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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 [207] had the largest ratio of [2.60000000000000009]

# 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 5 1.03 20 0.250
2 A 7 7 1.07 20 0.350
3 A 7 7 1.07 20 0.350
4 A 4 4 1.05 20 0.200
5 A 4 4 1.08 18 0.222
6 A 7 7 0.97 20 0.350
7 A 9 9 1.08 20 0.450
8 A 12 12 1.05 20 0.600
9 A 14 14 1.07 20 0.700
10 A 4 4 1.00 8 0.500
11 A 6 6 1.25 8 0.750
12 A 9 9 1.07 8 1.125
13 A 2 2 1.00 22 0.091
14 A 17 17 1.21 22 0.773
15 A 13 12 1.09 22 0.545
16 A 7 7 1.03 22 0.318
17 A 5 4 0.94 20 0.200
18 A 2 2 1.00 22 0.091
19 A 2 2 1.00 22 0.091
20 A 2 2 1.00 22 0.091
21 A 2 2 1.00 22 0.091
22 A 2 2 1.00 22 0.091
23 A 13 13 1.29 22 0.591
24 A 13 13 1.24 22 0.591
25 A 6 6 1.06 22 0.273
26 A 6 6 1.11 20 0.300
27 A 2 2 1.00 22 0.091
28 A 2 2 1.00 22 0.091
29 A 2 2 1.00 22 0.091
30 A 2 2 1.00 22 0.091
31 N/A 3 0 1.00 14 0.000
32 A 10 9 1.42 14 0.643
33 A 9 8 1.35 14 0.571
34 A 8 7 1.34 14 0.500
35 A 7 6 1.25 12 0.500
36 N/A 3 0 1.00 14 0.000
37 N/A 3 0 1.00 14 0.000
38 N/A 1 0 1.00 20 0.000
39 A 8 7 1.10 20 0.350
40 A 7 6 1.07 20 0.300
41 A 6 5 1.02 20 0.250
42 A 3 3 1.00 18 0.167
43 N/A 1 0 1.00 20 0.000
44 N/A 1 0 1.00 20 0.000
45 N/A 1 0 1.00 22 0.000
46 A 11 10 1.31 22 0.455
47 A 10 9 1.19 22 0.409
48 A 6 6 1.09 22 0.273
49 A 5 4 1.00 20 0.200
50 N/A 1 0 1.00 22 0.000
51 N/A 1 0 1.00 22 0.000
52 A 17 16 1.11 22 0.727
53 A 15 14 1.09 22 0.636
54 A 12 11 1.06 22 0.500
55 A 12 11 1.06 22 0.500
56 A 15 14 1.09 22 0.636
57 A 17 16 1.11 22 0.727
58 A 2 2 1.00 24 0.083
59 A 2 2 1.00 24 0.083
60 A 2 2 1.00 24 0.083
61 A 2 2 1.00 24 0.083
62 A 2 2 1.00 24 0.083
63 A 2 2 1.00 24 0.083
64 A 2 2 1.00 24 0.083
65 A 2 2 1.00 24 0.083
66 A 2 2 1.00 24 0.083
67 A 2 2 1.00 24 0.083
68 A 2 2 1.00 24 0.083
69 A 2 2 1.00 24 0.083
70 A 2 2 1.00 22 0.091
71 A 19 19 1.20 22 0.864
72 A 13 12 1.09 22 0.545
73 A 8 8 1.02 22 0.364
74 A 5 4 0.98 20 0.200
75 A 2 2 1.00 22 0.091
76 A 2 2 1.00 22 0.091
77 A 2 2 1.00 22 0.091
78 A 2 2 1.00 22 0.091
79 A 2 2 1.00 24 0.083
80 A 2 2 1.00 24 0.083
81 A 2 2 1.00 24 0.083
82 A 2 2 1.00 24 0.083
83 A 2 2 1.00 22 0.091
84 A 2 2 1.00 24 0.083
85 A 2 2 1.00 24 0.083
86 A 2 2 1.00 24 0.083
87 A 2 2 1.00 24 0.083
88 A 2 2 1.00 24 0.083
89 A 2 2 1.00 24 0.083
90 A 2 2 1.00 24 0.083
91 A 2 2 1.00 24 0.083
92 A 2 2 1.00 22 0.091
93 A 2 2 1.00 24 0.083
94 A 2 2 1.00 24 0.083
95 A 2 2 1.00 24 0.083
96 A 2 2 1.00 24 0.083
97 N/A 5 0 1.00 20 0.000
98 A 20 19 1.13 20 0.950
