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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [341] had the largest ratio of [36]

# 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 2 1.00 14 0.143
2 A 4 2 1.00 14 0.143
3 A 3 2 1.00 14 0.143
4 A 2 2 1.00 12 0.167
5 A 3 3 1.00 14 0.214
6 A 4 4 1.00 14 0.286
7 A 5 4 1.00 14 0.286
8 A 6 4 1.00 16 0.250
9 A 4 3 1.00 16 0.188
10 A 4 4 1.00 16 0.250
11 A 2 1 1.00 14 0.071
12 A 5 4 1.00 16 0.250
13 A 5 5 1.00 16 0.312
14 A 7 6 1.00 16 0.375
15 A 7 7 1.00 16 0.438
16 A 12 4 1.00 16 0.250
17 A 8 4 1.00 16 0.250
18 A 6 4 1.00 16 0.250
19 A 3 3 1.00 14 0.214
20 A 8 4 1.00 16 0.250
21 A 8 4 1.00 16 0.250
22 A 12 5 1.00 16 0.312
23 A 9 5 1.00 14 0.357
24 A 7 4 1.00 14 0.286
25 A 5 3 1.00 12 0.250
26 A 0 0 0.00 0 0.000
27 A 0 0 0.00 0 0.000
28 A 6 6 1.00 16 0.375
29 A 5 5 1.00 16 0.312
30 A 2 2 1.00 14 0.143
31 A 0 0 0.00 0 0.000
32 A 0 0 0.00 0 0.000
33 A 15 8 1.00 16 0.500
34 A 9 6 1.00 16 0.375
35 A 6 4 1.00 14 0.286
36 A 0 0 0.00 0 0.000
37 A 0 0 0.00 0 0.000
38 A 8 6 1.00 16 0.375
39 A 7 6 1.00 16 0.375
40 A 6 6 1.00 16 0.375
41 A 5 5 1.00 16 0.312
42 A 6 6 1.00 16 0.375
43 A 7 6 1.00 16 0.375
44 A 8 6 1.00 16 0.375
45 A 10 9 1.00 18 0.500
46 A 9 8 1.00 18 0.444
47 A 8 7 1.00 18 0.389
48 A 7 6 1.00 18 0.333
49 A 7 7 1.00 18 0.389
50 A 9 8 1.00 18 0.444
51 A 9 9 1.00 18 0.500
52 A 11 8 1.00 18 0.444
53 A 23 8 1.00 18 0.444
54 A 20 8 1.00 18 0.444
55 A 14 7 1.00 18 0.389
56 A 12 6 1.00 18 0.333
57 A 12 6 1.00 18 0.333
58 A 18 7 1.00 18 0.389
59 A 19 8 1.00 18 0.444
60 A 4 3 1.00 12 0.250
61 A 3 3 1.00 12 0.250
62 A 2 2 1.00 12 0.167
63 A 3 3 1.00 12 0.250
64 A 4 3 1.00 12 0.250
65 A 0 0 0.00 0 0.000
66 A 0 0 0.00 0 0.000
67 A 2 1 1.00 25 0.040
68 A 3 2 1.00 29 0.069
69 A 2 1 1.00 28 0.036
70 A 3 1 1.00 28 0.036
71 A 0 0 0.00 0 0.000
72 A 8 3 1.00 16 0.188
73 A 5 3 1.00 16 0.188
74 A 3 2 1.00 14 0.143
75 A 0 0 0.00 0 0.000
76 A 0 0 0.00 0 0.000
77 A 3 2 1.00 12 0.167
78 A 3 2 1.00 12 0.167
79 A 3 2 1.00 12 0.167
80 A 3 2 1.00 10 0.200
81 A 3 2 1.00 12 0.167
82 A 3 2 1.00 12 0.167
83 A 3 2 1.00 12 0.167
84 A 5 3 1.00 14 0.214
85 A 5 3 1.00 14 0.214
