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 [146] had the largest ratio of [1.56250000000000000]

# 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 F 0 0 N/A 0.000 N/A
2 F 0 0 N/A 0.000 N/A
3 F 0 0 N/A 0.000 N/A
4 F 0 0 N/A 0.000 N/A
5 F 0 0 N/A 0.000 N/A
6 F 0 0 N/A 0.000 N/A
7 F 0 0 N/A 0.000 N/A
8 F 0 0 N/A 0.000 N/A
9 F 0 0 N/A 0.000 N/A
10 F 0 0 N/A 0.000 N/A
11 F 0 0 N/A 0.000 N/A
12 F 0 0 N/A 0.000 N/A
13 N/A 3 0 1.00 14 0.000
14 F 0 0 N/A 0.000 N/A
15 F 0 0 N/A 0.000 N/A
16 A 13 13 1.22 14 0.929
17 A 10 10 1.19 14 0.714
18 A 8 8 1.15 14 0.571
19 A 5 5 1.13 12 0.417
20 A 3 3 1.00 10 0.300
21 A 7 6 1.00 14 0.429
22 A 6 5 1.00 14 0.357
23 A 9 8 1.00 14 0.571
24 A 11 10 1.02 14 0.714
25 A 14 13 1.04 14 0.929
26 A 3 3 1.00 14 0.214
27 A 3 3 1.00 14 0.214
28 A 3 3 1.00 12 0.250
29 A 3 3 1.00 10 0.300
30 A 3 3 1.00 14 0.214
31 A 3 3 1.00 14 0.214
32 A 3 3 1.00 14 0.214
33 A 3 3 1.00 14 0.214
34 A 15 15 1.22 14 1.071
35 A 12 12 1.19 14 0.857
36 A 12 12 1.07 12 1.000
37 A 6 6 1.00 10 0.600
38 A 10 9 1.00 14 0.643
39 A 3 3 0.95 14 0.214
40 A 3 3 1.01 14 0.214
41 A 3 3 0.98 14 0.214
42 A 3 3 1.00 14 0.214
43 A 3 3 1.00 14 0.214
44 A 3 3 1.00 12 0.250
45 A 3 3 1.00 10 0.300
46 A 3 3 1.00 14 0.214
47 A 3 3 1.00 14 0.214
48 A 3 3 1.00 14 0.214
49 A 3 3 1.00 14 0.214
50 A 11 11 1.19 14 0.786
51 A 8 8 1.15 14 0.571
52 A 6 6 1.13 12 0.500
53 A 3 3 1.00 10 0.300
54 A 7 6 1.00 14 0.429
55 A 6 5 1.00 14 0.357
56 A 8 7 1.02 14 0.500
57 A 11 10 1.02 14 0.714
58 A 13 12 1.04 14 0.857
59 A 3 3 1.00 14 0.214
60 A 3 3 1.00 14 0.214
61 A 3 3 1.00 12 0.250
62 A 3 3 1.00 10 0.300
63 A 3 3 1.00 14 0.214
64 A 3 3 1.00 14 0.214
65 A 3 3 1.00 14 0.214
66 A 3 3 1.00 14 0.214
67 A 15 15 1.24 14 1.071
68 A 12 12 1.21 14 0.857
69 A 12 12 1.07 12 1.000
70 A 6 6 1.03 10 0.600
71 A 10 9 1.04 14 0.643
72 A 3 3 1.00 14 0.214
73 A 3 3 1.04 14 0.214
74 A 3 3 1.00 14 0.214
75 A 3 3 1.03 14 0.214
76 A 16 15 1.18 16 0.938
77 A 14 13 1.24 14 0.929
78 A 13 12 1.23 12 1.000
79 A 17 16 1.31 16 1.000
80 A 7 6 1.04 16 0.375
81 A 8 7 1.02 16 0.438
82 A 12 11 1.01 16 0.688
83 A 14 13 1.03 16 0.812
84 A 16 15 1.03 16 0.938
85 A 16 15 1.13 16 0.938
86 A 16 15 1.18 16 0.938
87 A 14 13 1.24 14 0.929
88 A 13 12 1.23 12 1.000
89 A 18 17 1.30 16 1.062
90 A 8 7 1.04 16 0.438
91 A 9 8 1.02 16 0.500
92 A 13 12 1.01 16 0.750
93 A 15 14 1.02 16 0.875
94 A 18 17 1.14 16 1.062
95 A 17 16 1.18 16 1.000
96 A 15 14 1.23 14 1.000
97 A 14 13 1.21 12 1.083
