[prev] [prev-tail] [tail] [up]

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 [285] had the largest ratio of [.542857000000000034]

# 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 12 12 0.98 33 0.364
2 A 10 10 0.98 33 0.303
3 A 8 8 0.98 31 0.258
4 A 6 6 1.00 33 0.182
5 A 9 9 1.01 33 0.273
6 A 11 11 1.04 33 0.333
7 A 13 12 0.96 35 0.343
8 A 10 9 0.98 35 0.257
9 A 7 6 0.96 35 0.171
10 A 14 13 1.00 35 0.371
11 A 17 16 1.02 35 0.457
12 A 10 9 1.00 33 0.273
13 A 6 5 1.00 34 0.147
14 A 2 2 1.00 43 0.047
15 A 2 2 1.00 37 0.054
16 A 11 10 1.24 31 0.323
17 A 13 13 0.87 34 0.382
18 A 11 11 0.87 34 0.324
19 A 9 9 0.89 34 0.265
20 A 7 7 0.96 32 0.219
21 A 5 5 1.09 34 0.147
22 A 9 9 1.07 34 0.265
23 A 9 9 1.03 34 0.265
24 A 11 11 1.01 34 0.324
25 A 13 13 0.99 34 0.382
26 A 15 15 0.83 36 0.417
27 A 13 13 0.81 36 0.361
28 A 11 11 0.79 36 0.306
29 A 9 9 0.87 36 0.250
30 A 9 9 0.85 34 0.265
31 A 9 9 0.92 36 0.250
32 A 9 9 0.97 36 0.250
33 A 9 9 1.04 36 0.250
34 A 6 6 1.00 36 0.167
35 A 8 8 0.98 36 0.222
36 A 10 10 0.96 36 0.278
37 A 12 12 0.94 36 0.333
38 A 17 17 0.81 36 0.472
39 A 15 15 0.81 36 0.417
40 A 13 13 0.78 36 0.361
41 A 11 11 0.88 36 0.306
42 A 11 11 0.82 36 0.306
43 A 11 11 0.87 34 0.324
44 A 11 11 0.84 36 0.306
45 A 11 11 0.91 36 0.306
46 A 11 11 0.95 36 0.306
47 A 11 11 1.02 36 0.306
48 A 6 6 0.97 36 0.167
49 A 8 8 0.96 36 0.222
50 A 10 10 0.96 36 0.278
51 A 12 12 0.94 36 0.333
52 A 13 13 0.90 36 0.361
53 A 11 11 0.84 36 0.306
54 A 9 9 0.92 36 0.250
55 A 5 5 1.11 34 0.147
56 A 8 7 0.86 36 0.194
57 A 8 7 0.95 36 0.194
58 A 10 9 0.92 36 0.250
59 A 12 11 0.90 36 0.306
60 A 15 15 0.87 36 0.417
61 A 13 13 0.92 36 0.361
62 A 11 11 0.90 36 0.306
63 A 9 9 0.97 36 0.250
64 A 8 8 1.08 34 0.235
65 A 8 7 0.95 36 0.194
66 A 8 7 0.82 36 0.194
67 A 8 7 0.83 36 0.194
68 A 10 9 0.84 36 0.250
69 A 12 11 0.85 36 0.306
70 A 15 15 0.85 36 0.417
71 A 13 13 0.92 36 0.361
72 A 11 11 0.93 36 0.306
73 A 9 9 1.05 36 0.250
74 A 8 8 1.03 34 0.235
75 A 10 9 0.92 36 0.250
76 A 8 7 0.84 36 0.194
77 A 8 7 0.75 36 0.194
78 A 8 7 0.74 36 0.194
79 A 10 9 0.77 36 0.250
80 A 12 11 0.79 36 0.306
81 A 12 12 0.93 36 0.333
82 A 10 10 0.94 36 0.278
83 A 8 8 0.96 36 0.222
84 A 6 6 0.97 36 0.167
85 A 11 10 1.06 36 0.278
86 A 11 10 1.07 36 0.278
