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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 [299] had the largest ratio of [.848485000000000045]

# 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 2 1.00 29 0.069
2 A 2 2 1.00 29 0.069
3 A 2 2 1.00 27 0.074
4 A 2 2 1.00 20 0.100
5 A 2 2 1.00 29 0.069
6 A 4 4 1.14 29 0.138
7 A 4 4 1.07 29 0.138
8 A 2 2 1.00 31 0.065
9 A 2 2 1.00 31 0.065
10 A 2 2 1.00 29 0.069
11 A 2 2 1.00 22 0.091
12 A 2 2 1.00 31 0.065
13 A 4 4 1.22 31 0.129
14 A 6 6 1.05 31 0.194
15 A 2 2 1.00 31 0.065
16 A 2 2 1.00 31 0.065
17 A 2 2 1.00 29 0.069
18 A 2 2 1.00 22 0.091
19 A 2 2 1.00 31 0.065
20 A 4 4 1.31 31 0.129
21 A 6 6 1.44 31 0.194
22 A 2 2 1.00 31 0.065
23 A 2 2 1.00 31 0.065
24 A 2 2 1.00 31 0.065
25 A 2 2 1.00 29 0.069
26 A 2 2 1.00 22 0.091
27 A 2 2 1.00 31 0.065
28 A 3 3 1.08 31 0.097
29 F 0 0 N/A 0.000 N/A
30 A 4 4 1.26 31 0.129
31 A 4 4 1.21 31 0.129
32 A 4 4 1.14 29 0.138
33 A 2 2 1.00 22 0.091
34 A 3 3 1.08 31 0.097
35 A 5 5 1.08 31 0.161
36 F 0 0 N/A 0.000 N/A
37 A 6 6 1.36 31 0.194
38 A 6 6 1.13 31 0.194
39 A 4 4 1.06 29 0.138
40 A 2 2 1.00 22 0.091
41 A 4 4 1.11 31 0.129
42 A 7 7 1.11 31 0.226
43 F 0 0 N/A 0.000 N/A
44 A 7 7 1.48 31 0.226
45 A 6 6 1.14 31 0.194
46 A 5 5 1.11 29 0.172
47 A 2 2 1.00 31 0.065
48 A 3 3 0.97 31 0.097
49 A 4 4 1.02 31 0.129
50 A 6 5 0.95 29 0.172
51 A 6 5 0.94 29 0.172
52 A 18 18 1.18 35 0.514
53 A 17 17 1.27 35 0.486
54 A 15 15 1.31 35 0.429
55 A 2 2 1.71 32 0.062
56 A 14 14 0.97 35 0.400
57 A 13 13 0.92 35 0.371
58 A 15 15 0.70 35 0.429
59 A 18 18 0.62 35 0.514
60 A 9 9 0.90 33 0.273
61 A 8 8 0.89 33 0.242
62 A 6 6 0.92 30 0.200
63 A 7 7 0.96 33 0.212
64 A 6 6 0.96 33 0.182
65 A 10 10 1.08 33 0.303
66 A 11 11 1.08 33 0.333
67 A 13 13 1.08 33 0.394
68 F 0 0 N/A 0.000 N/A
69 F 0 0 N/A 0.000 N/A
70 F 0 0 N/A 0.000 N/A
71 F 0 0 N/A 0.000 N/A
72 A 6 6 1.01 32 0.188
73 F 0 0 N/A 0.000 N/A
74 F 0 0 N/A 0.000 N/A
75 F 0 0 N/A 0.000 N/A
76 F 0 0 N/A 0.000 N/A
77 F 0 0 N/A 0.000 N/A
78 F 0 0 N/A 0.000 N/A
79 A 8 8 0.92 32 0.250
80 F 0 0 N/A 0.000 N/A
81 F 0 0 N/A 0.000 N/A
82 F 0 0 N/A 0.000 N/A
83 A 19 19 1.18 35 0.543
84 A 17 17 1.27 35 0.486
85 A 16 16 1.28 35 0.457
86 A 2 2 1.59 32 0.062
87 A 16 16 0.96 35 0.457
88 A 18 18 0.77 35 0.514
89 A 19 19 0.59 35 0.543
90 A 9 9 0.91 33 0.273
91 A 7 7 0.90 30 0.233
92 A 8 8 0.97 33 0.242
93 A 10 10 0.94 33 0.303
