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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 [213] had the largest ratio of [36]

# 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 1 1 1.00 6 0.167
2 A 2 2 1.00 8 0.250
3 A 2 1 1.00 8 0.125
4 A 3 2 1.00 8 0.250
5 A 2 1 1.00 8 0.125
6 A 4 2 1.00 8 0.250
7 A 3 2 1.00 10 0.200
8 A 2 2 1.00 10 0.200
9 A 2 2 1.00 10 0.200
10 A 1 1 1.00 10 0.100
11 A 1 1 1.00 10 0.100
12 A 2 2 1.00 10 0.200
13 A 2 2 1.00 10 0.200
14 A 3 2 1.00 10 0.200
15 A 4 3 1.00 8 0.375
16 A 3 3 1.00 8 0.375
17 A 3 3 1.00 8 0.375
18 A 2 2 1.00 8 0.250
19 A 2 2 1.00 8 0.250
20 A 3 3 1.00 8 0.375
21 A 3 3 1.00 8 0.375
22 A 4 3 1.00 8 0.375
23 A 1 1 1.00 10 0.100
24 A 6 5 1.00 13 0.385
25 A 2 2 1.00 13 0.154
26 A 4 4 1.00 13 0.308
27 A 2 2 1.00 11 0.182
28 A 3 3 1.00 11 0.273
29 A 5 5 1.00 13 0.385
30 A 6 6 1.00 13 0.462
31 A 6 5 1.00 13 0.385
32 A 1 1 1.00 10 0.100
33 A 2 2 1.00 10 0.200
34 A 3 2 1.00 10 0.200
35 A 4 2 1.00 10 0.200
36 A 1 1 1.00 12 0.083
37 A 2 2 1.00 12 0.167
38 A 3 2 1.00 12 0.167
39 A 4 2 1.00 12 0.167
40 A 3 3 1.00 13 0.231
41 A 3 3 1.00 14 0.214
42 A 3 2 1.00 14 0.143
43 A 2 2 1.00 14 0.143
44 A 1 1 1.00 14 0.071
45 A 2 2 1.00 14 0.143
46 A 3 3 1.00 14 0.214
47 A 4 3 1.00 14 0.214
48 A 3 2 1.00 15 0.133
49 A 2 2 1.00 15 0.133
50 A 1 1 1.00 15 0.067
51 A 2 2 1.00 15 0.133
52 A 3 3 1.00 15 0.200
53 A 4 3 1.00 15 0.200
54 A 6 6 1.00 13 0.462
55 A 5 5 1.00 13 0.385
56 A 5 5 1.00 13 0.385
57 A 3 3 1.00 11 0.273
58 A 4 4 1.00 11 0.364
59 A 6 6 1.00 13 0.462
60 A 6 6 1.00 13 0.462
61 A 7 6 1.00 13 0.462
62 A 4 3 1.00 12 0.250
63 A 3 3 1.00 12 0.250
64 A 2 2 1.00 12 0.167
65 A 1 1 1.00 12 0.083
66 A 2 1 1.00 10 0.100
67 A 2 2 1.00 12 0.167
68 A 4 4 1.00 12 0.333
69 A 5 5 1.00 12 0.417
70 A 6 5 1.00 12 0.417
71 A 2 2 1.00 12 0.167
72 A 4 4 1.00 12 0.333
73 A 5 5 1.00 12 0.417
74 A 6 5 1.00 12 0.417
75 A 1 1 1.00 12 0.083
76 A 3 3 1.00 12 0.250
77 A 4 4 1.00 12 0.333
78 A 5 4 1.00 12 0.333
79 A 7 7 1.00 10 0.700
80 A 6 6 1.00 10 0.600
81 A 2 2 1.00 14 0.143
82 A 2 2 1.00 10 0.200
83 A 4 4 1.00 10 0.400
84 A 7 7 1.00 10 0.700
85 A 8 7 1.00 10 0.700
86 A 5 5 1.00 13 0.385
87 A 4 3 1.00 17 0.176
88 A 3 3 1.00 17 0.176
89 A 2 2 1.00 17 0.118
90 A 4 3 1.00 18 0.167
91 A 3 3 1.00 18 0.167
92 A 2 2 1.00 18 0.111
93 A 2 2 1.00 13 0.154
94 A 2 2 1.00 13 0.154
95 A 3 3 1.00 13 0.231
96 A 4 3 1.00 13 0.231
97 A 2 2 1.00 15 0.133
98 A 2 2 1.00 15 0.133
99 A 3 3 1.00 15 0.200
100 A 4 3 1.00 15 0.200
101 A 3 3 1.00 17 0.176
102 A 3 3 1.00 17 0.176
103 A 4 4 1.00 17 0.235
104 A 3 3 1.00 18 0.167
105 A 3 3 1.00 18 0.167
106 A 4 4 1.00 18 0.222
107 A 8 6 1.00 17 0.353
108 A 7 6 1.00 17 0.353
109 A 6 6 1.00 17 0.353
110 A 3 3 1.00 15 0.200
111 A 4 4 1.00 15 0.267