98 A 20 19 1.27 16 1.188
99 A 8 7 1.05 16 0.438
100 A 9 8 1.02 16 0.500
101 A 14 13 1.01 16 0.812
102 A 16 15 1.03 16 0.938
103 A 16 15 1.13 16 0.938
104 A 16 15 1.18 16 0.938
105 A 14 13 1.24 14 0.929
106 A 13 12 1.23 12 1.000
107 A 18 17 1.31 16 1.062
108 A 8 7 1.04 16 0.438
109 A 9 8 1.02 16 0.500
110 A 13 12 1.01 16 0.750
111 A 15 14 1.03 16 0.875
112 A 16 15 1.13 16 0.938
113 A 16 15 1.18 16 0.938
114 A 14 13 1.24 14 0.929
115 A 13 12 1.23 12 1.000
116 A 17 16 1.30 16 1.000
117 A 7 6 1.04 16 0.375
118 A 8 7 1.02 16 0.438
119 A 12 11 1.01 16 0.688
120 A 14 13 1.02 16 0.812
121 A 18 17 1.14 16 1.062
122 A 17 16 1.18 16 1.000
123 A 15 14 1.23 14 1.000
124 A 14 13 1.21 12 1.083
125 A 21 20 1.27 16 1.250
126 A 9 8 1.05 16 0.500
127 A 10 9 1.02 16 0.562
128 A 15 14 1.01 16 0.875
129 A 17 16 1.03 16 1.000
130 A 16 15 1.18 14 1.071
131 A 14 13 1.25 12 1.083
132 A 13 12 1.21 10 1.200
133 A 17 16 1.41 14 1.143
134 A 12 11 1.30 14 0.786
135 A 13 12 1.29 14 0.857
136 A 17 16 1.24 14 1.143
137 A 6 6 1.05 14 0.429
138 A 4 4 1.11 12 0.333
139 A 3 3 1.06 10 0.300
140 A 4 4 1.07 14 0.286
141 A 3 3 1.02 14 0.214
142 A 4 4 1.05 14 0.286
143 A 16 15 1.29 16 0.938
144 A 14 13 1.33 14 0.929
145 A 13 12 1.30 12 1.000
146 A 26 25 1.46 16 1.562
147 A 16 15 1.28 16 0.938
148 A 17 16 1.25 16 1.000
149 A 5 5 0.92 14 0.357
150 A 6 6 1.00 14 0.429
151 A 3 3 1.00 14 0.214
152 A 3 3 1.00 14 0.214
153 A 6 6 1.00 14 0.429
154 A 5 5 0.93 14 0.357
155 A 7 7 1.36 14 0.500
156 A 3 3 1.00 14 0.214
157 A 3 3 1.00 14 0.214
158 A 7 7 1.36 14 0.500
159 A 2 2 1.00 16 0.125
160 A 2 2 1.00 16 0.125
161 A 2 2 1.00 16 0.125
162 A 2 2 1.00 16 0.125
163 A 2 2 1.00 16 0.125
164 A 2 2 1.00 12 0.167
165 A 2 2 1.00 12 0.167
166 A 2 2 1.00 16 0.125
167 A 2 2 1.00 15 0.133
168 A 5 5 0.86 15 0.333
169 A 5 5 1.04 15 0.333
170 A 3 3 1.00 13 0.231
171 A 2 2 1.00 11 0.182
172 A 4 4 1.00 15 0.267
173 A 2 2 1.00 15 0.133
174 A 3 3 1.00 15 0.200
175 A 7 7 1.02 15 0.467
176 A 11 10 0.90 16 0.625
177 A 9 8 0.87 16 0.500
178 A 9 8 1.05 16 0.500
179 A 7 6 1.10 14 0.429
180 A 6 5 1.25 12 0.417
181 A 9 8 1.25 16 0.500
182 A 5 4 1.00 16 0.250
183 A 6 5 0.99 16 0.312
184 A 10 9 1.04 16 0.562
185 A 3 3 1.00 16 0.188
186 A 3 3 1.00 16 0.188
187 A 3 3 1.00 16 0.188
188 A 3 3 1.00 14 0.214
189 A 3 3 1.00 12 0.250
190 A 3 3 1.00 16 0.188
191 A 3 3 1.00 16 0.188
192 A 3 3 1.00 16 0.188
193 A 3 3 1.00 16 0.188
194 A 14 13 0.95 16 0.812
195 A 12 11 0.94 16 0.688
196 A 10 9 1.01 16 0.562
