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 [131] 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 A 13 13 1.38 14 0.929
2 A 10 10 1.39 14 0.714
3 A 8 8 1.23 14 0.571
4 A 5 5 1.45 12 0.417
5 A 3 3 1.00 10 0.300
6 A 7 6 1.00 14 0.429
7 A 6 5 1.00 14 0.357
8 A 9 8 1.00 14 0.571
9 A 11 10 1.02 14 0.714
10 A 14 13 1.04 14 0.929
11 A 3 3 1.00 14 0.214
12 A 3 3 1.00 14 0.214
13 A 3 3 1.00 12 0.250
14 A 3 3 1.00 10 0.300
15 A 3 3 1.00 14 0.214
16 A 3 3 1.00 14 0.214
17 A 3 3 1.00 14 0.214
18 A 3 3 1.00 14 0.214
19 A 15 15 1.12 14 1.071
20 A 12 12 1.23 14 0.857
21 A 12 12 0.97 12 1.000
22 A 6 6 1.00 10 0.600
23 A 10 9 0.98 14 0.643
24 A 3 3 1.00 14 0.214
25 A 3 3 1.00 14 0.214
26 A 3 3 1.00 14 0.214
27 A 3 3 1.00 14 0.214
28 A 3 3 1.00 14 0.214
29 A 3 3 1.00 12 0.250
30 A 3 3 1.00 10 0.300
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 3 3 1.00 14 0.214
35 A 11 11 1.39 14 0.786
36 A 8 8 1.23 14 0.571
37 A 6 6 1.45 12 0.500
38 A 3 3 1.00 10 0.300
39 A 7 6 1.00 14 0.429
40 A 6 5 1.00 14 0.357
41 A 8 7 1.02 14 0.500
42 A 11 10 1.02 14 0.714
43 A 13 12 1.04 14 0.857
44 A 3 3 1.00 14 0.214
45 A 3 3 1.00 14 0.214
46 A 3 3 1.00 12 0.250
47 A 3 3 1.00 10 0.300
48 A 3 3 1.00 14 0.214
49 A 3 3 1.00 14 0.214
50 A 3 3 1.00 14 0.214
51 A 3 3 1.00 14 0.214
52 A 15 15 1.12 14 1.071
53 A 12 12 1.23 14 0.857
54 A 12 12 0.97 12 1.000
55 A 6 6 1.00 10 0.600
56 A 10 9 0.96 14 0.643
57 A 3 3 1.00 14 0.214
58 A 3 3 1.00 14 0.214
59 A 3 3 1.00 14 0.214
60 A 3 3 1.00 14 0.214
61 A 16 15 0.94 16 0.938
62 A 14 13 0.95 14 0.929
63 A 13 12 0.89 12 1.000
64 A 17 16 1.00 16 1.000
65 A 7 6 1.04 16 0.375
66 A 8 7 1.02 16 0.438
67 A 12 11 1.01 16 0.688
68 A 14 13 1.03 16 0.812
69 A 16 15 1.03 16 0.938
70 A 16 15 0.98 16 0.938
71 A 16 15 0.94 16 0.938
72 A 14 13 0.95 14 0.929
73 A 13 12 0.89 12 1.000
74 A 18 17 1.00 16 1.062
75 A 8 7 1.04 16 0.438
76 A 9 8 1.02 16 0.500
77 A 13 12 1.01 16 0.750
78 A 15 14 1.02 16 0.875
79 A 18 17 1.00 16 1.062
80 A 17 16 0.95 16 1.000
81 A 15 14 0.97 14 1.000
82 A 14 13 0.91 12 1.083
83 A 20 19 1.00 16 1.188
84 A 8 7 1.05 16 0.438
85 A 9 8 1.02 16 0.500
86 A 14 13 1.01 16 0.812
87 A 16 15 1.03 16 0.938
88 A 16 15 0.98 16 0.938
89 A 16 15 0.94 16 0.938
