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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 [298] had the largest ratio of [1.19047999999999998]

# 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 7 6 0.77 19 0.316
2 A 7 6 0.78 19 0.316
3 A 7 6 0.76 19 0.316
4 A 7 6 0.81 19 0.316
5 A 7 6 0.88 17 0.353
6 A 5 4 1.00 17 0.235
7 A 7 6 0.89 19 0.316
8 A 7 6 0.85 19 0.316
9 A 7 6 0.83 19 0.316
10 A 10 10 1.15 19 0.526
11 A 8 8 1.13 19 0.421
12 A 5 5 1.12 19 0.263
13 A 3 3 1.07 19 0.158
14 A 3 3 1.00 19 0.158
15 A 6 6 1.05 19 0.316
16 A 9 9 1.10 19 0.474
17 A 12 12 1.07 19 0.632
18 A 15 15 1.13 19 0.789
19 A 7 6 0.69 21 0.286
20 A 7 6 0.71 21 0.286
21 A 7 6 0.70 21 0.286
22 A 7 6 0.77 21 0.286
23 A 7 6 0.75 19 0.316
24 A 6 5 0.83 19 0.263
25 A 7 6 0.80 21 0.286
26 A 7 6 0.81 21 0.286
27 A 7 6 0.78 21 0.286
28 A 7 6 0.76 21 0.286
29 A 3 3 1.00 21 0.143
30 A 3 3 1.00 21 0.143
31 A 3 3 1.00 21 0.143
32 A 3 3 1.00 21 0.143
33 A 3 3 1.00 21 0.143
34 A 3 3 1.00 21 0.143
35 A 3 3 1.00 21 0.143
36 A 3 3 1.00 21 0.143
37 A 7 6 0.69 21 0.286
38 A 7 6 0.72 21 0.286
39 A 7 6 0.70 21 0.286
40 A 7 6 0.71 21 0.286
41 A 7 6 0.73 19 0.316
42 A 7 6 0.81 19 0.316
43 A 7 6 0.85 21 0.286
44 A 7 6 0.85 21 0.286
45 A 7 6 0.79 21 0.286
46 A 7 6 0.77 21 0.286
47 A 3 3 1.00 21 0.143
48 A 3 3 1.00 21 0.143
49 A 3 3 1.00 21 0.143
50 A 3 3 1.00 21 0.143
51 A 3 3 1.00 21 0.143
52 A 3 3 1.00 21 0.143
53 A 3 3 1.00 21 0.143
54 A 3 3 1.00 21 0.143
55 A 3 3 1.00 21 0.143
56 A 7 6 0.68 21 0.286
57 A 7 6 0.74 21 0.286
58 A 7 6 0.70 21 0.286
59 A 7 6 0.93 21 0.286
60 A 5 4 1.00 19 0.211
61 A 7 6 0.84 19 0.316
62 A 7 6 0.79 21 0.286
63 A 7 6 0.77 21 0.286
64 A 11 11 1.14 21 0.524
65 A 8 8 1.12 21 0.381
66 A 6 6 1.08 21 0.286
67 A 3 3 1.00 21 0.143
68 A 9 9 1.05 21 0.429
69 A 12 12 1.11 21 0.571
70 A 15 15 1.07 21 0.714
71 A 7 6 0.70 21 0.286
72 A 7 6 0.77 21 0.286
73 A 7 6 0.75 21 0.286
74 A 6 5 0.82 21 0.238
75 A 7 6 0.78 19 0.316
76 A 7 6 0.80 19 0.316
77 A 7 6 0.77 21 0.286
78 A 7 6 0.76 21 0.286
79 A 5 5 1.03 21 0.238
80 A 5 5 1.06 21 0.238
81 A 9 8 1.12 21 0.381
82 A 5 5 1.18 21 0.238
83 A 5 5 1.04 21 0.238
84 A 5 5 1.03 21 0.238
85 A 5 5 1.02 21 0.238
86 A 7 6 0.72 21 0.286
87 A 7 6 0.71 21 0.286
88 A 7 6 0.77 21 0.286
89 A 7 6 0.80 21 0.286
90 A 7 6 0.91 21 0.286