197 A 8 7 1.05 14 0.500
198 A 7 6 1.16 12 0.500
199 A 10 9 1.21 16 0.562
200 A 6 5 1.05 16 0.312
201 A 7 6 0.96 16 0.375
202 A 14 13 1.05 16 0.812
203 A 12 11 0.90 16 0.688
204 A 9 8 0.89 16 0.500
205 A 9 8 1.05 16 0.500
206 A 7 6 1.10 14 0.429
207 A 6 5 1.25 12 0.417
208 A 9 8 1.25 16 0.500
209 A 5 4 1.00 16 0.250
210 A 6 5 0.99 16 0.312
211 A 12 11 1.04 16 0.688
212 A 3 3 1.00 16 0.188
213 A 3 3 1.00 16 0.188
214 A 3 3 1.00 16 0.188
215 A 3 3 1.00 14 0.214
216 A 3 3 1.00 12 0.250
217 A 3 3 1.00 16 0.188
218 A 3 3 1.00 16 0.188
219 A 3 3 0.98 16 0.188
220 A 3 3 0.98 16 0.188
221 A 13 12 0.95 16 0.750
222 A 11 10 0.94 16 0.625
223 A 11 10 1.01 16 0.625
224 A 8 7 1.06 14 0.500
225 A 7 6 1.16 12 0.500
226 A 10 9 1.22 16 0.562
227 A 6 5 1.05 16 0.312
228 A 7 6 0.97 16 0.375
229 A 13 12 1.07 16 0.750
230 A 16 15 1.06 18 0.833
231 A 14 13 1.13 16 0.812
232 A 13 12 1.22 14 0.857
233 A 15 14 1.37 18 0.778
234 A 7 6 1.27 18 0.333
235 A 16 15 1.06 18 0.833
236 A 14 13 1.13 16 0.812
237 A 13 12 1.22 14 0.857
238 A 19 18 1.24 18 1.000
239 A 8 7 1.06 18 0.389
240 A 16 15 1.06 18 0.833
241 A 14 13 1.13 16 0.812
242 A 13 12 1.22 14 0.857
243 A 14 13 1.37 18 0.722
244 A 6 5 1.24 18 0.278
245 A 16 15 1.06 18 0.833
246 A 14 13 1.13 16 0.812
247 A 13 12 1.22 14 0.857
248 A 18 17 1.24 18 0.944
249 A 7 6 1.07 18 0.333
250 A 4 4 1.04 14 0.286
251 A 5 5 0.83 14 0.357
252 A 5 5 1.03 14 0.357
253 A 3 3 1.00 12 0.250
254 A 2 2 1.00 10 0.200
255 A 5 5 1.06 14 0.357
256 A 2 2 1.00 14 0.143
257 A 3 3 0.99 14 0.214
258 A 3 3 1.00 19 0.158
259 A 2 2 1.00 19 0.105
260 A 2 2 1.00 17 0.118
261 A 2 2 1.00 6 0.333
262 A 1 1 1.00 19 0.053
263 A 3 3 1.00 19 0.158
264 A 4 4 1.02 19 0.211
265 A 5 5 1.03 19 0.263
266 A 6 6 1.04 19 0.316
267 A 3 3 1.00 21 0.143
268 A 3 3 1.00 21 0.143
269 A 3 3 1.00 21 0.143
270 A 1 1 1.00 21 0.048
271 A 2 2 1.00 21 0.095
272 A 3 3 1.07 21 0.143
273 A 3 3 1.00 21 0.143
274 A 2 2 1.00 21 0.095
275 A 2 2 1.00 19 0.105
276 A 2 2 1.00 8 0.250
277 A 1 1 1.00 21 0.048
278 A 3 3 1.00 21 0.143
279 A 4 4 1.02 21 0.190
280 A 5 5 1.03 21 0.238
281 A 3 3 1.00 23 0.130
282 A 3 3 1.00 23 0.130
283 A 3 3 1.00 23 0.130
284 A 1 1 1.00 23 0.043
285 A 2 2 1.00 23 0.087
286 A 3 3 1.07 23 0.130
287 A 3 3 1.00 21 0.143
288 A 2 2 1.00 21 0.095
289 A 2 2 1.00 19 0.105
290 A 2 2 1.00 8 0.250
291 A 1 1 1.00 21 0.048
292 A 3 3 1.00 21 0.143
293 A 4 4 1.02 21 0.190
294 A 5 5 1.03 21 0.238
295 A 3 3 1.00 23 0.130
296 A 3 3 1.00 23 0.130
297 A 3 3 1.00 23 0.130