87 A 11 10 1.07 36 0.278
88 A 13 12 1.03 36 0.333
89 A 12 12 0.90 38 0.316
90 A 10 10 0.91 38 0.263
91 A 8 8 0.94 38 0.211
92 A 6 6 0.95 38 0.158
93 A 12 11 0.99 38 0.289
94 A 12 11 0.98 38 0.289
95 A 12 11 0.97 38 0.289
96 A 12 11 0.98 38 0.289
97 A 14 13 0.96 38 0.342
98 A 12 12 0.90 38 0.316
99 A 10 10 0.93 38 0.263
100 A 8 8 0.93 38 0.211
101 A 6 6 0.95 38 0.158
102 A 14 13 1.00 38 0.342
103 A 14 13 0.97 38 0.342
104 A 14 13 0.93 38 0.342
105 A 14 13 0.97 38 0.342
106 A 14 13 0.98 38 0.342
107 A 16 15 0.96 38 0.395
108 A 12 12 0.91 38 0.316
109 A 10 10 0.92 38 0.263
110 A 8 8 0.95 38 0.211
111 A 6 6 1.00 38 0.158
112 A 8 7 0.98 38 0.184
113 A 10 9 0.96 38 0.237
114 A 12 11 0.91 38 0.289
115 A 14 14 0.90 38 0.368
116 A 12 12 0.91 38 0.316
117 A 10 10 0.94 38 0.263
118 A 8 8 0.96 38 0.211
119 A 6 6 1.01 38 0.158
120 A 10 9 0.93 38 0.237
121 A 12 11 0.94 38 0.289
122 A 14 13 0.90 38 0.342
123 A 14 14 0.91 38 0.368
124 A 12 12 0.89 38 0.316
125 A 10 10 0.93 38 0.263
126 A 8 8 0.96 38 0.211
127 A 6 6 0.98 38 0.158
128 A 12 11 0.93 38 0.289
129 A 14 13 0.90 38 0.342
130 A 16 15 0.91 38 0.395
131 A 4 4 1.00 40 0.100
132 A 4 4 1.00 40 0.100
133 A 4 4 1.00 40 0.100
134 A 4 4 1.00 40 0.100
135 A 9 8 1.01 40 0.200
136 A 9 8 1.01 40 0.200
137 A 4 4 1.00 40 0.100
138 A 4 4 1.00 40 0.100
139 A 6 6 0.99 40 0.150
140 A 6 6 0.99 40 0.150
141 A 6 6 1.01 40 0.150
142 A 4 4 1.00 40 0.100
143 A 10 9 1.00 40 0.225
144 A 10 9 0.98 40 0.225
145 A 10 9 1.01 40 0.225
146 A 4 4 1.00 40 0.100
147 A 6 6 1.00 40 0.150
148 A 6 6 0.99 40 0.150
149 A 8 8 0.97 40 0.200
150 A 8 8 1.02 40 0.200
151 A 6 6 1.00 40 0.150
152 A 4 4 1.00 40 0.100
153 A 12 11 0.99 40 0.275
154 A 12 11 0.95 40 0.275
155 A 12 11 0.95 40 0.275
156 A 12 11 1.02 40 0.275
157 A 4 4 1.00 40 0.100
158 A 6 6 1.00 40 0.150
159 A 8 8 1.00 40 0.200
160 A 10 10 0.97 40 0.250
161 A 10 10 1.03 40 0.250
162 A 8 8 0.99 40 0.200
163 A 6 6 1.00 40 0.150
164 A 4 4 1.00 40 0.100
165 A 14 13 1.00 40 0.325
166 A 14 13 0.93 40 0.325
167 A 14 13 0.95 40 0.325
168 A 14 13 0.96 40 0.325
169 A 14 13 1.01 40 0.325
170 A 4 4 1.00 40 0.100
171 A 6 6 1.00 40 0.150
172 A 8 8 0.98 40 0.200
173 A 10 10 1.00 40 0.250
174 A 12 11 0.97 40 0.275
175 A 10 9 0.99 40 0.225
176 A 9 8 1.02 40 0.200
177 A 8 7 1.03 40 0.175