99 A 16 15 1.09 20 0.750
100 A 13 12 1.06 20 0.600
101 A 9 8 1.00 18 0.444
102 N/A 7 0 1.00 20 0.000
103 N/A 9 0 1.00 20 0.000
104 N/A 2 0 1.00 16 0.000
105 A 13 12 1.35 16 0.750
106 A 12 11 1.29 16 0.688
107 A 11 10 1.24 16 0.625
108 A 7 7 1.05 14 0.500
109 N/A 2 0 1.00 16 0.000
110 N/A 2 0 1.00 16 0.000
111 N/A 3 0 1.00 22 0.000
112 A 15 14 1.78 22 0.636
113 A 14 13 1.73 22 0.591
114 A 13 12 1.81 22 0.545
115 A 11 10 1.63 20 0.500
116 N/A 3 0 1.00 22 0.000
117 N/A 3 0 1.00 22 0.000
118 A 2 2 1.00 24 0.083
119 A 2 2 1.00 24 0.083
120 A 2 2 1.00 24 0.083
121 A 2 2 1.00 24 0.083
122 A 2 2 1.00 24 0.083
123 A 2 2 1.00 24 0.083
124 A 2 2 1.00 26 0.077
125 A 2 2 1.00 26 0.077
126 A 2 2 1.00 26 0.077
127 A 2 2 1.00 26 0.077
128 A 2 2 1.00 26 0.077
129 A 2 2 1.00 26 0.077
130 A 2 2 1.00 26 0.077
131 A 2 2 1.00 26 0.077
132 A 2 2 1.00 26 0.077
133 A 2 2 1.00 26 0.077
134 A 2 2 1.00 26 0.077
135 A 2 2 1.00 26 0.077
136 A 2 2 1.00 22 0.091
137 A 13 13 1.29 22 0.591
138 A 13 13 1.24 22 0.591
139 A 6 6 1.06 22 0.273
140 A 6 6 1.11 20 0.300
141 A 2 2 1.00 22 0.091
142 A 2 2 1.00 22 0.091
143 A 2 2 1.00 22 0.091
144 A 2 2 1.00 22 0.091
145 A 2 2 1.00 24 0.083
146 A 2 2 1.00 24 0.083
147 A 2 2 1.00 24 0.083
148 A 2 2 1.00 24 0.083
149 A 2 2 1.00 22 0.091
150 A 2 2 1.00 24 0.083
151 A 2 2 1.00 24 0.083
152 A 2 2 1.00 24 0.083
153 A 2 2 1.00 24 0.083
154 A 2 2 1.00 24 0.083
155 A 2 2 1.00 24 0.083
156 A 2 2 1.00 24 0.083
157 A 2 2 1.00 24 0.083
158 A 2 2 1.00 22 0.091
159 A 2 2 1.00 24 0.083
160 A 2 2 1.00 24 0.083
161 A 2 2 1.00 24 0.083
162 A 2 2 1.00 24 0.083
163 N/A 9 0 1.00 22 0.000
164 A 18 17 1.24 22 0.773
165 A 17 16 1.21 22 0.727
166 A 13 12 1.20 22 0.545
167 A 12 11 1.18 20 0.550
168 N/A 11 0 1.00 22 0.000
169 N/A 13 0 1.00 22 0.000
170 N/A 6 0 1.00 22 0.000
171 A 21 20 1.10 22 0.909
172 A 18 17 1.07 22 0.773
173 A 14 13 1.04 22 0.591
174 A 9 9 1.00 20 0.450
175 N/A 7 0 1.00 22 0.000
176 N/A 10 0 1.00 22 0.000
177 N/A 3 0 1.00 16 0.000
178 A 24 23 1.35 16 1.438
179 A 22 21 1.25 16 1.312
180 A 18 17 1.22 16 1.062
181 A 13 12 1.14 14 0.857
182 N/A 3 0 1.00 16 0.000
183 N/A 3 0 1.00 16 0.000
184 A 2 2 1.00 24 0.083
185 A 2 2 1.00 24 0.083
186 A 2 2 1.00 24 0.083
187 A 2 2 1.00 24 0.083
188 A 2 2 1.00 24 0.083
189 A 2 2 1.00 24 0.083
190 A 2 2 1.00 26 0.077
191 A 2 2 1.00 26 0.077
192 A 2 2 1.00 26 0.077
193 A 2 2 1.00 26 0.077
194 A 2 2 1.00 26 0.077
195 A 2 2 1.00 26 0.077
196 A 2 2 1.00 26 0.077
197 A 2 2 1.00 26 0.077
198 A 2 2 1.00 26 0.077