298 A 1 1 1.00 23 0.043
299 A 2 2 1.00 23 0.087
300 A 3 3 1.07 23 0.130
301 A 3 3 1.00 21 0.143
302 A 2 2 1.00 21 0.095
303 A 2 2 1.00 19 0.105
304 A 2 2 1.00 8 0.250
305 A 1 1 1.00 21 0.048
306 A 3 3 1.00 21 0.143
307 A 4 4 1.02 21 0.190
308 A 5 5 1.03 21 0.238
309 A 3 3 1.00 23 0.130
310 A 3 3 1.00 23 0.130
311 A 3 3 1.00 23 0.130
312 A 1 1 1.00 23 0.043
313 A 2 2 1.00 23 0.087
314 A 3 3 1.07 23 0.130
315 A 3 3 1.00 24 0.125
316 A 5 5 1.06 24 0.208
317 A 3 3 1.00 24 0.125
318 A 4 4 1.08 24 0.167
319 A 2 2 1.00 24 0.083
320 A 2 2 1.00 24 0.083
321 A 4 4 1.08 24 0.167
322 A 3 3 1.00 24 0.125
323 A 5 5 1.06 24 0.208
324 A 4 4 0.60 25 0.160
325 A 6 5 1.17 25 0.200
326 A 4 4 0.69 25 0.160
327 A 5 4 1.08 25 0.160
328 A 3 3 1.00 25 0.120
329 A 3 3 1.00 25 0.120
330 A 5 4 1.08 25 0.160
331 A 4 4 0.70 25 0.160
332 A 6 5 1.17 25 0.200
333 A 3 3 1.00 24 0.125
334 A 3 3 1.03 24 0.125
335 A 2 2 1.00 24 0.083
336 A 3 3 1.37 24 0.125
337 A 3 3 1.00 24 0.125
338 A 3 3 1.00 24 0.125
339 A 3 3 1.37 24 0.125
340 A 2 2 1.00 24 0.083
341 A 3 3 1.03 24 0.125
342 A 4 4 0.69 25 0.160
343 A 3 3 1.12 25 0.120
344 A 3 3 1.00 25 0.120
345 A 3 3 1.09 25 0.120
346 A 4 4 0.67 25 0.160
347 A 4 4 0.67 25 0.160
348 A 3 3 1.09 25 0.120
349 A 3 3 1.00 25 0.120
350 A 3 3 1.12 25 0.120
351 A 2 2 1.00 21 0.095
352 A 2 2 1.00 19 0.105
353 A 2 2 1.00 8 0.250
354 A 5 5 1.59 24 0.208
355 A 5 5 1.00 24 0.208
356 A 3 3 0.98 22 0.136
357 A 1 1 1.00 21 0.048
358 A 3 3 1.85 24 0.125
359 A 8 8 1.80 24 0.333
360 A 10 10 1.77 24 0.417
361 A 5 5 0.87 21 0.238
362 A 3 3 1.00 23 0.130
363 A 3 3 1.00 23 0.130
364 A 3 3 1.00 23 0.130
365 A 6 6 0.83 26 0.231
366 A 6 6 0.84 26 0.231
367 A 6 6 0.71 26 0.231
368 A 6 6 0.87 26 0.231
369 A 4 4 0.91 24 0.167
370 A 3 3 1.00 23 0.130
371 A 3 3 1.00 26 0.115
372 A 4 4 0.87 26 0.154
373 A 8 8 0.82 26 0.308
374 A 3 3 1.00 23 0.130
375 A 3 3 1.00 23 0.130
376 A 3 3 1.00 23 0.130
377 A 3 3 1.00 23 0.130
378 A 2 2 1.00 22 0.091
379 A 2 2 1.00 24 0.083
380 A 2 2 1.00 24 0.083
381 A 2 2 1.00 24 0.083
382 A 3 3 1.00 26 0.115
383 A 3 3 1.00 26 0.115
384 A 3 3 1.00 26 0.115
385 A 3 3 1.00 21 0.143
386 A 3 3 1.00 24 0.125
387 A 3 3 1.00 24 0.125
388 A 1 1 1.00 35 0.029
389 A 2 2 1.00 26 0.077
390 A 2 2 1.00 26 0.077
391 A 2 2 1.00 26 0.077
392 A 2 2 1.00 26 0.077
393 A 2 2 1.00 26 0.077
394 A 3 3 1.00 28 0.107
395 A 3 3 1.00 28 0.107
396 A 4 4 0.58 28 0.143
397 A 4 4 0.59 28 0.143
398 A 3 3 1.00 28 0.107
399 A 3 3 1.00 28 0.107