90 A 14 13 0.95 14 0.929
91 A 13 12 0.89 12 1.000
92 A 18 17 1.00 16 1.062
93 A 8 7 1.04 16 0.438
94 A 9 8 1.02 16 0.500
95 A 13 12 1.01 16 0.750
96 A 15 14 1.03 16 0.875
97 A 16 15 0.98 16 0.938
98 A 16 15 0.94 16 0.938
99 A 14 13 0.95 14 0.929
100 A 13 12 0.89 12 1.000
101 A 17 16 1.00 16 1.000
102 A 7 6 1.04 16 0.375
103 A 8 7 1.02 16 0.438
104 A 12 11 1.01 16 0.688
105 A 14 13 1.02 16 0.812
106 A 18 17 1.00 16 1.062
107 A 17 16 0.95 16 1.000
108 A 15 14 0.97 14 1.000
109 A 14 13 0.91 12 1.083
110 A 21 20 1.00 16 1.250
111 A 9 8 1.05 16 0.500
112 A 10 9 1.02 16 0.562
113 A 15 14 1.01 16 0.875
114 A 17 16 1.03 16 1.000
115 A 16 15 0.95 14 1.071
116 A 14 13 0.97 12 1.083
117 A 13 12 0.90 10 1.200
118 A 17 16 1.02 14 1.143
119 A 12 11 1.02 14 0.786
120 A 13 12 1.05 14 0.857
121 A 17 16 1.03 14 1.143
122 A 6 6 1.05 14 0.429
123 A 4 4 1.11 12 0.333
124 A 3 3 1.06 10 0.300
125 A 4 4 1.07 14 0.286
126 A 3 3 1.02 14 0.214
127 A 4 4 1.05 14 0.286
128 A 16 15 0.99 16 0.938
129 A 14 13 1.01 14 0.929
130 A 13 12 0.97 12 1.000
131 A 26 25 1.07 16 1.562
132 A 16 15 1.01 16 0.938
133 A 17 16 1.02 16 1.000
134 A 5 5 1.00 14 0.357
135 A 6 6 1.00 14 0.429
136 A 3 3 1.00 14 0.214
137 A 3 3 1.00 14 0.214
138 A 6 6 1.00 14 0.429
139 A 5 5 1.00 14 0.357
140 A 7 7 1.01 14 0.500
141 A 3 3 1.00 14 0.214
142 A 3 3 1.00 14 0.214
143 A 7 7 1.01 14 0.500
144 A 2 2 1.00 16 0.125
145 A 2 2 1.00 16 0.125
146 A 2 2 1.00 16 0.125
147 A 2 2 1.00 16 0.125
148 A 2 2 1.00 16 0.125
149 A 2 2 1.00 16 0.125
150 A 2 2 1.00 12 0.167
151 A 2 2 1.00 12 0.167
152 A 2 2 1.00 16 0.125
153 A 2 2 1.00 15 0.133
154 A 5 5 1.04 15 0.333
155 A 5 5 1.04 15 0.333
156 A 3 3 1.00 13 0.231
157 A 2 2 1.00 11 0.182
158 A 4 4 1.00 15 0.267
159 A 2 2 1.00 15 0.133
160 A 3 3 1.00 15 0.200
161 A 7 7 1.02 15 0.467
162 A 11 10 1.03 16 0.625
163 A 9 8 1.03 16 0.500
164 A 9 8 1.05 16 0.500
165 A 7 6 1.10 14 0.429
166 A 6 5 1.25 12 0.417
167 A 9 8 1.25 16 0.500
168 A 5 4 1.00 16 0.250
169 A 6 5 0.99 16 0.312
170 A 10 9 1.04 16 0.562
171 A 3 3 1.00 16 0.188
172 A 3 3 1.00 16 0.188
173 A 3 3 1.00 16 0.188
174 A 3 3 1.00 14 0.214
175 A 3 3 1.00 12 0.250
176 A 3 3 1.00 16 0.188
177 A 3 3 1.00 16 0.188
178 A 3 3 1.00 16 0.188