199 A 2 2 1.00 26 0.077
200 A 2 2 1.00 26 0.077
201 A 2 2 1.00 26 0.077
202 A 19 18 1.23 12 1.500
203 A 18 17 1.23 12 1.417
204 A 10 10 1.00 10 1.000
205 F 0 0 N/A 0.000 N/A
206 F 0 0 N/A 0.000 N/A
207 A 27 26 1.27 10 2.600
208 N/A 2 0 1.00 14 0.000
209 A 9 8 1.23 14 0.571
210 A 8 7 1.17 14 0.500
211 A 7 6 1.18 14 0.429
212 A 6 5 1.11 12 0.417
213 N/A 2 0 1.00 14 0.000
214 N/A 2 0 1.00 14 0.000
215 N/A 6 0 1.00 20 0.000
216 A 17 16 1.09 20 0.800
217 A 13 12 1.06 20 0.600
218 A 10 9 1.00 18 0.500
219 N/A 7 0 1.00 20 0.000
220 N/A 10 0 1.00 20 0.000
221 N/A 8 0 1.00 22 0.000
222 A 16 15 1.12 22 0.682
223 A 12 11 1.11 22 0.500
224 A 11 10 1.10 20 0.500
225 N/A 10 0 1.00 22 0.000
226 N/A 12 0 1.00 22 0.000
227 N/A 1 0 1.00 20 0.000
228 A 9 8 1.22 20 0.400
229 A 8 7 1.13 20 0.350
230 A 7 6 1.10 20 0.300
231 A 6 5 1.03 18 0.278
232 N/A 3 0 1.00 20 0.000
233 N/A 3 0 1.00 20 0.000
234 N/A 1 0 1.00 22 0.000
235 A 5 5 1.11 22 0.227
236 A 5 5 1.15 22 0.227
237 A 2 2 0.98 20 0.100
238 N/A 1 0 1.00 22 0.000
239 N/A 1 0 1.00 22 0.000
240 N/A 1 0 1.00 22 0.000
241 A 6 6 1.08 22 0.273
242 A 6 6 1.18 22 0.273
243 A 2 2 0.98 20 0.100
244 N/A 1 0 1.00 22 0.000
245 N/A 1 0 1.00 22 0.000
246 N/A 1 0 1.00 20 0.000
247 A 8 7 1.09 20 0.350
248 A 7 6 1.06 20 0.300
249 A 6 5 1.02 20 0.250
250 A 3 3 1.00 18 0.167
251 N/A 1 0 1.00 20 0.000
252 N/A 1 0 1.00 20 0.000
253 N/A 2 0 1.00 16 0.000
254 A 10 9 1.18 16 0.562
255 A 9 8 1.16 16 0.500
256 A 5 5 1.00 14 0.357
257 N/A 2 0 1.00 16 0.000
258 N/A 2 0 1.00 16 0.000
259 N/A 5 0 1.00 22 0.000
260 A 17 16 1.07 22 0.727
261 A 14 13 1.03 22 0.591
262 A 8 8 1.00 20 0.400
263 N/A 7 0 1.00 22 0.000
264 N/A 9 0 1.00 22 0.000
265 N/A 1 0 1.00 22 0.000
266 A 6 6 1.08 22 0.273
267 A 6 6 1.11 22 0.273
268 A 6 6 1.16 22 0.273
269 A 2 2 1.07 20 0.100
270 N/A 1 0 1.00 22 0.000
271 N/A 1 0 1.00 22 0.000
272 N/A 1 0 1.00 24 0.000
273 A 11 10 1.36 24 0.417
274 A 10 9 1.28 24 0.375
275 A 6 6 1.26 22 0.273
276 N/A 3 0 1.00 24 0.000
277 N/A 3 0 1.00 24 0.000
278 N/A 1 0 1.00 24 0.000
279 A 6 6 1.04 24 0.250
280 A 6 6 1.10 24 0.250
281 A 2 2 1.11 22 0.091
282 N/A 1 0 1.00 24 0.000
283 N/A 1 0 1.00 24 0.000
284 N/A 1 0 1.00 20 0.000
285 A 4 4 1.08 20 0.200
286 A 4 4 1.00 20 0.200
287 A 2 2 1.00 18 0.111
288 N/A 1 0 1.00 20 0.000
289 N/A 1 0 1.00 20 0.000
290 N/A 1 0 1.00 22 0.000
291 A 11 10 1.19 22 0.455
292 A 10 9 1.11 22 0.409
293 A 6 6 1.04 22 0.273
294 A 5 4 1.00 20 0.200
295 N/A 1 0 1.00 22 0.000
296 N/A 1 0 1.00 22 0.000
297 N/A 3 0 1.00 22 0.000
298 A 14 13 1.72 22 0.591
