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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 [114] had the largest ratio of [25]

# 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 5 4 1.00 19 0.210
2 A 5 4 1.00 19 0.210
3 A 5 4 1.00 19 0.210
4 A 5 4 1.00 19 0.210
5 A 4 3 1.00 17 0.176
6 A 6 6 1.00 17 0.353
7 A 5 4 1.00 19 0.210
8 A 5 4 1.00 19 0.210
9 A 5 4 1.00 19 0.210
10 A 11 7 1.00 19 0.368
11 A 10 7 1.00 19 0.368
12 A 9 7 1.00 19 0.368
13 A 7 7 1.00 19 0.368
14 A 7 7 1.00 19 0.368
15 A 8 6 1.00 19 0.316
16 A 8 6 1.00 19 0.316
17 A 8 6 1.00 19 0.316
18 A 8 6 1.00 19 0.316
19 A 5 4 1.00 21 0.190
20 A 5 4 1.00 21 0.190
21 A 5 4 1.00 21 0.190
22 A 5 4 1.00 21 0.190
23 A 5 4 1.00 19 0.210
24 A 5 4 1.00 19 0.210
25 A 5 4 1.00 21 0.190
26 A 5 4 1.00 21 0.190
27 A 5 4 1.00 21 0.190
28 A 5 4 1.00 21 0.190
29 A 27 8 1.00 21 0.381
30 A 18 8 1.00 21 0.381
31 A 14 8 1.00 21 0.381
32 A 9 7 1.00 21 0.333
33 A 11 9 1.00 21 0.429
34 A 8 8 1.00 21 0.381
35 A 12 8 1.00 21 0.381
36 A 12 8 1.00 21 0.381
37 A 12 8 1.00 21 0.381
38 A 5 4 1.00 21 0.190
39 A 5 4 1.00 21 0.190
40 A 5 4 1.00 21 0.190
41 A 4 3 1.00 21 0.143
42 A 5 4 1.00 19 0.210
43 A 5 4 1.00 19 0.210
44 A 5 4 1.00 21 0.190
45 A 5 4 1.00 21 0.190
46 A 5 4 1.00 21 0.190
47 A 5 4 1.00 21 0.190
48 A 29 9 1.00 21 0.429
49 A 18 9 1.00 21 0.429
50 A 16 9 1.00 21 0.429
51 A 11 8 1.00 21 0.381
52 A 9 7 1.00 21 0.333
53 A 11 8 1.00 21 0.381
54 A 10 9 1.00 21 0.429
55 A 17 9 1.00 21 0.429
56 A 17 9 1.00 21 0.429
57 A 7 6 1.00 21 0.286
58 A 7 6 1.00 21 0.286
59 A 7 6 1.00 21 0.286
60 A 6 5 1.00 21 0.238
61 A 5 4 1.00 19 0.210
62 A 6 6 1.00 19 0.316
63 A 7 7 1.00 21 0.333
64 A 8 7 1.00 21 0.333
65 A 9 7 1.00 21 0.333
66 A 8 7 1.00 21 0.333
67 A 7 7 1.00 21 0.333
68 A 5 5 1.00 21 0.238
69 A 6 5 1.00 21 0.238
70 A 7 6 1.00 21 0.286
71 A 7 6 1.00 21 0.286
72 A 7 6 1.00 21 0.286
73 A 7 6 1.00 21 0.286
74 A 5 4 1.00 21 0.190
75 A 5 4 1.00 21 0.190
76 A 5 4 1.00 21 0.190
77 A 5 4 1.00 21 0.190
78 A 5 4 1.00 21 0.190
79 A 5 4 1.00 19 0.210
80 A 6 5 1.00 19 0.263
81 A 4 4 1.00 21 0.190
82 A 6 5 1.00 21 0.238
83 A 16 8 1.00 21 0.381
84 A 7 6 1.00 21 0.286
85 A 11 6 1.00 21 0.286
86 A 9 8 1.00 21 0.381
87 A 11 6 1.00 21 0.286
88 A 13 7 1.00 21 0.333
89 A 13 7 1.00 21 0.333
90 A 13 7 1.00 21 0.333
91 A 5 4 1.00 21 0.190
92 A 5 4 1.00 21 0.190
93 A 5 4 1.00 21 0.190
94 A 5 4 1.00 21 0.190
95 A 5 4 1.00 21 0.190
96 A 5 4 1.00 19 0.210
97 A 6 5 1.00 19 0.263
98 A 5 4 1.00 21 0.190
99 A 6 5 1.00 21 0.238
100 A 19 9 1.00 21 0.429
101 A 15 6 1.00 21 0.286
