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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 [111] had the largest ratio of [25]

# 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 3 2 1.00 19 0.105
2 A 3 2 1.00 19 0.105
3 A 3 2 1.00 19 0.105
4 A 3 2 1.00 19 0.105
5 A 3 2 1.00 17 0.118
6 A 2 2 1.00 17 0.118
7 A 3 2 1.00 19 0.105
8 A 3 2 1.00 19 0.105
9 A 3 2 1.00 19 0.105
10 A 6 2 1.00 19 0.105
11 A 5 2 1.00 19 0.105
12 A 4 2 1.00 19 0.105
13 A 3 2 1.00 19 0.105
14 A 2 2 1.00 19 0.105
15 A 3 2 1.00 19 0.105
16 A 4 2 1.00 19 0.105
17 A 5 2 1.00 19 0.105
18 A 6 2 1.00 19 0.105
19 A 3 2 1.00 21 0.095
20 A 3 2 1.00 21 0.095
21 A 3 2 1.00 21 0.095
22 A 3 2 1.00 21 0.095
23 A 3 2 1.00 19 0.105
24 A 3 2 1.00 19 0.105
25 A 3 2 1.00 21 0.095
26 A 3 2 1.00 21 0.095
27 A 3 2 1.00 21 0.095
28 A 3 2 1.00 21 0.095
29 A 12 7 1.00 21 0.333
30 A 10 7 1.00 21 0.333
31 A 8 7 1.00 21 0.333
32 A 8 5 1.00 21 0.238
33 A 9 6 1.00 21 0.286
34 A 11 7 1.00 21 0.333
35 A 12 7 1.00 21 0.333
36 A 13 7 1.00 21 0.333
37 A 3 2 1.00 21 0.095
38 A 3 2 1.00 21 0.095
39 A 3 2 1.00 21 0.095
40 A 3 2 1.00 21 0.095
41 A 3 2 1.00 19 0.105
42 A 3 2 1.00 19 0.105
43 A 3 2 1.00 21 0.095
44 A 3 2 1.00 21 0.095
45 A 3 2 1.00 21 0.095
46 A 3 2 1.00 21 0.095
47 A 17 8 1.00 21 0.381
48 A 14 8 1.00 21 0.381
49 A 11 8 1.00 21 0.381
50 A 11 8 1.00 21 0.381
51 A 11 6 1.00 21 0.286
52 A 14 8 1.00 21 0.381
53 A 15 8 1.00 21 0.381
54 A 16 8 1.00 21 0.381
55 A 17 8 1.00 21 0.381
56 A 3 2 1.00 21 0.095
57 A 3 2 1.00 21 0.095
58 A 3 2 1.00 21 0.095
59 A 3 2 1.00 21 0.095
60 A 2 2 1.00 19 0.105
61 A 3 2 1.00 19 0.105
62 A 3 2 1.00 21 0.095
63 A 3 2 1.00 21 0.095
64 A 6 3 1.00 21 0.143
65 A 5 3 1.00 21 0.143
66 A 4 3 1.00 21 0.143
67 A 3 2 1.00 21 0.095
68 A 4 3 1.00 21 0.143
69 A 5 3 1.00 21 0.143
70 A 6 3 1.00 21 0.143
71 A 3 2 1.00 21 0.095
72 A 3 2 1.00 21 0.095
73 A 3 2 1.00 21 0.095
74 A 3 2 1.00 21 0.095
75 A 3 2 1.00 19 0.105
76 A 3 2 1.00 19 0.105
77 A 3 2 1.00 21 0.095
78 A 3 2 1.00 21 0.095
79 A 11 8 1.00 21 0.381
80 A 9 8 1.00 21 0.381
81 A 5 5 1.00 21 0.238
82 A 9 6 1.06 21 0.286
83 A 12 8 1.00 21 0.381
84 A 13 8 1.00 21 0.381
85 A 14 8 1.00 21 0.381
86 A 3 2 1.00 21 0.095
87 A 3 2 1.00 21 0.095
88 A 3 2 1.00 21 0.095
89 A 3 2 1.00 21 0.095
90 A 3 2 1.00 21 0.095