94 A 11 11 0.92 33 0.333
95 A 12 12 1.10 33 0.364
96 A 13 13 1.09 33 0.394
97 F 0 0 N/A 0.000 N/A
98 F 0 0 N/A 0.000 N/A
99 A 9 9 0.95 32 0.281
100 F 0 0 N/A 0.000 N/A
101 F 0 0 N/A 0.000 N/A
102 F 0 0 N/A 0.000 N/A
103 F 0 0 N/A 0.000 N/A
104 F 0 0 N/A 0.000 N/A
105 B 21 21 2.14 32 0.656
106 F 0 0 N/A 0.000 N/A
107 F 0 0 N/A 0.000 N/A
108 F 0 0 N/A 0.000 N/A
109 F 0 0 N/A 0.000 N/A
110 A 16 16 1.23 35 0.457
111 A 14 14 1.30 35 0.400
112 A 12 12 1.36 35 0.343
113 A 2 2 1.86 32 0.062
114 A 11 11 0.99 35 0.314
115 A 12 12 0.91 35 0.343
116 A 7 7 0.90 33 0.212
117 A 6 6 0.92 33 0.182
118 A 5 5 0.93 30 0.167
119 A 5 5 0.98 33 0.152
120 A 7 7 1.15 33 0.212
121 A 9 9 1.10 33 0.273
122 A 10 10 1.10 33 0.303
123 F 0 0 N/A 0.000 N/A
124 F 0 0 N/A 0.000 N/A
125 F 0 0 N/A 0.000 N/A
126 A 1 1 1.00 32 0.031
127 F 0 0 N/A 0.000 N/A
128 F 0 0 N/A 0.000 N/A
129 F 0 0 N/A 0.000 N/A
130 F 0 0 N/A 0.000 N/A
131 F 0 0 N/A 0.000 N/A
132 F 0 0 N/A 0.000 N/A
133 A 12 12 1.28 32 0.375
134 F 0 0 N/A 0.000 N/A
135 F 0 0 N/A 0.000 N/A
136 F 0 0 N/A 0.000 N/A
137 A 14 14 1.53 35 0.400
138 A 13 13 1.68 35 0.371
139 A 2 2 1.94 32 0.062
140 A 16 16 1.34 35 0.457
141 A 16 16 1.23 35 0.457
142 A 19 19 1.00 35 0.543
143 A 8 8 1.06 33 0.242
144 A 7 7 1.14 33 0.212
145 A 6 6 1.26 30 0.200
146 A 9 9 1.44 33 0.273
147 A 11 11 1.33 33 0.333
148 A 13 13 1.25 33 0.394
149 F 0 0 N/A 0.000 N/A
150 F 0 0 N/A 0.000 N/A
151 A 3 3 1.00 32 0.094
152 F 0 0 N/A 0.000 N/A
153 F 0 0 N/A 0.000 N/A
154 F 0 0 N/A 0.000 N/A
155 F 0 0 N/A 0.000 N/A
156 F 0 0 N/A 0.000 N/A
157 B 22 22 2.84 32 0.688
158 F 0 0 N/A 0.000 N/A
159 F 0 0 N/A 0.000 N/A
160 F 0 0 N/A 0.000 N/A
161 F 0 0 N/A 0.000 N/A
162 F 0 0 N/A 0.000 N/A
163 A 6 6 1.19 33 0.182
164 A 9 9 1.03 34 0.265
165 A 9 9 1.03 34 0.265
166 A 9 9 1.03 35 0.257
167 A 14 14 1.47 35 0.400
168 A 12 12 1.55 35 0.343
169 A 2 2 1.60 32 0.062
170 A 11 11 1.69 35 0.314
171 A 14 14 1.95 35 0.400
172 A 16 16 1.82 35 0.457
173 A 17 17 1.71 35 0.486
174 A 9 9 0.93 33 0.273
175 A 7 7 0.96 33 0.212
176 A 5 5 0.94 33 0.152
177 A 4 4 1.00 30 0.133
178 A 6 6 1.19 33 0.182
179 A 8 8 1.14 33 0.242
180 A 9 9 1.12 33 0.273
181 F 0 0 N/A 0.000 N/A
182 F 0 0 N/A 0.000 N/A
183 F 0 0 N/A 0.000 N/A
184 F 0 0 N/A 0.000 N/A
185 A 3 3 0.47 32 0.094
186 F 0 0 N/A 0.000 N/A
187 F 0 0 N/A 0.000 N/A
188 F 0 0 N/A 0.000 N/A
189 F 0 0 N/A 0.000 N/A