91 A 7 6 0.79 19 0.316
92 A 7 6 0.78 19 0.316
93 A 7 6 0.76 21 0.286
94 A 7 6 0.75 21 0.286
95 A 6 6 1.02 21 0.286
96 A 6 6 1.03 21 0.286
97 A 6 6 1.04 21 0.286
98 A 11 10 1.12 21 0.476
99 A 6 6 1.20 21 0.286
100 A 6 6 1.23 21 0.286
101 A 6 6 1.02 21 0.286
102 A 6 6 1.04 21 0.286
103 A 6 6 1.01 21 0.286
104 A 24 23 0.95 23 1.000
105 A 22 21 0.96 23 0.913
106 A 21 20 0.93 23 0.870
107 A 19 18 0.94 23 0.783
108 A 24 23 0.95 23 1.000
109 A 22 21 0.96 23 0.913
110 A 27 26 0.96 23 1.130
111 A 3 3 1.00 25 0.120
112 A 3 3 1.00 25 0.120
113 A 3 3 1.00 25 0.120
114 A 3 3 1.00 25 0.120
115 A 3 3 1.00 25 0.120
116 A 3 3 1.00 25 0.120
117 A 3 3 1.00 25 0.120
118 A 28 27 0.97 25 1.080
119 A 27 26 0.93 25 1.040
120 A 25 24 0.95 25 0.960
121 A 24 23 0.92 25 0.920
122 A 22 21 0.93 25 0.840
123 A 27 26 0.95 25 1.040
124 A 25 24 0.97 25 0.960
125 A 30 29 0.95 25 1.160
126 A 28 27 0.98 25 1.080
127 A 5 5 1.00 25 0.200
128 A 5 5 1.01 25 0.200
129 A 5 5 1.01 25 0.200
130 A 5 5 1.01 25 0.200
131 A 5 5 1.02 25 0.200
132 A 5 5 1.02 25 0.200
133 A 5 5 1.04 25 0.200
134 A 5 5 1.04 25 0.200
135 A 7 6 0.91 23 0.261
136 A 11 10 0.96 23 0.435
137 A 7 6 0.96 21 0.286
138 A 10 9 0.99 21 0.429
139 A 13 12 1.05 23 0.522
140 A 18 17 1.07 23 0.739
141 A 5 4 0.92 23 0.174
142 A 5 4 0.93 23 0.174
143 A 6 5 0.97 23 0.217
144 A 8 7 1.04 23 0.304
145 A 12 11 1.05 23 0.478
146 A 16 15 1.05 23 0.652
147 A 7 6 0.92 23 0.261
148 A 12 11 0.96 23 0.478
149 A 8 7 0.96 21 0.333
150 A 10 9 1.00 21 0.429
151 A 11 10 1.03 23 0.435
152 A 16 15 1.04 23 0.652
153 A 5 4 0.91 23 0.174
154 A 5 4 0.92 23 0.174
155 A 5 4 0.92 23 0.174
156 A 5 4 0.95 23 0.174
157 A 9 8 1.01 23 0.348
158 A 14 13 1.05 23 0.565
159 A 7 6 0.91 23 0.261
160 A 13 12 0.94 23 0.522
161 A 9 8 0.94 21 0.381
162 A 13 12 1.00 21 0.571
163 A 11 10 1.01 23 0.435
164 A 14 13 1.03 23 0.565
165 A 5 4 0.91 23 0.174
166 A 5 4 0.92 23 0.174
167 A 5 4 0.92 23 0.174
168 A 5 4 0.97 23 0.174
169 A 6 5 0.95 23 0.217
170 A 11 10 1.01 23 0.435
171 A 7 6 0.90 23 0.261
172 A 10 9 0.95 23 0.391
173 A 6 5 1.00 21 0.238
174 A 13 12 1.07 21 0.571
175 A 15 14 1.11 23 0.609
176 A 20 19 1.10 23 0.826
177 A 5 4 0.94 23 0.174
178 A 6 5 0.98 23 0.217
179 A 5 4 1.03 23 0.174
180 A 9 8 1.04 23 0.348
181 A 14 13 1.05 23 0.565
182 A 17 16 1.05 23 0.696