178 A 6 6 1.00 40 0.150
179 A 8 8 1.00 40 0.200
180 A 14 13 0.93 40 0.325
181 A 12 11 0.95 40 0.275
182 A 10 9 0.97 40 0.225
183 A 9 8 1.02 40 0.200
184 A 6 6 1.00 40 0.150
185 A 8 8 0.99 40 0.200
186 A 10 10 0.95 40 0.250
187 A 16 15 0.93 40 0.375
188 A 14 13 0.95 40 0.325
189 A 12 11 0.96 40 0.275
190 A 10 9 1.02 40 0.225
191 A 4 4 1.00 40 0.100
192 A 8 8 1.01 40 0.200
193 A 10 10 0.97 40 0.250
194 A 12 12 1.01 40 0.300
195 A 9 8 1.21 36 0.222
196 A 9 8 0.94 36 0.222
197 A 9 8 0.94 36 0.222
198 A 9 8 0.96 34 0.235
199 A 6 6 1.00 23 0.261
200 A 9 8 0.99 36 0.222
201 A 9 8 0.93 36 0.222
202 A 9 8 0.93 36 0.222
203 A 8 7 1.04 38 0.184
204 A 8 7 1.04 38 0.184
205 A 8 8 0.84 38 0.211
206 A 6 6 1.05 38 0.158
207 A 4 4 1.00 38 0.105
208 A 8 7 1.04 38 0.184
209 A 8 7 1.04 38 0.184
210 A 8 7 1.04 38 0.184
211 A 8 8 0.87 40 0.200
212 A 6 6 0.92 40 0.150
213 A 4 4 1.00 40 0.100
214 A 9 8 1.23 40 0.200
215 A 9 8 1.24 38 0.211
216 A 9 8 1.23 40 0.200
217 A 9 8 1.22 40 0.200
218 A 4 4 1.00 46 0.087
219 A 4 4 1.00 45 0.089
220 A 5 5 1.00 44 0.114
221 A 5 5 1.00 43 0.116
222 A 2 2 1.00 47 0.043
223 A 2 2 1.00 46 0.043
224 A 3 3 1.00 32 0.094
225 A 3 3 1.00 32 0.094
226 A 3 3 1.00 30 0.100
227 A 9 9 1.00 24 0.375
228 A 3 3 1.00 30 0.100
229 A 5 5 1.00 32 0.156
230 A 3 3 1.00 32 0.094
231 A 3 3 1.00 32 0.094
232 A 3 3 1.00 32 0.094
233 A 5 5 1.02 32 0.156
234 A 3 3 1.00 32 0.094
235 A 3 3 1.00 32 0.094
236 A 3 3 1.00 32 0.094
237 A 3 3 1.00 32 0.094
238 A 3 3 1.00 30 0.100
239 A 6 6 1.05 24 0.250
240 A 3 3 1.00 30 0.100
241 A 5 5 1.00 32 0.156
242 A 3 3 1.00 32 0.094
243 A 3 3 1.00 32 0.094
244 A 10 10 1.03 33 0.303
245 A 8 8 1.03 33 0.242
246 A 6 6 1.11 31 0.194
247 A 2 2 1.00 21 0.095
248 A 11 10 1.11 33 0.303
249 A 12 11 1.25 33 0.333
250 A 14 13 1.09 33 0.394
251 A 14 14 1.03 35 0.400
252 A 12 12 1.04 35 0.343
253 A 8 8 0.87 33 0.242
254 A 4 4 0.88 23 0.174
255 A 13 12 1.08 35 0.343
256 A 14 13 1.08 35 0.371
257 A 14 13 1.19 35 0.371
258 A 16 16 1.04 35 0.457
259 A 14 14 1.05 35 0.400
260 A 9 9 0.81 33 0.273
261 A 5 5 0.80 23 0.217
262 A 16 15 1.09 35 0.429
263 A 16 15 1.04 35 0.429
264 A 17 16 1.08 35 0.457
265 A 6 6 1.00 35 0.171
266 A 4 4 0.96 35 0.114
267 A 8 8 1.03 33 0.242
268 A 4 4 1.00 23 0.174
269 A 9 8 1.06 35 0.229