112 A 5 4 1.00 15 0.267
113 A 6 4 1.00 15 0.267
114 A 3 3 1.00 20 0.150
115 A 2 2 1.00 20 0.100
116 A 2 2 1.00 15 0.133
117 A 2 2 1.00 13 0.154
118 A 5 5 1.00 17 0.294
119 A 6 6 1.00 17 0.353
120 A 7 6 1.00 17 0.353
121 A 5 3 1.00 10 0.300
122 A 4 3 1.00 10 0.300
123 A 3 3 1.00 10 0.300
124 A 2 2 1.00 10 0.200
125 A 2 2 1.00 10 0.200
126 A 3 3 1.00 10 0.300
127 A 4 3 1.00 10 0.300
128 A 6 3 1.00 10 0.300
129 A 4 3 1.00 10 0.300
130 A 3 3 1.00 10 0.300
131 A 3 3 1.00 10 0.300
132 A 4 3 1.00 10 0.300
133 A 6 3 1.00 10 0.300
134 A 7 3 1.00 10 0.300
135 A 5 3 1.00 10 0.300
136 A 3 3 1.00 10 0.300
137 A 3 3 1.00 10 0.300
138 A 3 2 1.00 10 0.200
139 A 3 2 1.00 10 0.200
140 A 2 2 1.00 9 0.222
141 A 2 2 1.00 11 0.182
142 A 2 2 1.00 11 0.182
143 A 2 2 1.00 13 0.154
144 A 3 2 1.00 11 0.182
145 A 3 2 1.00 13 0.154
146 A 2 2 1.00 9 0.222
147 A 2 2 1.00 11 0.182
148 A 1 1 1.00 11 0.091
149 A 1 1 1.00 13 0.077
150 A 3 2 1.00 11 0.182
151 A 3 2 1.00 13 0.154
152 A 5 3 1.00 13 0.231
153 A 3 2 1.00 13 0.154
154 A 4 3 1.00 13 0.231
155 A 3 2 1.00 13 0.154
156 A 3 3 1.00 13 0.231
157 A 2 1 1.00 13 0.077
158 A 2 2 1.00 13 0.154
159 A 2 2 1.00 11 0.182
160 A 4 3 1.00 11 0.273
161 A 3 3 1.00 13 0.231
162 A 4 3 1.00 13 0.231
163 A 3 2 1.00 13 0.154
164 A 4 3 1.00 13 0.231
165 A 3 2 1.00 13 0.154
166 A 6 5 1.00 13 0.385
167 A 3 2 1.00 13 0.154
168 A 5 5 1.00 13 0.385
169 A 3 2 1.00 13 0.154
170 A 4 4 1.00 13 0.308
171 A 2 2 1.00 11 0.182
172 A 6 4 1.00 11 0.364
173 A 4 4 1.00 13 0.308
174 A 4 3 1.00 13 0.231
175 A 5 5 1.00 13 0.385
176 A 5 4 1.00 13 0.308
177 A 6 5 1.00 13 0.385
178 A 4 4 1.00 13 0.308
179 A 6 6 1.00 13 0.462
180 A 3 2 1.00 13 0.154
181 A 6 6 1.00 13 0.462
182 A 4 4 1.00 11 0.364
183 A 3 2 1.00 11 0.182
184 A 7 6 1.00 13 0.462
185 A 4 3 1.00 13 0.231
186 A 12 8 1.00 13 0.615
187 A 6 5 1.00 13 0.385
188 A 5 4 1.00 13 0.308
189 A 5 5 1.00 13 0.385
190 A 5 4 1.00 13 0.308
191 A 4 4 1.00 13 0.308
192 A 4 4 1.00 11 0.364
193 A 5 5 1.00 11 0.454
194 A 5 4 1.00 13 0.308
195 A 6 5 1.00 13 0.385
196 A 6 5 1.00 13 0.385
197 A 4 4 1.00 13 0.308
198 A 3 3 1.00 13 0.231
199 A 6 5 1.00 15 0.333
200 A 5 4 1.00 13 0.308
201 A 5 4 1.00 15 0.267
202 A 8 7 1.00 15 0.467
203 A 7 5 1.00 15 0.333
204 A 5 5 1.00 15 0.333
205 A 11 8 1.00 15 0.533
206 A 6 6 1.00 31 0.194
207 A 7 7 1.00 31 0.226
208 A 8 7 1.00 31 0.226
209 A 9 7 1.00 31 0.226
210 A 9 6 1.00 12 0.500
211 A 11 7 1.00 14 0.500
212 A 13 8 1.00 14 0.571
213 A 5 3 1.00 36 0.083
214 A 4 3 1.00 36 0.083
215 A 2 2 1.00 34 0.059
216 A 0 0 0.00 0 0.000
217 A 0 0 0.00 0 0.000
218 A 3 3 1.00 12 0.250
219 A 5 5 1.00 12 0.417
220 A 13 5 1.00 20 0.250
221 A 0 0 0.00 0 0.000
222 A 11 6 1.00 22 0.273
223 A 9 5 1.00 22 0.227
224 A 7 4 1.00 20 0.200
225 A 2 2 1.00 19 0.105