102 A 13 8 1.00 21 0.381
103 A 10 8 1.00 21 0.381
104 A 15 8 1.00 21 0.381
105 A 16 7 1.00 21 0.333
106 A 16 7 1.00 21 0.333
107 A 16 7 1.00 21 0.333
108 A 11 11 1.00 23 0.478
109 A 11 11 1.00 23 0.478
110 A 9 9 1.00 23 0.391
111 A 9 9 1.00 23 0.391
112 A 11 11 1.00 23 0.478
113 A 11 11 1.00 23 0.478
114 A 15 12 1.00 25 0.480
115 A 15 12 1.00 25 0.480
116 A 13 10 1.00 25 0.400
117 A 13 10 1.00 25 0.400
118 A 16 13 1.00 25 0.520
119 A 16 13 1.00 25 0.520
120 A 8 8 1.00 25 0.320
121 A 7 7 1.00 25 0.280
122 A 7 7 1.00 25 0.280
123 A 7 7 1.00 25 0.280
124 A 7 7 1.00 25 0.280
125 A 8 8 1.00 25 0.320
126 A 8 8 1.00 25 0.320
127 A 14 8 1.00 25 0.320
128 A 14 9 1.00 25 0.360
129 A 14 9 1.00 25 0.360
130 A 15 9 1.00 25 0.360
131 A 15 9 1.00 25 0.360
132 A 17 9 1.00 25 0.360
133 A 17 9 1.00 25 0.360
134 A 9 6 1.00 23 0.261
135 A 7 6 1.00 23 0.261
136 A 5 5 1.00 21 0.238
137 A 5 5 1.00 23 0.217
138 A 9 6 1.00 23 0.261
139 A 12 7 1.00 23 0.304
140 A 5 4 1.00 25 0.160
141 A 5 4 1.00 25 0.160
142 A 5 4 1.00 25 0.160
143 A 5 4 1.00 25 0.160
144 A 5 4 1.00 23 0.174
145 A 4 4 1.00 21 0.190
146 A 4 4 1.00 21 0.190
147 A 3 3 1.00 21 0.143
148 A 2 2 1.00 19 0.105
149 A 2 2 1.00 19 0.105
150 A 4 4 1.00 21 0.190
151 A 5 5 1.00 21 0.238
152 A 11 9 1.00 21 0.429
153 A 6 5 1.00 21 0.238
154 A 4 4 1.00 21 0.190
155 A 7 6 1.00 21 0.286
156 A 5 4 1.00 23 0.174
157 A 5 4 1.00 23 0.174
158 A 5 4 1.00 23 0.174
159 A 5 4 1.00 23 0.174
160 A 5 4 1.00 19 0.210
161 A 5 4 1.00 19 0.210
162 A 5 4 1.00 19 0.210
163 A 4 3 1.00 17 0.176
164 A 5 5 1.00 17 0.294
165 A 7 6 1.00 19 0.316
166 A 9 7 1.00 19 0.368
167 A 10 7 1.00 19 0.368
168 A 10 7 1.00 19 0.368
169 A 9 7 1.00 19 0.368
170 A 7 7 1.00 19 0.368
171 A 7 7 1.00 19 0.368
172 A 8 6 1.00 19 0.316
173 A 8 6 1.00 19 0.316
174 A 5 4 1.00 21 0.190
175 A 5 4 1.00 21 0.190
176 A 5 4 1.00 19 0.210
177 A 5 4 1.00 19 0.210
178 A 6 5 1.00 21 0.238
179 A 12 10 1.00 21 0.476
180 A 7 7 1.00 21 0.333
181 A 10 8 1.00 21 0.381
182 A 8 6 1.00 21 0.286
183 A 9 6 1.00 21 0.286
184 A 9 6 1.00 21 0.286
185 A 5 4 1.00 21 0.190
186 A 4 3 1.00 21 0.143
187 A 5 4 1.00 19 0.210
188 A 5 4 1.00 19 0.210
189 A 6 5 1.00 21 0.238
190 A 21 11 1.00 21 0.524
191 A 8 7 1.00 21 0.333
192 A 8 8 1.00 21 0.381
193 A 15 10 1.00 21 0.476
194 A 17 9 1.00 21 0.429
195 A 17 9 1.00 21 0.429
196 A 5 4 1.00 21 0.190
197 A 5 4 1.00 21 0.190
198 A 5 4 1.00 21 0.190
199 A 5 4 1.00 19 0.210
200 A 4 3 1.00 19 0.158
201 A 6 5 1.00 21 0.238
202 A 7 5 1.00 21 0.238
203 A 7 5 1.00 21 0.238
204 A 6 5 1.00 21 0.238
205 A 5 5 1.00 21 0.238