190 F 0 0 N/A 0.000 N/A
191 F 0 0 N/A 0.000 N/A
192 F 0 0 N/A 0.000 N/A
193 A 8 8 1.05 32 0.250
194 F 0 0 N/A 0.000 N/A
195 F 0 0 N/A 0.000 N/A
196 F 0 0 N/A 0.000 N/A
197 F 0 0 N/A 0.000 N/A
198 F 0 0 N/A 0.000 N/A
199 F 0 0 N/A 0.000 N/A
200 F 0 0 N/A 0.000 N/A
201 F 0 0 N/A 0.000 N/A
202 F 0 0 N/A 0.000 N/A
203 F 0 0 N/A 0.000 N/A
204 A 18 18 1.64 36 0.500
205 A 17 17 1.68 36 0.472
206 A 2 2 1.92 33 0.061
207 A 17 17 1.67 36 0.472
208 A 20 20 1.71 36 0.556
209 A 23 23 1.68 36 0.639
210 A 25 25 1.63 36 0.694
211 A 10 10 1.06 34 0.294
212 A 9 9 1.06 34 0.265
213 A 8 8 1.02 34 0.235
214 A 7 7 1.00 31 0.226
215 A 9 9 1.03 34 0.265
216 A 12 12 1.05 34 0.353
217 A 14 14 1.06 34 0.412
218 F 0 0 N/A 0.000 N/A
219 F 0 0 N/A 0.000 N/A
220 F 0 0 N/A 0.000 N/A
221 F 0 0 N/A 0.000 N/A
222 A 3 3 1.00 33 0.091
223 F 0 0 N/A 0.000 N/A
224 F 0 0 N/A 0.000 N/A
225 F 0 0 N/A 0.000 N/A
226 F 0 0 N/A 0.000 N/A
227 F 0 0 N/A 0.000 N/A
228 F 0 0 N/A 0.000 N/A
229 F 0 0 N/A 0.000 N/A
230 A 11 11 1.01 33 0.333
231 F 0 0 N/A 0.000 N/A
232 F 0 0 N/A 0.000 N/A
233 A 14 14 1.62 35 0.400
234 A 13 13 1.70 35 0.371
235 A 11 11 1.80 35 0.314
236 B 2 2 3.10 32 0.062
237 A 13 13 1.99 35 0.371
238 B 17 17 2.15 35 0.486
239 B 18 18 2.08 35 0.514
240 A 8 8 1.09 33 0.242
241 A 6 6 1.12 33 0.182
242 A 5 5 1.17 33 0.152
243 A 3 3 1.00 30 0.100
244 A 9 9 1.36 33 0.273
245 A 10 10 1.33 33 0.303
246 A 11 11 1.33 33 0.333
247 F 0 0 N/A 0.000 N/A
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 A 6 6 1.00 32 0.188
253 F 0 0 N/A 0.000 N/A
254 F 0 0 N/A 0.000 N/A
255 F 0 0 N/A 0.000 N/A
256 F 0 0 N/A 0.000 N/A
257 F 0 0 N/A 0.000 N/A
258 F 0 0 N/A 0.000 N/A
259 F 0 0 N/A 0.000 N/A
260 A 15 15 1.58 32 0.469
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 F 0 0 N/A 0.000 N/A
267 F 0 0 N/A 0.000 N/A
268 F 0 0 N/A 0.000 N/A
269 F 0 0 N/A 0.000 N/A
270 A 19 19 1.58 36 0.528
271 A 18 18 1.67 36 0.500
272 B 2 2 2.17 33 0.061
273 A 20 20 1.75 36 0.556
274 A 22 22 1.65 36 0.611
275 A 11 11 1.01 34 0.324
276 A 10 10 1.03 34 0.294
277 A 9 9 1.05 34 0.265
278 A 8 8 1.05 31 0.258
279 A 11 11 1.10 34 0.324
280 A 13 13 1.05 34 0.382
281 A 9 9 1.03 27 0.333
282 A 8 8 1.05 27 0.296
283 A 4 4 1.00 27 0.148
284 A 9 9 1.08 24 0.375
285 A 11 11 1.09 27 0.407
286 A 13 13 1.04 27 0.481
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 F 0 0 N/A 0.000 N/A
291 A 16 16 1.33 33 0.485
