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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 [171] had the largest ratio of [.714285999999999976]

# 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 2 2 0.96 37 0.054
2 A 3 3 0.96 37 0.081
3 A 14 13 1.67 30 0.433
4 A 11 10 1.49 30 0.333
5 A 10 9 1.27 28 0.321
6 A 7 6 1.13 27 0.222
7 A 11 10 1.00 30 0.333
8 A 12 11 0.99 30 0.367
9 A 14 13 0.90 30 0.433
10 A 13 12 0.98 30 0.400
11 A 13 12 0.97 30 0.400
12 A 10 9 0.94 30 0.300
13 A 11 10 0.98 30 0.333
14 A 14 13 0.98 30 0.433
15 A 16 15 1.01 30 0.500
16 F 0 0 N/A 0.000 N/A
17 F 0 0 N/A 0.000 N/A
18 A 10 9 1.17 30 0.300
19 A 9 8 1.02 29 0.276
20 A 12 11 1.05 32 0.344
21 A 13 12 1.02 32 0.375
22 A 15 14 1.04 32 0.438
23 A 16 15 0.95 32 0.469
24 A 15 14 1.20 32 0.438
25 A 15 14 1.02 32 0.438
26 A 12 11 0.91 32 0.344
27 A 14 13 0.96 32 0.406
28 A 17 16 0.96 32 0.500
29 A 19 18 0.99 32 0.562
30 A 14 13 1.07 32 0.406
31 A 12 11 1.07 30 0.367
32 A 10 9 1.06 29 0.310
33 A 14 13 1.36 32 0.406
34 A 2 2 1.44 32 0.062
35 A 2 2 1.35 32 0.062
36 A 2 2 1.02 32 0.062
37 A 2 2 1.11 32 0.062
38 A 16 15 1.23 32 0.469
39 A 12 11 1.27 32 0.344
40 A 11 10 1.29 30 0.333
41 A 11 10 1.38 29 0.345
42 A 13 12 1.25 32 0.375
43 A 2 2 1.49 32 0.062
44 A 2 2 1.64 32 0.062
45 A 2 2 1.43 32 0.062
46 A 2 2 1.42 32 0.062
47 A 14 13 1.55 30 0.433
48 A 12 11 1.35 30 0.367
49 A 11 10 1.14 28 0.357
50 A 8 7 1.03 27 0.259
51 A 13 12 0.95 30 0.400
52 A 13 12 0.98 30 0.400
53 A 15 14 0.95 30 0.467
54 A 15 14 0.91 30 0.467
55 A 16 15 0.91 30 0.500
56 A 15 14 0.94 30 0.467
57 A 15 14 0.92 30 0.467
58 A 11 10 0.88 30 0.333
59 A 12 11 0.92 30 0.367
60 A 14 13 0.94 30 0.433
61 A 15 14 1.35 32 0.438
62 F 0 0 N/A 0.000 N/A
63 A 12 11 1.07 30 0.367
64 A 10 9 0.89 29 0.310
65 A 14 13 1.00 32 0.406
66 A 15 14 0.99 32 0.438
67 A 16 15 1.06 32 0.469
68 A 17 16 0.97 32 0.500
69 A 17 16 1.12 32 0.500
70 A 18 17 0.95 32 0.531
71 A 17 16 1.12 32 0.500
72 A 17 16 0.97 32 0.500
73 A 13 12 0.81 32 0.375
74 A 15 14 0.90 32 0.438
75 A 17 16 0.87 32 0.500
76 A 16 15 1.04 32 0.469
77 A 14 13 0.99 30 0.433
78 A 12 11 0.98 29 0.379
79 A 17 16 1.31 32 0.500
80 A 2 2 1.33 32 0.062
81 A 2 2 1.54 32 0.062
82 A 2 2 1.90 32 0.062
83 A 2 2 1.99 32 0.062