299 A 13 12 1.82 22 0.545
300 A 11 10 1.64 20 0.500
301 N/A 3 0 1.00 22 0.000
302 N/A 3 0 1.00 22 0.000
303 N/A 2 0 1.00 16 0.000
304 A 17 16 1.14 16 1.000
305 A 13 12 1.12 16 0.750
306 A 10 9 1.06 14 0.643
307 N/A 2 0 1.00 16 0.000
308 N/A 2 0 1.00 16 0.000
309 N/A 1 0 1.00 22 0.000
310 A 6 6 1.11 22 0.273
311 A 6 6 1.07 22 0.273
312 A 6 6 1.16 22 0.273
313 A 2 2 0.99 20 0.100
314 N/A 1 0 1.00 22 0.000
315 N/A 1 0 1.00 22 0.000
316 N/A 1 0 1.00 24 0.000
317 A 6 6 1.06 24 0.250
318 A 6 6 1.09 24 0.250
319 A 2 2 1.10 22 0.091
320 N/A 1 0 1.00 24 0.000
321 N/A 1 0 1.00 24 0.000
322 N/A 1 0 1.00 24 0.000
323 A 12 11 1.15 24 0.458
324 A 10 9 1.15 24 0.375
325 A 8 7 1.14 22 0.318
326 N/A 3 0 1.00 24 0.000
327 N/A 3 0 1.00 24 0.000
328 A 7 7 1.16 18 0.389
329 A 5 5 1.13 18 0.278
330 A 5 5 1.13 18 0.278
331 A 3 3 1.00 18 0.167
332 A 3 3 1.00 18 0.167
333 A 5 5 1.07 18 0.278
334 A 5 5 1.13 18 0.278
335 A 7 7 1.11 18 0.389
336 A 9 9 1.09 18 0.500
337 A 7 7 1.10 18 0.389
338 A 7 7 1.05 18 0.389
339 A 5 5 1.00 18 0.278
340 A 5 5 1.00 18 0.278
341 A 7 7 1.10 18 0.389
342 A 7 7 1.10 18 0.389
343 A 9 9 1.13 18 0.500
344 A 7 7 1.15 18 0.389
345 A 5 5 1.12 18 0.278
346 A 5 5 1.12 18 0.278
347 A 3 3 1.00 18 0.167
348 A 3 3 1.00 18 0.167
349 A 5 5 1.06 18 0.278
350 A 5 5 1.12 18 0.278
351 A 7 7 1.10 18 0.389
352 A 9 9 1.08 18 0.500
353 A 7 7 1.09 18 0.389
354 A 7 7 1.05 18 0.389
355 A 5 5 1.00 18 0.278
356 A 5 5 1.00 18 0.278
357 A 7 7 1.09 18 0.389
358 A 7 7 1.09 18 0.389
359 A 9 9 1.12 18 0.500
360 A 2 2 1.00 8 0.250
361 A 2 2 1.00 14 0.143
362 A 2 2 1.00 14 0.143
363 A 2 2 1.00 14 0.143
364 A 2 2 1.00 12 0.167
365 A 2 2 1.00 14 0.143
366 A 2 2 1.00 14 0.143
367 A 2 2 1.00 14 0.143
368 A 2 2 1.00 23 0.087
369 A 2 2 1.00 23 0.087
370 A 2 2 1.00 23 0.087
371 A 2 2 1.00 21 0.095
372 A 2 2 1.00 23 0.087
373 A 2 2 1.00 23 0.087
374 A 2 2 1.00 23 0.087
375 A 2 2 1.00 23 0.087
376 A 2 2 1.00 25 0.080
377 A 2 2 1.00 25 0.080
378 A 2 2 1.00 23 0.087
379 N/A 2 0 1.00 25 0.000
380 N/A 2 0 1.00 25 0.000
381 N/A 2 0 1.00 25 0.000
382 A 2 2 1.00 23 0.087
383 A 2 2 1.00 23 0.087
384 A 2 2 1.00 23 0.087
385 A 2 2 1.00 21 0.095
386 N/A 2 0 1.00 23 0.000
387 N/A 2 0 1.00 23 0.000
388 N/A 2 0 1.00 23 0.000
389 A 2 2 1.00 25 0.080
390 A 2 2 1.00 25 0.080
391 A 2 2 1.00 23 0.087
392 N/A 2 0 1.00 25 0.000
393 N/A 2 0 1.00 25 0.000
394 N/A 2 0 1.00 25 0.000
395 A 2 2 1.00 8 0.250
396 A 2 2 1.00 10 0.200
397 A 2 2 1.00 10 0.200

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