270 A 11 10 1.04 35 0.286
271 A 14 13 1.07 35 0.371
272 A 6 6 1.03 35 0.171
273 A 10 10 1.05 35 0.286
274 A 9 9 1.05 33 0.273
275 A 4 4 0.98 23 0.174
276 A 11 10 1.09 35 0.286
277 A 13 12 1.05 35 0.343
278 A 15 14 1.08 35 0.400
279 A 12 12 1.05 35 0.343
280 A 11 11 1.06 35 0.314
281 A 9 9 1.02 33 0.273
282 A 6 6 0.97 23 0.261
283 A 14 13 1.13 35 0.371
284 A 17 16 1.07 35 0.457
285 A 20 19 1.08 35 0.543
286 A 11 11 0.92 37 0.297
287 A 9 9 0.97 37 0.243
288 A 9 9 1.09 35 0.257
289 A 4 4 1.00 25 0.160
290 A 6 5 1.00 37 0.135
291 A 6 5 1.00 37 0.135
292 A 8 7 0.97 37 0.189
293 A 14 14 0.84 37 0.378
294 A 12 12 0.91 37 0.324
295 A 11 11 0.99 35 0.314
296 A 6 6 0.98 25 0.240
297 A 9 8 1.04 37 0.216
298 A 9 8 1.04 37 0.216
299 A 9 8 1.04 37 0.216
300 A 17 17 0.79 37 0.459
301 A 15 15 0.86 37 0.405
302 A 13 13 0.93 35 0.371
303 A 8 8 0.96 25 0.320
304 A 12 11 1.06 37 0.297
305 A 12 11 1.04 37 0.297
306 A 12 11 1.05 37 0.297
307 F 0 0 N/A 0.000 N/A
308 A 14 13 1.07 37 0.351
309 A 11 10 1.05 35 0.286
310 A 6 5 1.00 25 0.200
311 A 8 7 1.00 37 0.189
312 A 11 10 1.11 37 0.270
313 F 0 0 N/A 0.000 N/A
314 A 17 16 1.06 37 0.432
315 A 14 13 1.04 37 0.351
316 A 11 10 1.03 35 0.286
317 A 6 5 1.00 25 0.200
318 A 11 10 1.07 37 0.270
319 A 14 13 1.09 37 0.351
320 A 17 16 1.10 37 0.432
321 A 17 16 1.05 37 0.432
322 A 14 13 1.05 37 0.351
323 A 11 10 1.04 35 0.286
324 A 8 7 0.98 25 0.280
325 A 14 13 1.10 37 0.351
326 A 17 16 1.11 37 0.432
327 A 20 19 1.11 37 0.514
328 A 7 6 1.00 35 0.171
329 A 12 11 1.00 33 0.333
330 A 10 9 1.00 35 0.257
331 A 7 6 1.00 35 0.171
332 A 16 15 1.00 37 0.405
333 A 7 6 1.00 37 0.162
334 A 11 10 1.01 37 0.270
335 A 8 7 0.99 37 0.189
336 A 12 12 0.99 35 0.343
337 A 10 10 1.01 33 0.303
338 A 6 6 1.00 23 0.261
339 A 11 10 1.07 35 0.286
340 A 14 13 1.06 35 0.371
341 A 16 15 1.08 35 0.429
342 A 9 8 1.08 37 0.216
343 A 9 8 1.09 37 0.216
344 A 9 8 1.09 37 0.216
345 A 9 8 1.08 37 0.216
346 A 9 8 1.09 35 0.229
347 A 10 9 1.04 39 0.231
348 A 7 6 1.11 36 0.167
349 A 7 6 1.10 40 0.150
350 A 2 2 1.00 55 0.036
351 A 2 2 1.00 51 0.039
352 A 12 11 1.18 35 0.314
353 A 15 15 1.01 39 0.385
354 A 8 8 0.99 39 0.205
355 A 5 5 1.00 39 0.128
356 A 8 8 1.06 39 0.205
357 A 11 11 1.05 39 0.282
358 N/A 2 0 1.00 35 0.000

[prev] [prev-tail] [front] [up]