84 A 2 2 1.89 32 0.062
85 A 2 2 1.79 32 0.062
86 A 14 13 1.10 32 0.406
87 A 13 12 1.11 30 0.400
88 A 13 12 1.16 29 0.414
89 A 16 15 1.50 32 0.469
90 A 2 2 1.48 32 0.062
91 A 2 2 1.66 32 0.062
92 A 2 2 1.71 32 0.062
93 A 2 2 1.76 32 0.062
94 A 13 12 1.86 30 0.400
95 A 10 9 1.69 30 0.300
96 A 9 8 1.42 28 0.286
97 A 6 5 1.27 27 0.185
98 A 10 9 1.04 30 0.300
99 A 11 10 1.09 30 0.333
100 A 11 10 1.03 30 0.333
101 A 9 8 1.03 30 0.267
102 A 10 9 1.06 30 0.300
103 A 13 12 1.07 30 0.400
104 A 15 14 1.07 30 0.467
105 A 12 11 1.43 32 0.344
106 A 10 9 1.32 30 0.300
107 A 8 7 1.18 29 0.241
108 A 11 10 1.09 32 0.312
109 A 12 11 1.09 32 0.344
110 A 13 12 1.10 32 0.375
111 A 13 12 1.06 32 0.375
112 A 11 10 1.03 32 0.312
113 A 13 12 1.05 32 0.375
114 A 16 15 1.05 32 0.469
115 A 13 12 1.13 32 0.375
116 A 12 11 1.11 32 0.344
117 A 10 9 1.07 30 0.300
118 A 8 7 1.04 29 0.241
119 A 9 8 1.36 32 0.250
120 A 2 2 1.00 32 0.062
121 A 2 2 1.10 32 0.062
122 A 2 2 1.12 32 0.062
123 A 2 2 1.21 32 0.062
124 A 14 13 1.25 32 0.406
125 A 10 9 1.21 32 0.281
126 A 10 9 1.20 30 0.300
127 A 8 7 1.11 29 0.241
128 A 7 6 1.71 32 0.188
129 A 2 2 1.22 32 0.062
130 A 2 2 1.24 32 0.062
131 A 2 2 1.24 32 0.062
132 A 10 9 1.00 30 0.300
133 A 9 8 0.99 30 0.267
134 A 7 6 0.91 28 0.214
135 A 6 5 0.93 27 0.185
136 A 10 9 0.94 30 0.300
137 A 7 6 0.93 30 0.200
138 A 9 8 0.94 30 0.267
139 A 11 10 0.98 30 0.333
140 A 12 11 0.97 30 0.367
141 A 9 8 1.00 32 0.250
142 A 8 7 0.84 30 0.233
143 A 6 5 0.84 29 0.172
144 A 10 9 0.98 32 0.281
145 A 12 11 0.97 32 0.344
146 A 9 8 0.99 32 0.250
147 A 12 11 0.99 32 0.344
148 A 13 12 1.00 32 0.375
149 A 12 11 1.14 32 0.344
150 A 10 9 1.11 32 0.281
151 A 10 9 1.08 32 0.281
152 A 9 8 1.04 30 0.267
153 A 6 5 1.00 29 0.172
154 A 8 7 1.64 32 0.219
155 A 2 2 1.11 32 0.062
156 A 2 2 1.19 32 0.062
157 A 12 11 1.20 32 0.344
158 A 11 10 1.18 32 0.312
159 A 11 10 1.14 32 0.312
160 A 7 6 1.01 30 0.200
161 A 6 5 1.01 29 0.172
162 A 9 8 1.92 32 0.250
163 A 2 2 1.23 32 0.062
164 A 2 2 1.24 32 0.062
165 B 20 19 2.12 30 0.633
166 F 0 0 N/A 0.000 N/A
167 A 18 17 1.00 35 0.486
168 A 16 15 0.99 35 0.429
169 A 14 13 0.97 33 0.394
170 A 12 11 0.98 32 0.344
171 A 26 25 1.53 35 0.714
172 B 19 18 2.70 35 0.514
173 B 21 20 2.76 35 0.571
174 B 22 21 2.72 35 0.600