91 A 3 2 1.00 19 0.105
92 A 3 2 1.00 19 0.105
93 A 3 2 1.00 21 0.095
94 A 3 2 1.00 21 0.095
95 A 18 9 1.00 21 0.429
96 A 15 9 1.00 21 0.429
97 A 12 9 1.00 21 0.429
98 A 6 6 1.00 21 0.286
99 A 12 9 1.04 21 0.429
100 A 12 7 1.18 21 0.333
101 A 16 9 1.00 21 0.429
102 A 17 9 1.00 21 0.429
103 A 18 9 1.00 21 0.429
104 A 17 14 1.00 23 0.609
105 A 16 13 1.00 23 0.565
106 A 16 13 1.00 23 0.565
107 A 15 12 1.00 23 0.522
108 A 17 14 1.00 23 0.609
109 A 16 13 1.00 23 0.565
110 A 18 14 1.00 23 0.609
111 A 21 17 1.00 25 0.680
112 A 20 16 1.00 25 0.640
113 A 19 15 1.00 25 0.600
114 A 18 14 1.00 25 0.560
115 A 20 16 1.00 25 0.640
116 A 20 16 1.00 25 0.640
117 A 22 17 1.00 25 0.680
118 A 18 14 1.00 25 0.560
119 A 18 15 1.00 25 0.600
120 A 17 14 1.00 25 0.560
121 A 17 14 1.00 25 0.560
122 A 16 13 1.00 25 0.520
123 A 18 15 1.00 25 0.600
124 A 17 14 1.00 25 0.560
125 A 19 15 1.00 25 0.600
126 A 18 14 1.00 25 0.560
127 A 22 18 1.00 25 0.720
128 A 21 17 1.00 25 0.680
129 A 20 16 1.00 25 0.640
130 A 19 15 1.00 25 0.600
131 A 21 17 1.00 25 0.680
132 A 21 17 1.00 25 0.680
133 A 23 18 1.00 25 0.720
134 A 23 17 1.00 25 0.680
135 A 8 5 1.00 23 0.217
136 A 6 5 1.00 23 0.217
137 A 4 4 1.00 21 0.190
138 A 6 4 1.00 21 0.190
139 A 8 6 1.00 23 0.261
140 A 10 7 1.00 23 0.304
141 A 4 3 1.00 23 0.130
142 A 4 3 1.00 23 0.130
143 A 4 4 1.00 23 0.174
144 A 5 4 1.00 23 0.174
145 A 7 5 1.00 23 0.217
146 A 9 6 1.00 23 0.261
147 A 9 5 1.00 23 0.217
148 A 7 5 1.00 23 0.217
149 A 5 4 1.00 21 0.190
150 A 6 4 1.00 21 0.190
151 A 7 5 1.00 23 0.217
152 A 9 7 1.00 23 0.304
153 A 4 3 1.00 23 0.130
154 A 4 3 1.00 23 0.130
155 A 4 3 1.00 23 0.130
156 A 3 3 1.00 23 0.130
157 A 6 5 1.00 23 0.217
158 A 8 5 1.00 23 0.217
159 A 10 5 1.00 23 0.217
160 A 8 5 1.00 23 0.217
161 A 6 4 1.00 21 0.190
162 A 7 5 1.00 21 0.238
163 A 7 5 1.00 23 0.217
164 A 8 6 1.00 23 0.261
165 A 4 3 1.00 23 0.130
166 A 4 3 1.00 23 0.130
167 A 4 3 1.00 23 0.130
168 A 3 3 1.00 23 0.130
169 A 4 3 1.00 23 0.130
170 A 7 5 1.00 23 0.217
171 A 7 5 1.00 23 0.217
172 A 5 5 1.00 23 0.217
173 A 3 3 1.00 21 0.143
174 A 7 5 1.00 21 0.238
175 A 9 6 1.00 23 0.261
176 A 11 7 1.00 23 0.304
177 A 4 3 1.00 23 0.130
178 A 5 4 1.00 23 0.174
179 A 3 3 1.00 23 0.130
180 A 6 5 1.00 23 0.217
181 A 8 6 1.00 23 0.261