206 A 5 5 1.00 21 0.238
207 A 6 5 1.00 21 0.238
208 A 7 5 1.00 21 0.238
209 A 5 4 1.00 21 0.190
210 A 5 4 1.00 21 0.190
211 A 5 4 1.00 21 0.190
212 A 5 4 1.00 19 0.210
213 A 5 4 1.00 19 0.210
214 A 6 5 1.00 21 0.238
215 A 7 5 1.00 21 0.238
216 A 10 8 1.00 21 0.381
217 A 8 7 1.00 21 0.333
218 A 8 8 1.00 21 0.381
219 A 11 7 1.00 21 0.333
220 A 15 8 1.00 21 0.381
221 A 5 4 1.00 21 0.190
222 A 5 4 1.00 21 0.190
223 A 5 4 1.00 21 0.190
224 A 5 4 1.00 19 0.210
225 A 5 4 1.00 19 0.210
226 A 5 4 1.00 21 0.190
227 A 7 5 1.00 21 0.238
228 A 11 8 1.00 21 0.381
229 A 9 7 1.00 21 0.333
230 A 9 8 1.00 21 0.381
231 A 16 8 1.00 21 0.381
232 A 20 9 1.00 21 0.429
233 A 15 12 1.00 25 0.480
234 A 14 12 1.00 25 0.480
235 A 14 12 1.00 25 0.480
236 A 13 11 1.00 25 0.440
237 A 13 11 1.00 25 0.440
238 A 14 12 1.00 25 0.480
239 A 14 12 1.00 25 0.480
240 A 15 12 1.00 25 0.480
241 A 35 16 1.00 25 0.640
242 A 35 16 1.00 25 0.640
243 A 32 15 1.00 25 0.600
244 A 32 15 1.00 25 0.600
245 A 27 13 1.00 25 0.520
246 A 27 13 1.00 25 0.520
247 A 33 16 1.00 25 0.640
248 A 33 16 1.00 25 0.640
249 A 1 1 1.00 14 0.071
250 A 2 2 1.00 23 0.087
251 A 5 5 1.00 14 0.357
252 A 4 4 1.00 23 0.174
253 A 1 1 1.00 14 0.071
254 A 6 6 1.00 23 0.261
255 A 6 6 1.00 14 0.429
256 A 6 6 1.00 23 0.261
257 A 9 6 1.00 23 0.261
258 A 9 8 1.00 23 0.348
259 A 5 5 1.00 21 0.238
260 A 4 4 1.00 23 0.174
261 A 6 4 1.00 23 0.174
262 A 7 4 1.00 23 0.174
263 A 0 0 0.00 0 0.000
264 A 0 0 0.00 0 0.000
265 A 0 0 0.00 0 0.000
266 A 0 0 0.00 0 0.000
267 A 0 0 0.00 0 0.000
268 A 6 3 1.00 21 0.143
269 A 3 3 1.00 21 0.143
270 A 2 2 1.00 19 0.105
271 A 4 3 1.00 19 0.158
272 A 9 4 1.00 21 0.190
273 A 0 0 0.00 0 0.000
274 A 0 0 0.00 0 0.000
275 A 4 4 1.00 21 0.190
276 F 0 0 N/A 0. N/A
277 A 0 0 0.00 0 0.000
278 A 0 0 0.00 0 0.000
279 A 0 0 0.00 0 0.000
280 A 0 0 0.00 0 0.000
281 A 11 11 1.00 23 0.478
282 A 11 11 1.00 23 0.478
283 A 9 9 1.00 23 0.391
284 A 9 9 1.00 23 0.391
285 A 11 11 1.00 23 0.478
286 A 11 11 1.00 23 0.478
287 A 15 13 1.00 25 0.520
288 A 15 13 1.00 25 0.520
289 A 12 10 1.00 25 0.400
290 A 12 10 1.00 25 0.400
291 A 14 12 1.00 25 0.480
292 A 14 12 1.00 25 0.480
293 A 8 8 1.00 25 0.320
294 A 8 8 1.00 25 0.320
295 A 7 7 1.00 25 0.280
296 A 7 7 1.00 25 0.280
297 A 7 7 1.00 25 0.280
298 A 7 7 1.00 25 0.280
299 A 8 8 1.00 25 0.320
300 A 16 9 1.00 25 0.360
301 A 16 9 1.00 25 0.360
302 A 14 9 1.00 25 0.360
303 A 14 9 1.00 25 0.360
304 A 13 9 1.00 25 0.360
305 A 13 9 1.00 25 0.360
306 A 13 8 1.00 25 0.320

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