175 B 23 22 2.58 35 0.629
176 A 18 17 0.97 35 0.486
177 A 16 15 0.96 33 0.455
178 A 14 13 0.96 32 0.406
179 F 0 0 N/A 0.000 N/A
180 F 0 0 N/A 0.000 N/A
181 F 0 0 N/A 0.000 N/A
182 F 0 0 N/A 0.000 N/A
183 F 0 0 N/A 0.000 N/A
184 F 0 0 N/A 0.000 N/A
185 A 16 15 1.04 35 0.429
186 A 14 13 1.03 35 0.371
187 A 12 11 1.02 33 0.333
188 A 10 9 1.02 32 0.281
189 A 14 13 1.14 35 0.371
190 A 16 15 1.14 35 0.429
191 A 18 17 1.11 35 0.486
192 A 16 15 1.11 35 0.429
193 A 14 13 1.08 35 0.371
194 A 13 12 1.06 33 0.364
195 A 10 9 1.01 32 0.281
196 A 24 23 1.49 35 0.657
197 B 19 18 2.16 35 0.514
198 B 20 19 2.28 35 0.543
199 A 16 15 1.08 35 0.429
200 A 15 14 1.05 35 0.400
201 A 13 12 1.03 33 0.364
202 A 12 11 1.03 32 0.344
203 A 19 18 1.68 35 0.514
204 B 25 24 3.11 35 0.686
205 B 24 23 3.24 35 0.657
206 A 9 8 0.99 34 0.235
207 A 16 15 1.14 35 0.429
208 A 14 13 1.11 35 0.371
209 A 12 11 1.09 35 0.314
210 A 10 9 1.05 33 0.273
211 A 10 9 1.06 32 0.281
212 F 0 0 N/A 0.000 N/A
213 F 0 0 N/A 0.000 N/A
214 F 0 0 N/A 0.000 N/A
215 A 16 15 1.09 35 0.429
216 A 14 13 1.07 35 0.371
217 A 12 11 1.05 35 0.314
218 A 12 11 1.04 33 0.333
219 A 12 11 1.04 32 0.344
220 F 0 0 N/A 0.000 N/A
221 F 0 0 N/A 0.000 N/A
222 F 0 0 N/A 0.000 N/A
223 A 16 15 1.07 35 0.429
224 A 14 13 1.06 35 0.371
225 A 14 13 1.05 35 0.371
226 A 14 13 1.05 33 0.394
227 A 14 13 1.04 32 0.406
228 F 0 0 N/A 0.000 N/A
229 F 0 0 N/A 0.000 N/A
230 F 0 0 N/A 0.000 N/A
231 A 16 15 1.09 35 0.429
232 A 14 13 1.07 35 0.371
233 A 12 11 1.03 35 0.314
234 A 12 11 1.03 35 0.314
235 A 12 11 1.04 33 0.333
236 A 12 11 1.05 32 0.344
237 F 0 0 N/A 0.000 N/A
238 F 0 0 N/A 0.000 N/A
239 F 0 0 N/A 0.000 N/A
240 A 18 17 1.04 45 0.378
241 A 16 15 1.04 43 0.349
242 A 14 13 1.03 42 0.310
243 A 18 17 1.12 45 0.378
244 A 18 17 1.13 45 0.378
245 A 18 17 1.10 45 0.378
246 A 20 19 1.10 45 0.422
247 A 22 21 1.09 45 0.467
248 A 16 15 1.05 32 0.469
249 A 12 11 1.01 32 0.344
250 A 7 6 1.01 32 0.188
251 A 4 3 0.99 32 0.094
252 A 4 3 1.15 32 0.094
253 A 11 10 1.13 31 0.323
254 A 9 8 1.14 31 0.258
255 A 6 5 1.11 31 0.161
256 A 4 3 1.24 31 0.097
257 A 4 3 1.35 31 0.097
258 F 0 0 N/A 0.000 N/A
259 C 2 2 3.66 43 0.047
260 A 5 5 0.71 36 0.139

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