183 A 7 6 0.92 23 0.261
184 A 9 8 1.04 23 0.348
185 A 7 6 0.96 21 0.286
186 A 15 14 1.07 21 0.667
187 A 17 16 1.12 23 0.696
188 A 22 21 1.11 23 0.913
189 A 6 5 0.96 23 0.217
190 A 5 4 0.99 23 0.174
191 A 5 4 0.98 23 0.174
192 A 13 12 1.06 23 0.522
193 A 17 16 1.06 23 0.696
194 A 20 19 1.06 23 0.826
195 A 7 6 0.97 23 0.261
196 A 9 8 1.04 23 0.348
197 A 8 7 1.00 21 0.333
198 A 17 16 1.07 21 0.762
199 A 19 18 1.13 23 0.783
200 A 24 23 1.11 23 1.000
201 A 5 4 0.97 23 0.174
202 A 6 5 1.01 23 0.217
203 A 6 5 1.17 23 0.217
204 A 14 13 1.06 23 0.565
205 A 18 17 1.06 23 0.739
206 A 23 22 1.06 23 0.957
207 A 10 9 1.46 23 0.391
208 A 2 2 1.00 23 0.087
209 A 3 3 1.00 23 0.130
210 A 3 3 1.00 23 0.130
211 A 7 6 1.00 21 0.286
212 A 10 9 1.06 23 0.391
213 A 5 5 1.04 23 0.217
214 A 6 6 1.03 23 0.261
215 A 2 2 1.00 25 0.080
216 A 2 2 1.00 25 0.080
217 A 2 2 1.00 25 0.080
218 A 2 2 1.00 25 0.080
219 A 8 7 0.98 21 0.333
220 A 7 6 0.98 21 0.286
221 A 8 7 1.06 21 0.333
222 A 5 4 1.00 19 0.211
223 A 9 8 1.09 19 0.421
224 A 11 10 1.08 21 0.476
225 A 2 2 1.00 21 0.095
226 A 2 2 1.00 21 0.095
227 A 2 2 1.00 21 0.095
228 A 2 2 1.00 21 0.095
229 A 2 2 1.00 23 0.087
230 A 2 2 1.00 23 0.087
231 A 2 2 1.00 23 0.087
232 A 2 2 1.00 23 0.087
233 A 24 23 0.75 23 1.000
234 A 26 25 0.74 23 1.087
235 A 21 20 0.76 23 0.870
236 A 23 22 0.78 23 0.957
237 A 24 23 0.76 23 1.000
238 A 5 5 0.75 25 0.200
239 A 5 5 0.76 25 0.200
240 A 5 5 0.76 25 0.200
241 A 5 5 0.77 25 0.200
242 A 5 5 0.76 25 0.200
243 F 0 0 N/A 0.000 N/A
244 A 27 26 0.75 25 1.040
245 A 29 28 0.76 25 1.120
246 A 24 23 0.73 25 0.920
247 A 26 25 0.73 25 1.000
248 A 27 26 0.74 25 1.040
249 A 29 28 0.73 25 1.120
250 A 7 7 0.76 25 0.280
251 A 7 7 0.75 25 0.280
252 A 7 7 0.74 25 0.280
253 A 7 7 0.74 25 0.280
254 A 7 7 0.74 25 0.280
255 A 7 7 0.74 25 0.280
256 A 21 20 1.08 19 1.053
257 A 17 16 1.10 19 0.842
258 A 13 12 1.07 19 0.632
259 A 9 8 1.00 17 0.471
260 A 10 9 0.95 17 0.529
261 A 13 12 0.99 19 0.632
262 A 16 15 1.03 19 0.789
263 A 20 19 1.06 19 1.000
264 A 8 8 1.13 19 0.421
265 A 5 5 1.12 19 0.263
266 A 3 3 1.07 19 0.158
267 A 3 3 1.00 19 0.158
268 A 6 6 1.05 19 0.316
269 A 9 9 1.10 19 0.474
270 A 12 12 1.07 19 0.632
271 A 6 5 1.17 21 0.238
272 A 6 5 1.15 21 0.238
273 A 6 5 1.16 21 0.238
274 A 6 5 1.06 21 0.238