179 A 3 3 1.00 16 0.188
180 A 14 13 1.06 16 0.812
181 A 12 11 1.06 16 0.688
182 A 10 9 1.01 16 0.562
183 A 8 7 1.05 14 0.500
184 A 7 6 1.16 12 0.500
185 A 10 9 1.21 16 0.562
186 A 6 5 1.05 16 0.312
187 A 7 6 0.96 16 0.375
188 A 14 13 1.05 16 0.812
189 A 12 11 1.03 16 0.688
190 A 9 8 1.03 16 0.500
191 A 9 8 1.05 16 0.500
192 A 7 6 1.10 14 0.429
193 A 6 5 1.25 12 0.417
194 A 9 8 1.25 16 0.500
195 A 5 4 1.00 16 0.250
196 A 6 5 0.99 16 0.312
197 A 12 11 1.04 16 0.688
198 A 3 3 1.00 16 0.188
199 A 3 3 1.00 16 0.188
200 A 3 3 1.00 16 0.188
201 A 3 3 1.00 14 0.214
202 A 3 3 1.00 12 0.250
203 A 3 3 1.00 16 0.188
204 A 3 3 1.00 16 0.188
205 A 3 3 0.98 16 0.188
206 A 3 3 0.98 16 0.188
207 A 13 12 1.06 16 0.750
208 A 11 10 1.06 16 0.625
209 A 11 10 1.01 16 0.625
210 A 8 7 1.06 14 0.500
211 A 7 6 1.16 12 0.500
212 A 10 9 1.22 16 0.562
213 A 6 5 1.05 16 0.312
214 A 7 6 0.97 16 0.375
215 A 13 12 1.07 16 0.750
216 A 16 15 0.84 18 0.833
217 A 14 13 0.87 16 0.812
218 A 13 12 0.88 14 0.857
219 A 15 14 1.11 18 0.778
220 A 7 6 1.27 18 0.333
221 A 16 15 0.84 18 0.833
222 A 14 13 0.87 16 0.812
223 A 13 12 0.88 14 0.857
224 A 19 18 1.00 18 1.000
225 A 8 7 1.06 18 0.389
226 A 16 15 0.84 18 0.833
227 A 14 13 0.87 16 0.812
228 A 13 12 0.88 14 0.857
229 A 14 13 1.11 18 0.722
230 A 6 5 1.24 18 0.278
231 A 16 15 0.84 18 0.833
232 A 14 13 0.87 16 0.812
233 A 13 12 0.88 14 0.857
234 A 18 17 1.00 18 0.944
235 A 7 6 1.07 18 0.333
236 A 4 4 1.00 14 0.286
237 A 5 5 1.02 14 0.357
238 A 5 5 1.03 14 0.357
239 A 3 3 1.00 12 0.250
240 A 2 2 1.00 10 0.200
241 A 5 5 1.06 14 0.357
242 A 2 2 1.00 14 0.143
243 A 3 3 0.99 14 0.214
244 A 3 3 1.00 19 0.158
245 A 2 2 1.00 19 0.105
246 A 2 2 1.00 17 0.118
247 A 2 2 1.00 6 0.333
248 A 1 1 1.00 19 0.053
249 A 3 3 1.00 19 0.158
250 A 4 4 1.02 19 0.211
251 A 5 5 1.03 19 0.263
252 A 6 6 1.04 19 0.316
253 A 3 3 1.00 21 0.143
254 A 3 3 1.00 21 0.143
255 A 3 3 1.00 21 0.143
256 A 1 1 1.00 21 0.048
257 A 2 2 1.00 21 0.095
258 A 3 3 1.07 21 0.143
259 A 3 3 1.00 21 0.143
260 A 2 2 1.00 21 0.095
261 A 2 2 1.00 19 0.105
262 A 2 2 1.00 8 0.250
263 A 1 1 1.00 21 0.048
264 A 3 3 1.00 21 0.143
265 A 4 4 1.02 21 0.190
266 A 5 5 1.03 21 0.238
267 A 3 3 1.00 23 0.130