86 A 5 3 1.00 14 0.214
87 A 5 3 1.00 12 0.250
88 A 5 3 1.00 14 0.214
89 A 5 3 1.00 14 0.214
90 A 5 3 1.00 14 0.214
91 A 4 2 1.00 28 0.071
92 A 7 5 1.00 32 0.156
93 A 4 2 1.00 28 0.071
94 A 5 2 1.00 28 0.071
95 A 6 3 1.00 18 0.167
96 A 5 3 1.00 18 0.167
97 A 4 3 1.00 16 0.188
98 A 5 4 1.00 18 0.222
99 A 6 5 1.00 18 0.278
100 A 7 5 1.00 18 0.278
101 A 10 6 1.00 20 0.300
102 A 9 7 1.00 20 0.350
103 A 6 4 1.00 18 0.222
104 A 9 5 1.00 20 0.250
105 A 9 5 1.00 20 0.250
106 A 15 8 1.00 20 0.400
107 A 7 7 1.00 20 0.350
108 A 6 6 1.00 20 0.300
109 A 3 3 1.00 18 0.167
110 A 0 0 0.00 0 0.000
111 A 0 0 0.00 0 0.000
112 A 10 9 1.00 20 0.450
113 A 9 9 1.00 20 0.450
114 A 4 4 1.00 18 0.222
115 A 0 0 0.00 0 0.000
116 A 0 0 0.00 0 0.000
117 A 7 7 1.00 21 0.333
118 A 6 6 1.00 21 0.286
119 A 3 3 1.00 19 0.158
120 A 0 0 0.00 0 0.000
121 A 0 0 0.00 0 0.000
122 A 5 3 1.00 18 0.167
123 A 4 3 1.00 18 0.167
124 A 3 3 1.00 16 0.188
125 A 4 4 1.00 18 0.222
126 A 5 5 1.00 18 0.278
127 A 6 5 1.00 18 0.278
128 A 9 5 1.00 18 0.278
129 A 7 5 1.00 18 0.278
130 A 4 4 1.00 16 0.250
131 A 9 5 1.00 18 0.278
132 A 9 5 1.00 18 0.278
133 A 13 6 1.00 18 0.333
134 A 10 6 1.00 18 0.333
135 A 8 5 1.00 18 0.278
136 A 6 4 1.00 16 0.250
137 A 0 0 0.00 0 0.000
138 A 0 0 0.00 0 0.000
139 A 16 9 1.00 18 0.500
140 A 10 7 1.00 18 0.389
141 A 7 5 1.00 16 0.312
142 A 0 0 0.00 0 0.000
143 A 0 0 0.00 0 0.000
144 A 0 0 0.00 0 0.000
145 A 0 0 0.00 0 0.000
146 A 12 5 1.00 20 0.250
147 A 9 5 1.00 20 0.250
148 A 5 3 1.00 18 0.167
149 A 0 0 0.00 0 0.000
150 A 0 0 0.00 0 0.000
151 A 6 3 1.00 18 0.167
152 A 5 3 1.00 18 0.167
153 A 4 3 1.00 16 0.188
154 A 5 4 1.00 18 0.222
155 A 6 5 1.00 18 0.278
156 A 7 5 1.00 18 0.278
157 A 10 6 1.00 20 0.300
158 A 9 7 1.00 20 0.350
159 A 6 4 1.00 18 0.222
160 A 10 5 1.00 20 0.250
161 A 11 7 1.00 20 0.350
162 A 14 8 1.00 20 0.400
163 A 12 7 1.00 20 0.350
164 A 10 6 1.00 20 0.300
165 A 8 5 1.00 18 0.278
166 A 0 0 0.00 0 0.000
167 A 0 0 0.00 0 0.000
168 A 22 9 1.00 20 0.450
169 A 18 10 1.00 20 0.500
170 A 11 8 1.00 18 0.444
171 A 0 0 0.00 0 0.000
172 A 0 0 0.00 0 0.000
173 A 0 0 0.00 0 0.000
174 A 18 5 1.00 20 0.250
175 A 10 5 1.00 20 0.250
