158
275 A 8 8 1.00 17 0.471
276 A 3 2 1.00 21 0.095
277 A 3 2 1.00 17 0.118
278 A 4 4 1.00 17 0.235
279 A 9 9 1.00 17 0.529
280 A 4 3 1.00 17 0.176
281 A 3 3 1.00 24 0.125
282 A 3 3 1.00 24 0.125
283 A 3 3 1.00 20 0.150
284 A 2 1 1.00 17 0.059
285 A 2 1 1.00 17 0.059
286 A 2 1 1.00 17 0.059
287 A 2 1 1.00 15 0.067
288 A 2 2 1.00 17 0.118
289 A 2 2 1.00 17 0.118
290 A 2 2 1.00 17 0.118
291 A 2 2 1.00 17 0.118
292 A 2 1 1.00 19 0.053
293 A 2 1 1.00 19 0.053
294 A 2 1 1.00 17 0.059
295 A 3 3 1.00 19 0.158
296 A 3 3 1.00 19 0.158
297 A 3 3 1.00 19 0.158
298 A 5 4 1.00 19 0.210
299 A 4 4 1.00 19 0.210
300 A 3 3 1.00 19 0.158
301 A 2 2 1.00 17 0.118
302 A 3 2 1.00 19 0.105
303 A 4 3 1.00 19 0.158
304 A 5 4 1.00 19 0.210
305 A 5 4 1.00 19 0.210
306 A 4 4 1.00 19 0.210
307 A 3 3 1.00 19 0.158
308 A 2 2 1.00 17 0.118
309 A 4 3 1.00 19 0.158
310 A 5 4 1.00 19 0.210
311 A 6 4 1.00 19 0.210
312 A 3 2 1.00 19 0.105
313 A 5 5 1.00 19 0.263
314 A 4 4 0.98 19 0.210
315 A 3 3 0.91 17 0.176
316 A 2 2 1.00 9 0.222
317 A 2 2 1.00 19 0.105
318 A 2 2 1.00 19 0.105
319 A 2 2 1.00 19 0.105
320 A 1 1 1.00 28 0.036
321 A 4 2 1.00 25 0.080
322 A 3 2 1.00 25 0.080
323 A 2 2 1.00 23 0.087
324 A 1 1 1.00 15 0.067
325 A 1 1 1.00 23 0.043
326 A 1 1 1.00 25 0.040
327 A 1 1 1.00 25 0.040
328 A 2 2 0.93 28 0.071
329 A 1 1 1.00 69 0.014
330 A 5 3 1.00 25 0.120
331 A 3 3 1.00 23 0.130
332 A 2 2 1.00 15 0.133
333 A 2 2 1.00 25 0.080
334 A 2 2 1.00 23 0.087
335 A 2 2 1.00 25 0.080
336 A 2 2 1.00 25 0.080
337 A 6 4 1.08 31 0.129
338 A 4 4 1.08 31 0.129
339 A 2 2 1.07 29 0.069
340 A 5 5 1.00 31 0.161
341 A 5 5 1.19 31 0.161
342 A 5 4 1.36 31 0.129
343 A 9 8 1.00 31 0.258
344 A 7 7 1.00 31 0.226
345 A 5 5 1.00 28 0.179
346 A 5 5 1.00 31 0.161
347 A 6 6 1.00 31 0.194
348 A 5 5 1.00 29 0.172
349 A 4 4 1.00 29 0.138
350 A 3 3 1.00 29 0.103
351 A 2 2 1.00 27 0.074
352 A 2 2 1.00 26 0.077
353 A 3 3 1.00 29 0.103
354 A 2 2 1.00 29 0.069
355 A 3 3 1.00 29 0.103
356 A 2 2 1.00 29 0.069
357 A 5 5 1.00 29 0.172
358 A 8 7 1.00 31 0.226
359 A 4 4 1.00 31 0.129
360 A 6 6 1.00 31 0.194
361 A 2 2 1.00 29 0.069
362 A 4 4 1.00 28 0.143
363 A 3 3 1.00 31 0.097
364 A 4 4 1.00 31 0.129
365 A 3 3 1.00 31 0.097
366 A 2 2 1.00 31 0.065
367 A 5 5 1.00 31 0.161
368 A 8 8 1.00 31 0.258
369 A 4 4 1.00 31 0.129
370 A 7 7 1.00 31 0.226
371 A 2 2 1.00 29 0.069
372 A 4 4 1.00 28 0.143
373 A 3 3 1.00 31 0.097
374 A 2 2 1.00 31 0.065
375 A 5 5 1.00 31 0.161
376 A 4 4 1.00 31 0.129
377 A 7 7 1.00 31 0.226
378 A 3 3 1.00 31 0.097
379 A 1 1 1.00 57 0.018
380 A 3 3 1.00 32 0.094
381 A 4 4 1.00 41 0.098
382 A 4 3 1.00 31 0.097
383 A 4 4 1.00 35 0.114
384 A 3 3 1.00 31 0.097
385 A 2 2 1.08 76 0.026

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