268 A 3 3 1.00 23 0.130
269 A 3 3 1.00 23 0.130
270 A 1 1 1.00 23 0.043
271 A 2 2 1.00 23 0.087
272 A 3 3 1.07 23 0.130
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 24 0.125
302 A 5 5 1.00 24 0.208
303 A 3 3 1.00 24 0.125
304 A 4 4 1.00 24 0.167
305 A 2 2 1.00 24 0.083
306 A 2 2 1.00 24 0.083
307 A 4 4 1.00 24 0.167
308 A 3 3 1.00 24 0.125
309 A 5 5 1.00 24 0.208
310 A 4 4 0.60 25 0.160
311 A 6 5 1.17 25 0.200
312 A 4 4 0.69 25 0.160
313 A 5 4 1.08 25 0.160
314 A 3 3 1.00 25 0.120
315 A 3 3 1.00 25 0.120
316 A 5 4 1.08 25 0.160
317 A 4 4 0.70 25 0.160
318 A 6 5 1.17 25 0.200
319 A 3 3 1.00 24 0.125
320 A 3 3 1.00 24 0.125
321 A 2 2 1.00 24 0.083
322 A 3 3 1.00 24 0.125
323 A 3 3 1.00 24 0.125
324 A 3 3 1.00 24 0.125
325 A 3 3 1.00 24 0.125
326 A 2 2 1.00 24 0.083
327 A 3 3 1.00 24 0.125
328 A 4 4 0.69 25 0.160
329 A 3 3 1.12 25 0.120
330 A 3 3 1.00 25 0.120
331 A 3 3 1.09 25 0.120
332 A 4 4 0.67 25 0.160
333 A 4 4 0.67 25 0.160
334 A 3 3 1.09 25 0.120
335 A 3 3 1.00 25 0.120
336 A 3 3 1.12 25 0.120
337 A 2 2 1.00 21 0.095
338 A 2 2 1.00 19 0.105
339 A 2 2 1.00 8 0.250
340 A 5 5 1.59 24 0.208
341 A 5 5 1.00 24 0.208
342 A 3 3 0.98 22 0.136
343 A 1 1 1.00 21 0.048
344 A 3 3 1.85 24 0.125
345 A 8 8 1.80 24 0.333
346 A 10 10 1.77 24 0.417
347 A 5 5 0.87 21 0.238
348 A 3 3 1.00 23 0.130
349 A 3 3 1.00 23 0.130
350 A 3 3 1.00 23 0.130
351 A 6 6 0.83 26 0.231
352 A 6 6 0.84 26 0.231
353 A 6 6 0.85 26 0.231
354 A 6 6 0.87 26 0.231
355 A 4 4 0.91 24 0.167
356 A 3 3 1.00 23 0.130
357 A 3 3 1.00 26 0.115
358 A 4 4 0.87 26 0.154
359 A 8 8 0.82 26 0.308
360 A 3 3 1.00 23 0.130
361 A 3 3 1.00 23 0.130
362 A 3 3 1.00 23 0.130
363 A 3 3 1.00 23 0.130
364 A 2 2 1.00 22 0.091
365 A 2 2 1.00 24 0.083
366 A 2 2 1.00 24 0.083
367 A 2 2 1.00 24 0.083
368 A 3 3 1.00 26 0.115
369 A 3 3 1.00 26 0.115
370 A 3 3 1.00 26 0.115
371 A 3 3 1.00 21 0.143
372 A 3 3 1.00 24 0.125
373 A 3 3 1.00 24 0.125
374 A 1 1 1.00 35 0.029
375 A 2 2 1.00 26 0.077
376 A 2 2 1.00 26 0.077
377 A 2 2 1.00 26 0.077
378 A 2 2 1.00 26 0.077
379 A 2 2 1.00 26 0.077
380 A 3 3 1.00 28 0.107
381 A 3 3 1.00 28 0.107
382 A 4 4 0.58 28 0.143
383 A 4 4 0.59 28 0.143
384 A 3 3 1.00 28 0.107
385 A 3 3 1.00 28 0.107