176 A 5 3 1.00 18 0.167
177 A 0 0 0.00 0 0.000
178 A 0 0 0.00 0 0.000
179 A 9 9 1.00 26 0.346
180 A 8 8 1.00 26 0.308
181 A 5 4 1.00 24 0.167
182 A 2 2 1.00 19 0.105
183 A 0 0 0.00 0 0.000
184 A 0 0 0.00 0 0.000
185 A 14 11 1.00 28 0.393
186 A 12 10 1.00 28 0.357
187 A 8 6 1.00 26 0.231
188 A 4 4 1.00 21 0.190
189 A 0 0 0.00 0 0.000
190 A 0 0 0.00 0 0.000
191 A 19 13 1.00 28 0.464
192 A 17 13 1.00 28 0.464
193 A 11 7 1.00 26 0.269
194 A 2 2 1.00 21 0.095
195 A 0 0 0.00 0 0.000
196 A 0 0 0.00 0 0.000
197 A 17 10 1.00 26 0.385
198 A 14 11 1.00 26 0.423
199 A 9 7 1.00 24 0.292
200 A 3 3 1.00 19 0.158
201 A 0 0 0.00 0 0.000
202 A 0 0 0.00 0 0.000
203 A 24 10 1.00 28 0.357
204 A 20 11 1.00 28 0.393
205 A 12 7 1.00 26 0.269
206 A 5 5 1.00 21 0.238
207 A 0 0 0.00 0 0.000
208 A 0 0 0.00 0 0.000
209 A 40 13 1.00 28 0.464
210 A 30 13 1.00 28 0.464
211 A 19 8 1.00 26 0.308
212 A 6 6 1.00 21 0.286
213 A 0 0 0.00 0 0.000
214 A 0 0 0.00 0 0.000
215 A 0 0 0.00 0 0.000
216 A 0 0 0.00 0 0.000
217 A 0 0 0.00 0 0.000
218 A 0 0 0.00 0 0.000
219 A 0 0 0.00 0 0.000
220 A 14 9 1.00 26 0.346
221 A 12 8 1.00 26 0.308
222 A 10 6 1.00 24 0.250
223 A 4 4 1.00 19 0.210
224 A 19 11 1.00 28 0.393
225 A 16 10 1.00 28 0.357
226 A 13 8 1.00 26 0.308
227 A 6 6 1.00 21 0.286
228 A 24 13 1.00 28 0.464
229 A 21 13 1.00 28 0.464
230 A 16 9 1.00 26 0.346
231 A 6 6 1.00 21 0.286
232 A 22 9 1.00 26 0.346
233 A 18 8 1.00 26 0.308
234 A 14 7 1.00 24 0.292
235 A 5 5 1.00 19 0.263
236 A 29 11 1.00 28 0.393
237 A 24 12 1.00 28 0.429
238 A 17 9 1.00 26 0.346
239 A 7 7 1.00 21 0.333
240 A 0 0 0.00 0 0.000
241 A 0 0 0.00 0 0.000
242 A 0 0 0.00 0 0.000
243 A 0 0 0.00 0 0.000
244 A 0 0 0.00 0 0.000
245 A 21 9 1.00 24 0.375
246 A 30 11 1.00 26 0.423
247 A 36 10 1.00 26 0.385
248 A 48 11 1.00 24 0.458
249 A 73 16 1.00 26 0.615
250 A 92 14 1.00 26 0.538
251 A 6 6 1.00 26 0.231
252 A 5 5 1.00 26 0.192
253 A 4 4 1.00 24 0.167
254 A 2 2 1.00 19 0.105
255 A 0 0 0.00 0 0.000
256 A 0 0 0.00 0 0.000
257 A 6 4 1.00 28 0.143
258 A 5 4 1.00 28 0.143
259 A 4 3 1.00 26 0.115
260 A 2 2 1.00 21 0.095
261 A 5 5 1.00 28 0.179
262 A 6 6 1.00 28 0.214
263 A 10 8 1.00 28 0.286
