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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 [189] had the largest ratio of [.560000000000000053]

# 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 1.00 19 0.105
2 A 2 2 1.00 19 0.105
3 A 2 2 1.00 17 0.118
4 A 2 2 1.00 16 0.125
5 A 2 2 1.00 19 0.105
6 A 2 2 1.00 19 0.105
7 A 2 2 1.00 19 0.105
8 A 2 2 1.00 19 0.105
9 A 2 2 1.00 19 0.105
10 A 2 2 1.00 19 0.105
11 A 2 2 1.00 19 0.105
12 A 2 2 1.00 19 0.105
13 A 2 2 1.00 21 0.095
14 A 2 2 1.00 19 0.105
15 A 2 2 1.00 18 0.111
16 A 2 2 1.00 21 0.095
17 A 2 2 1.00 21 0.095
18 A 2 2 1.00 21 0.095
19 A 2 2 1.00 21 0.095
20 A 2 2 1.00 21 0.095
21 A 2 2 1.00 21 0.095
22 A 2 2 1.00 21 0.095
23 A 2 2 1.00 21 0.095
24 A 2 2 1.00 21 0.095
25 A 2 2 1.00 21 0.095
26 A 2 2 1.00 19 0.105
27 A 2 2 1.00 18 0.111
28 A 2 2 1.00 21 0.095
29 A 2 2 1.00 21 0.095
30 A 2 2 1.00 21 0.095
31 A 2 2 1.00 21 0.095
32 A 2 2 1.00 21 0.095
33 A 2 2 1.00 21 0.095
34 A 2 2 1.00 21 0.095
35 A 2 2 1.00 21 0.095
36 A 2 2 1.00 21 0.095
37 A 2 2 1.00 21 0.095
38 A 2 2 1.00 21 0.095
39 A 2 2 1.00 21 0.095
40 A 2 2 1.00 21 0.095
41 A 2 2 1.00 21 0.095
42 A 2 2 1.00 19 0.105
43 A 5 4 1.00 18 0.222
44 A 2 2 1.00 21 0.095
45 A 2 2 1.00 21 0.095
46 A 2 2 1.00 21 0.095
47 A 2 2 1.00 21 0.095
48 A 4 4 1.00 21 0.190
49 A 4 4 1.01 21 0.190
50 A 7 6 1.19 21 0.286
51 A 4 3 1.14 19 0.158
52 A 4 3 1.00 18 0.167
53 A 4 4 1.23 21 0.190
54 A 4 4 1.15 21 0.190
55 A 4 4 1.11 21 0.190
56 A 2 2 1.00 21 0.095
57 A 2 2 1.00 21 0.095
58 A 2 2 1.00 21 0.095
59 A 2 2 1.00 21 0.095
60 A 2 2 1.00 21 0.095
61 A 2 2 1.00 21 0.095
62 A 2 2 1.00 21 0.095
63 A 2 2 1.00 21 0.095
64 A 2 2 1.00 21 0.095
65 A 2 2 1.00 23 0.087
66 A 2 2 1.00 23 0.087
67 A 2 2 1.00 23 0.087
68 A 2 2 1.00 23 0.087
69 A 2 2 1.00 23 0.087
70 A 2 2 1.00 23 0.087
71 A 2 2 1.00 23 0.087
72 A 2 2 1.00 23 0.087
73 A 2 2 1.00 23 0.087
74 A 2 2 1.00 23 0.087
75 A 2 2 1.00 23 0.087
76 A 2 2 1.00 23 0.087
77 A 2 2 1.00 23 0.087
78 A 2 2 1.00 23 0.087
79 A 2 2 1.00 23 0.087
80 A 2 2 1.00 23 0.087
81 A 2 2 1.00 23 0.087
82 A 2 2 1.00 23 0.087
83 A 2 2 1.00 23 0.087
84 A 10 9 1.05 23 0.391
85 A 8 7 1.04 23 0.304
86 A 6 5 1.02 23 0.217
87 A 4 3 1.01 23 0.130
88 A 6 5 0.99 23 0.217
89 F 0 0 N/A 0.000 N/A
90 F 0 0 N/A 0.000 N/A
91 F 0 0 N/A 0.000 N/A
92 A 8 7 1.00 23 0.304
93 A 6 5 0.98 23 0.217
94 A 6 5 0.97 23 0.217
95 A 6 5 0.96 23 0.217
96 A 7 6 0.95 23 0.261
97 A 9 8 1.01 23 0.348
98 A 8 7 1.01 23 0.304
99 A 8 7 1.00 23 0.304
100 A 8 7 1.00 23 0.304
101 A 8 7 0.91 23 0.304
102 A 8 7 1.00 23 0.304
103 A 10 9 0.87 23 0.391
104 A 11 10 0.95 23 0.435
105 A 9 8 0.95 23 0.348
106 A 7 6 0.95 23 0.261
107 A 5 4 0.94 21 0.190