182 A 10 6 1.00 23 0.261
183 A 6 5 1.00 23 0.217
184 A 4 4 1.00 23 0.174
185 A 4 4 1.00 21 0.190
186 A 8 6 1.00 21 0.286
187 A 10 6 1.00 23 0.261
188 A 12 7 1.00 23 0.304
189 A 5 4 1.00 23 0.174
190 A 4 3 1.00 23 0.130
191 A 4 3 1.00 23 0.130
192 A 7 6 1.00 23 0.261
193 A 9 6 1.00 23 0.261
194 A 11 6 1.00 23 0.261
195 A 5 4 1.00 23 0.174
196 A 4 4 1.00 23 0.174
197 A 5 4 1.00 21 0.190
198 A 9 6 1.00 21 0.286
199 A 11 6 1.00 23 0.261
200 A 13 7 1.00 23 0.304
201 A 4 3 1.00 23 0.130
202 A 5 4 1.00 23 0.174
203 A 5 4 1.00 23 0.174
204 A 8 6 1.00 23 0.261
205 A 10 6 1.00 23 0.261
206 A 12 6 1.00 23 0.261
207 A 7 5 1.28 23 0.217
208 A 1 1 1.00 23 0.043
209 A 8 6 1.00 23 0.261
210 A 7 6 1.00 23 0.261
211 A 4 4 1.00 21 0.190
212 A 5 5 1.00 23 0.217
213 A 8 7 1.00 23 0.304
214 A 9 7 1.00 23 0.304
215 A 1 1 1.00 25 0.040
216 A 1 1 1.00 25 0.040
217 A 1 1 1.00 25 0.040
218 A 1 1 1.00 25 0.040
219 A 4 3 1.00 21 0.143
220 A 4 3 1.00 21 0.143
221 A 3 3 1.00 21 0.143
222 A 2 2 1.00 19 0.105
223 A 4 4 1.00 19 0.210
224 A 5 5 1.00 21 0.238
225 A 1 1 1.00 21 0.048
226 A 1 1 1.00 21 0.048
227 A 1 1 1.00 21 0.048
228 A 1 1 1.00 21 0.048
229 A 1 1 1.00 23 0.043
230 A 1 1 1.00 23 0.043
231 A 1 1 1.00 23 0.043
232 A 1 1 1.00 23 0.043
233 A 17 14 1.00 23 0.609
234 A 18 15 1.00 23 0.652
235 A 16 13 1.00 23 0.565
236 A 17 14 1.00 23 0.609
237 A 17 14 1.00 23 0.609
238 A 21 17 1.00 25 0.680
239 A 21 17 1.00 25 0.680
240 A 19 15 1.00 25 0.600
241 A 20 16 1.00 25 0.640
242 A 21 17 1.00 25 0.680
243 A 20 16 1.00 25 0.640
244 A 18 15 1.00 25 0.600
245 A 19 16 1.00 25 0.640
246 A 17 14 1.00 25 0.560
247 A 18 15 1.00 25 0.600
248 A 18 15 1.00 25 0.600
249 A 19 16 1.00 25 0.640
250 A 24 19 1.00 25 0.760
251 A 22 18 1.00 25 0.720
252 A 22 18 1.00 25 0.720
253 A 20 16 1.00 25 0.640
254 A 21 17 1.00 25 0.680
255 A 22 18 1.00 25 0.720
256 A 7 5 1.00 19 0.263
257 A 6 5 1.00 19 0.263
258 A 5 5 1.00 19 0.263
259 A 4 4 1.00 17 0.235
260 A 5 4 1.00 17 0.235
261 A 6 5 1.00 19 0.263
262 A 7 5 1.00 19 0.263
263 A 8 5 1.00 19 0.263
264 A 5 2 1.00 19 0.105
265 A 4 2 1.00 19 0.105
266 A 3 2 1.00 19 0.105
267 A 2 2 1.00 19 0.105
268 A 3 2 1.00 19 0.105
269 A 4 2 1.00 19 0.105
270 A 5 2 1.00 19 0.105
271 A 3 2 1.17 21 0.095
272 A 3 2 1.13 21 0.095
273 A 3 2 1.14 21 0.095