264 A 7 5 1.00 28 0.179
265 A 6 6 1.00 26 0.231
266 A 2 1 1.00 21 0.048
267 A 9 6 1.00 28 0.214
268 A 11 7 1.00 28 0.250
269 A 22 13 1.00 26 0.500
270 A 13 10 1.00 26 0.385
271 A 10 8 1.00 24 0.333
272 A 4 3 1.00 19 0.158
273 A 0 0 0.00 0 0.000
274 A 0 0 0.00 0 0.000
275 A 20 12 1.00 28 0.429
276 A 16 12 1.00 28 0.429
277 A 7 7 1.00 26 0.269
278 A 3 3 1.00 21 0.143
279 A 0 0 0.00 0 0.000
280 A 0 0 0.00 0 0.000
281 A 32 16 1.00 28 0.571
282 A 17 12 1.00 28 0.429
283 A 11 7 1.00 26 0.269
284 A 4 3 1.00 21 0.143
285 A 0 0 0.00 0 0.000
286 A 0 0 0.00 0 0.000
287 A 14 6 1.00 28 0.214
288 A 9 6 1.00 28 0.214
289 A 5 4 1.00 28 0.143
290 A 0 0 0.00 0 0.000
291 A 0 0 0.00 0 0.000
292 A 0 0 0.00 0 0.000
293 A 0 0 0.00 0 0.000
294 A 11 6 1.00 26 0.231
295 A 9 5 1.00 26 0.192
296 A 7 4 1.00 24 0.167
297 A 2 2 1.00 19 0.105
298 A 18 11 1.00 28 0.393
299 A 15 10 1.00 28 0.357
300 A 12 8 1.00 26 0.308
301 A 5 5 1.00 21 0.238
302 A 21 14 1.00 28 0.500
303 A 16 10 1.00 28 0.357
304 A 13 10 1.00 26 0.385
305 A 3 2 1.00 21 0.095
306 A 29 10 1.00 26 0.385
307 A 24 9 1.00 26 0.346
308 A 19 8 1.00 24 0.333
309 A 6 4 1.00 19 0.210
310 A 29 13 1.00 28 0.464
311 A 24 14 1.00 28 0.500
312 A 15 11 1.00 26 0.423
313 A 5 5 1.00 21 0.238
314 A 0 0 0.00 0 0.000
315 A 0 0 0.00 0 0.000
316 A 0 0 0.00 0 0.000
317 A 0 0 0.00 0 0.000
318 A 0 0 0.00 0 0.000
319 A 4 4 1.00 24 0.167
320 A 9 6 1.00 26 0.231
321 A 11 7 1.00 26 0.269
322 A 6 6 1.00 24 0.250
323 A 12 9 1.00 26 0.346
324 A 19 11 1.00 26 0.423
325 A 33 14 1.00 32 0.438
326 A 27 13 1.00 32 0.406
327 A 21 11 1.00 30 0.367
328 A 6 6 1.00 25 0.240
329 A 34 17 1.00 34 0.500
330 A 26 13 1.00 34 0.382
331 A 22 13 1.00 32 0.406
332 A 4 3 1.00 27 0.111
333 A 53 18 1.00 34 0.529
334 A 41 18 1.00 34 0.529
335 A 31 14 1.00 32 0.438
336 A 6 6 1.00 27 0.222
337 A 48 19 1.00 34 0.559
338 A 37 17 1.00 34 0.500
339 A 28 15 1.00 32 0.469
340 A 4 3 1.00 27 0.111
341 A 66 20 1.00 36 0.556
342 A 53 22 1.00 36 0.611
343 A 38 16 1.00 34 0.471
344 A 6 6 1.00 29 0.207
345 A 85 21 1.00 36 0.583
346 A 60 20 1.00 36 0.556
347 A 45 17 1.00 34 0.500
348 A 4 3 1.00 29 0.103

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