292 F 0 0 N/A 0.000 N/A
293 F 0 0 N/A 0.000 N/A
294 F 0 0 N/A 0.000 N/A
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 A 28 28 1.65 33 0.848
300 F 0 0 N/A 0.000 N/A
301 F 0 0 N/A 0.000 N/A
302 F 0 0 N/A 0.000 N/A
303 F 0 0 N/A 0.000 N/A
304 F 0 0 N/A 0.000 N/A
305 F 0 0 N/A 0.000 N/A
306 F 0 0 N/A 0.000 N/A
307 F 0 0 N/A 0.000 N/A
308 F 0 0 N/A 0.000 N/A
309 F 0 0 N/A 0.000 N/A
310 F 0 0 N/A 0.000 N/A
311 F 0 0 N/A 0.000 N/A
312 F 0 0 N/A 0.000 N/A
313 F 0 0 N/A 0.000 N/A
314 F 0 0 N/A 0.000 N/A
315 F 0 0 N/A 0.000 N/A
316 F 0 0 N/A 0.000 N/A
317 F 0 0 N/A 0.000 N/A
318 F 0 0 N/A 0.000 N/A
319 A 8 7 1.03 34 0.206
320 F 0 0 N/A 0.000 N/A
321 F 0 0 N/A 0.000 N/A
322 F 0 0 N/A 0.000 N/A
323 F 0 0 N/A 0.000 N/A
324 F 0 0 N/A 0.000 N/A
325 F 0 0 N/A 0.000 N/A
326 A 9 8 1.56 34 0.235
327 F 0 0 N/A 0.000 N/A
328 F 0 0 N/A 0.000 N/A
329 F 0 0 N/A 0.000 N/A
330 F 0 0 N/A 0.000 N/A
331 F 0 0 N/A 0.000 N/A
332 F 0 0 N/A 0.000 N/A
333 F 0 0 N/A 0.000 N/A
334 F 0 0 N/A 0.000 N/A
335 F 0 0 N/A 0.000 N/A
336 F 0 0 N/A 0.000 N/A
337 F 0 0 N/A 0.000 N/A
338 F 0 0 N/A 0.000 N/A
339 F 0 0 N/A 0.000 N/A
340 A 3 2 1.00 34 0.059
341 F 0 0 N/A 0.000 N/A
342 F 0 0 N/A 0.000 N/A
343 F 0 0 N/A 0.000 N/A
344 F 0 0 N/A 0.000 N/A
345 F 0 0 N/A 0.000 N/A
346 F 0 0 N/A 0.000 N/A
347 F 0 0 N/A 0.000 N/A
348 F 0 0 N/A 0.000 N/A
349 F 0 0 N/A 0.000 N/A
350 F 0 0 N/A 0.000 N/A
351 F 0 0 N/A 0.000 N/A
352 F 0 0 N/A 0.000 N/A
353 F 0 0 N/A 0.000 N/A
354 F 0 0 N/A 0.000 N/A
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 F 0 0 N/A 0.000 N/A
359 F 0 0 N/A 0.000 N/A
360 F 0 0 N/A 0.000 N/A
361 F 0 0 N/A 0.000 N/A
362 A 3 2 1.02 34 0.059
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 F 0 0 N/A 0.000 N/A
367 F 0 0 N/A 0.000 N/A
368 F 0 0 N/A 0.000 N/A
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 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 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 F 0 0 N/A 0.000 N/A
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 F 0 0 N/A 0.000 N/A
385 F 0 0 N/A 0.000 N/A
386 F 0 0 N/A 0.000 N/A
387 F 0 0 N/A 0.000 N/A
388 F 0 0 N/A 0.000 N/A
389 F 0 0 N/A 0.000 N/A
390 F 0 0 N/A 0.000 N/A
391 F 0 0 N/A 0.000 N/A
392 F 0 0 N/A 0.000 N/A
393 F 0 0 N/A 0.000 N/A
394 F 0 0 N/A 0.000 N/A
395 F 0 0 N/A 0.000 N/A
396 F 0 0 N/A 0.000 N/A

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