226 A 0 0 0.00 0 0.000
227 A 0 0 0.00 0 0.000
228 A 18 11 1.00 24 0.458
229 A 15 10 1.00 24 0.417
230 A 12 9 1.00 22 0.409
231 A 4 4 1.00 21 0.190
232 A 0 0 0.00 0 0.000
233 A 0 0 0.00 0 0.000
234 A 21 14 1.00 24 0.583
235 A 16 11 1.00 24 0.458
236 A 13 10 1.00 22 0.454
237 A 3 2 1.00 21 0.095
238 A 0 0 0.00 0 0.000
239 A 1 1 1.00 11 0.091
240 A 2 2 1.00 13 0.154
241 A 2 2 1.00 13 0.154
242 A 3 2 1.00 13 0.154
243 A 1 1 1.01 15 0.067
244 A 2 2 1.02 17 0.118
245 A 2 2 1.00 17 0.118
246 A 3 2 1.00 17 0.118
247 A 2 1 1.00 15 0.067
248 A 3 2 1.00 17 0.118
249 A 3 1 1.00 17 0.059
250 A 4 2 1.00 17 0.118
251 A 3 1 1.00 17 0.059
252 A 3 2 1.00 19 0.105
253 A 3 2 1.00 19 0.105
254 A 2 1 1.00 19 0.053
255 A 2 1 1.00 19 0.053
256 A 3 2 1.00 19 0.105
257 A 3 2 1.00 19 0.105
258 A 8 8 1.00 18 0.444
259 A 6 6 1.00 18 0.333
260 A 3 3 1.00 18 0.167
261 A 4 4 1.00 18 0.222
262 A 5 5 1.00 14 0.357
263 A 6 6 1.00 16 0.375
264 A 4 3 1.00 16 0.188
265 A 5 4 1.00 16 0.250
266 A 4 3 1.00 16 0.188
267 A 4 3 1.00 14 0.214
268 A 3 3 1.00 14 0.214
269 A 4 4 1.00 16 0.250
270 A 3 3 1.00 16 0.188
271 A 6 5 1.00 16 0.312
272 A 5 4 1.00 16 0.250
273 A 4 3 1.00 10 0.300
274 A 4 3 1.00 8 0.375
275 A 11 8 1.00 8 1.000
276 A 12 9 1.00 10 0.900
277 A 4 3 1.00 10 0.300
278 A 4 3 1.00 8 0.375
279 A 9 9 1.00 8 1.125
280 A 13 9 1.00 10 0.900
281 A 4 3 1.00 10 0.300
282 A 4 3 1.00 8 0.375
283 A 21 9 1.00 8 1.125
284 A 22 9 1.00 10 0.900
285 A 2 2 1.00 18 0.111
286 A 2 2 1.00 18 0.111
287 A 1 1 1.00 16 0.062
288 A 1 1 1.00 16 0.062
289 A 1 1 1.00 18 0.056
290 A 2 2 1.00 18 0.111
291 A 2 2 1.00 18 0.111
292 A 6 5 1.00 25 0.200
293 A 6 5 1.00 25 0.200
294 A 5 4 1.00 25 0.160
295 A 4 4 1.00 25 0.160
296 A 4 4 1.00 25 0.160
297 A 6 5 1.00 25 0.200
298 A 6 5 1.00 25 0.200
299 A 1 1 1.00 10 0.100
300 A 6 4 1.00 12 0.333
301 A 6 4 1.00 15 0.267
302 A 6 3 1.00 12 0.250
303 A 4 2 1.00 14 0.143
304 A 6 3 1.00 17 0.176
305 A 8 5 1.00 16 0.312
306 A 9 6 1.00 18 0.333
307 A 14 5 1.00 18 0.278
308 A 8 5 1.00 19 0.263
309 A 9 6 1.00 21 0.286
310 A 14 5 1.00 21 0.238
311 A 8 4 1.00 16 0.250
312 A 9 4 1.00 18 0.222
313 A 14 4 1.00 18 0.222
314 A 6 4 1.00 18 0.222
315 A 7 4 1.00 20 0.200
316 A 10 4 1.00 20 0.200
317 A 8 5 1.00 21 0.238
318 A 9 5 1.00 23 0.217
319 A 14 5 1.00 23 0.217
320 A 8 4 1.00 19 0.210
321 A 10 4 1.00 21 0.190
322 A 14 4 1.00 21 0.190
323 A 8 5 1.00 21 0.238
324 A 10 5 1.00 23 0.217
325 A 14 5 1.00 23 0.217
326 A 8 5 1.00 24 0.208
327 A 10 5 1.00 26 0.192
328 A 14 5 1.00 26 0.192
329 A 2 1 1.00 17 0.059
330 A 2 1 1.00 20 0.050
331 A 3 1 1.00 20 0.050
332 A 3 2 1.00 21 0.095
333 A 6 5 1.00 6 0.833
334 A 9 6 1.00 6 1.000
335 A 8 4 1.00 16 0.250
336 A 8 4 1.00 19 0.210

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