274 A 3 2 1.00 21 0.095
275 A 3 2 1.00 19 0.105
276 A 3 2 1.00 19 0.105
277 A 4 3 1.00 21 0.143
278 A 5 4 1.00 21 0.190
279 A 12 7 1.00 21 0.333
280 A 10 7 1.00 21 0.333
281 A 8 7 1.00 21 0.333
282 A 8 5 1.00 21 0.238
283 A 9 6 1.00 21 0.286
284 A 11 7 1.00 21 0.333
285 A 12 7 1.00 21 0.333
286 A 3 2 1.00 21 0.095
287 A 3 2 1.00 21 0.095
288 A 3 2 1.00 21 0.095
289 A 3 2 1.00 21 0.095
290 A 4 4 1.00 19 0.210
291 A 3 2 1.00 19 0.105
292 A 3 2 1.00 21 0.095
293 A 3 2 1.00 21 0.095
294 A 15 8 1.37 21 0.381
295 A 6 6 1.00 21 0.286
296 A 7 7 1.00 21 0.333
297 A 9 8 1.27 21 0.381
298 A 15 8 1.45 21 0.381
299 A 3 2 1.00 21 0.095
300 A 3 2 1.00 21 0.095
301 A 3 2 1.00 21 0.095
302 A 3 2 1.00 21 0.095
303 A 3 2 1.00 19 0.105
304 A 3 2 1.00 19 0.105
305 A 3 2 1.00 21 0.095
306 A 3 2 1.00 21 0.095
307 A 16 10 1.42 21 0.476
308 A 6 6 1.00 21 0.286
309 A 6 6 1.00 21 0.286
310 A 11 7 1.00 21 0.333
311 A 15 8 1.00 21 0.381
312 A 38 22 1.00 25 0.880
313 A 35 19 1.00 25 0.760
314 A 21 16 1.00 25 0.640
315 A 19 14 1.00 25 0.560
316 A 39 23 1.00 25 0.920
317 A 36 20 1.00 25 0.800
318 A 5 4 1.00 23 0.174
319 A 5 4 1.00 23 0.174
320 A 4 4 1.00 21 0.190
321 A 7 5 1.00 21 0.238
322 A 13 9 1.00 23 0.391
323 A 7 7 1.00 23 0.304
324 A 1 1 1.00 14 0.071
325 A 5 4 1.00 23 0.174
326 A 5 4 1.00 23 0.174
327 A 5 4 1.00 23 0.174
328 A 3 3 1.00 21 0.143
329 A 7 5 1.00 21 0.238
330 A 11 6 1.00 23 0.261
331 A 11 8 1.51 23 0.348
332 A 6 6 1.00 23 0.261
333 A 1 1 1.00 14 0.071
334 A 9 8 1.00 23 0.348
335 A 5 4 1.00 23 0.174
336 A 5 4 1.00 23 0.174
337 A 4 4 1.00 21 0.190
338 A 7 4 1.00 21 0.190
339 A 11 5 1.34 23 0.217
340 A 17 11 1.71 23 0.478
341 A 7 7 1.00 23 0.304
342 A 6 6 1.00 14 0.429
343 A 14 11 1.48 23 0.478
344 A 8 6 1.00 23 0.261
345 A 7 6 1.00 23 0.261
346 A 4 4 1.00 21 0.190
347 F 0 0 N/A 0. N/A
348 A 0 0 0.00 0 0.000
349 A 0 0 0.00 0 0.000
350 A 0 0 0.00 0 0.000
351 A 0 0 0.00 0 0.000
352 A 0 0 0.00 0 0.000
353 A 5 4 1.00 21 0.190
354 A 4 4 1.00 21 0.190
355 A 2 2 1.00 19 0.105
356 A 8 5 1.00 19 0.263
357 A 10 5 1.00 21 0.238
358 A 0 0 0.00 0 0.000
359 A 0 0 0.00 0 0.000
360 A 0 0 0.00 0 0.000
361 A 0 0 0.00 0 0.000
362 A 0 0 0.00 0 0.000
363 A 0 0 0.00 0 0.000
364 A 0 0 0.00 0 0.000
365 A 0 0 0.00 0 0.000

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