275 A 6 5 0.91 19 0.263
276 A 7 6 1.15 19 0.316
277 A 8 7 1.26 21 0.333
278 A 10 9 1.38 21 0.429
279 A 3 3 1.00 21 0.143
280 A 3 3 1.00 21 0.143
281 A 3 3 1.00 21 0.143
282 A 3 3 1.00 21 0.143
283 A 3 3 1.00 21 0.143
284 A 3 3 1.00 21 0.143
285 A 3 3 1.00 21 0.143
286 A 6 5 0.92 21 0.238
287 A 6 5 0.92 21 0.238
288 A 6 5 0.92 21 0.238
289 A 6 5 0.98 21 0.238
290 A 7 6 0.97 19 0.316
291 A 6 5 1.06 19 0.263
292 A 6 5 1.05 21 0.238
293 A 6 5 1.05 21 0.238
294 A 5 5 1.37 21 0.238
295 A 12 11 1.16 21 0.524
296 A 14 13 1.16 21 0.619
297 A 17 16 1.18 21 0.762
298 A 26 25 1.25 21 1.190
299 A 6 5 0.91 21 0.238
300 A 6 5 0.92 21 0.238
301 A 6 5 0.90 21 0.238
302 A 6 5 1.00 21 0.238
303 A 6 5 0.93 19 0.263
304 A 6 5 1.01 19 0.263
305 A 6 5 1.01 21 0.238
306 A 6 5 1.03 21 0.238
307 A 5 5 1.42 21 0.238
308 A 12 11 1.16 21 0.524
309 A 11 10 1.06 21 0.476
310 A 5 5 1.00 21 0.238
311 A 5 5 1.00 21 0.238
312 F 0 0 N/A 0.000 N/A
313 F 0 0 N/A 0.000 N/A
314 A 24 23 0.85 25 0.920
315 A 22 21 0.98 25 0.840
316 F 0 0 N/A 0.000 N/A
317 F 0 0 N/A 0.000 N/A
318 A 8 7 0.78 23 0.304
319 A 7 6 0.81 23 0.261
320 A 7 6 0.96 21 0.286
321 A 7 6 1.11 21 0.286
322 A 14 13 1.25 23 0.565
323 A 13 13 1.00 23 0.565
324 A 2 2 1.00 14 0.143
325 A 3 3 1.00 23 0.130
326 A 8 7 0.83 23 0.304
327 A 7 6 0.90 23 0.261
328 A 6 5 1.00 21 0.238
329 A 7 6 1.11 21 0.286
330 A 8 7 1.05 23 0.304
331 A 3 3 1.51 23 0.130
332 A 10 10 1.00 23 0.435
333 A 2 2 1.00 14 0.143
334 A 3 3 1.00 23 0.130
335 A 8 7 0.80 23 0.304
336 A 7 6 0.90 23 0.261
337 A 7 6 0.96 21 0.286
338 A 7 6 1.01 21 0.286
339 A 8 7 1.31 23 0.304
340 A 3 3 1.71 23 0.130
341 A 13 13 1.11 23 0.565
342 A 11 11 1.08 14 0.786
343 A 3 3 1.48 23 0.130
344 A 3 3 1.00 23 0.130
345 A 3 3 1.00 23 0.130
346 A 7 6 1.00 21 0.286
347 F 0 0 N/A 0.000 N/A
348 N/A 2 0 1.00 25 0.000
349 N/A 2 0 1.00 25 0.000
350 N/A 2 0 1.00 25 0.000
351 N/A 2 0 1.00 25 0.000
352 N/A 2 0 1.00 23 0.000
353 A 6 5 0.90 21 0.238
354 A 6 5 0.97 21 0.238
355 A 5 4 1.00 19 0.211
356 A 6 5 1.06 19 0.263
357 A 6 5 1.02 21 0.238
358 N/A 2 0 1.00 21 0.000
359 N/A 16 0 1.00 21 0.000
360 N/A 2 0 1.00 21 0.000
361 N/A 2 0 1.00 21 0.000
362 N/A 2 0 1.00 23 0.000
363 N/A 2 0 1.00 23 0.000
364 N/A 2 0 1.00 23 0.000
365 N/A 2 0 1.00 23 0.000

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