108 A 5 4 1.00 20 0.200
109 A 8 7 1.05 23 0.304
110 A 8 7 1.00 23 0.304
111 F 0 0 N/A 0.000 N/A
112 A 5 4 1.00 23 0.174
113 A 7 6 0.99 23 0.261
114 A 9 8 0.98 23 0.348
115 A 11 10 0.97 23 0.435
116 A 12 11 0.86 23 0.478
117 A 10 9 0.87 23 0.391
118 A 8 7 0.88 23 0.304
119 A 6 5 0.90 21 0.238
120 A 6 5 0.99 20 0.250
121 A 10 9 1.07 23 0.391
122 A 10 9 1.05 23 0.391
123 A 10 9 1.02 23 0.391
124 F 0 0 N/A 0.000 N/A
125 A 10 9 1.08 23 0.391
126 A 6 5 0.99 23 0.217
127 A 8 7 0.95 23 0.304
128 A 10 9 0.91 23 0.391
129 A 13 12 0.80 23 0.522
130 A 11 10 0.81 23 0.435
131 A 9 8 0.84 23 0.348
132 A 7 6 0.88 21 0.286
133 A 7 6 0.98 20 0.300
134 A 12 11 1.08 23 0.478
135 A 12 11 1.06 23 0.478
136 A 12 11 1.05 23 0.478
137 A 12 11 1.03 23 0.478
138 A 12 11 1.04 23 0.478
139 A 12 11 1.04 23 0.478
140 A 12 11 1.08 23 0.478
141 A 7 6 0.98 23 0.261
142 A 9 8 0.92 23 0.348
143 A 11 10 0.86 23 0.435
144 A 8 7 1.08 23 0.304
145 A 6 5 1.06 23 0.217
146 A 4 3 1.00 21 0.143
147 A 4 3 1.00 20 0.150
148 A 6 5 1.00 23 0.217
149 A 4 3 1.00 23 0.130
150 A 6 5 1.05 23 0.217
151 A 8 7 1.08 23 0.304
152 A 11 10 1.10 23 0.435
153 A 8 7 1.04 23 0.304
154 A 6 5 1.07 23 0.217
155 A 6 5 1.08 23 0.217
156 A 4 3 1.00 21 0.143
157 A 1 1 1.00 20 0.050
158 A 5 4 1.00 23 0.174
159 A 6 5 1.15 23 0.217
160 A 9 8 1.09 23 0.348
161 A 11 10 1.10 23 0.435
162 A 8 7 1.10 23 0.304
163 A 6 5 1.13 23 0.217
164 A 2 2 1.00 23 0.087
165 A 2 2 0.99 21 0.095
166 A 2 2 1.00 20 0.100
167 A 7 6 1.13 23 0.261
168 A 8 7 1.14 23 0.304
169 A 10 9 1.11 23 0.391
170 A 3 3 1.04 20 0.150
171 A 4 4 1.06 20 0.200
172 A 3 2 1.00 21 0.095
173 A 10 9 0.80 25 0.360
174 A 8 7 0.76 25 0.280
175 A 8 7 0.78 25 0.280
176 A 8 7 0.76 25 0.280
177 F 0 0 N/A 0.000 N/A
178 A 12 11 0.79 25 0.440
179 A 13 12 1.12 25 0.480
180 A 12 11 1.11 25 0.440
181 A 11 10 1.10 25 0.400
182 A 8 7 1.08 25 0.280
183 A 7 6 1.06 25 0.240
184 A 7 6 1.06 25 0.240
185 A 7 6 1.07 25 0.240
186 A 8 7 1.07 25 0.280
187 A 11 10 1.08 25 0.400
188 A 12 11 1.09 25 0.440
189 A 15 14 1.12 25 0.560
190 A 12 11 1.11 25 0.440
191 A 10 9 1.10 25 0.360
192 A 9 8 1.08 25 0.320
193 A 9 8 1.08 25 0.320
194 A 9 8 1.10 25 0.320
195 A 8 7 1.07 25 0.280
196 A 9 8 1.05 25 0.320
197 A 10 9 1.08 25 0.360
198 A 11 10 1.09 25 0.400
199 A 14 13 1.10 25 0.520
200 A 7 6 0.73 27 0.222
201 A 12 11 1.10 25 0.440
202 A 10 9 1.10 25 0.360
203 A 9 8 1.09 25 0.320
204 A 6 5 1.07 25 0.200
205 A 5 4 1.06 25 0.160
206 A 6 5 1.10 25 0.200
207 A 8 7 1.07 25 0.280
208 A 11 10 1.10 25 0.400
209 A 11 10 1.11 25 0.400
210 A 9 8 1.08 25 0.320
211 A 7 6 1.06 25 0.240
212 A 7 6 1.07 25 0.240
213 A 6 5 1.10 25 0.200
214 A 9 8 1.10 25 0.320
215 A 11 10 1.07 25 0.400
216 A 12 11 1.07 25 0.440
217 A 15 14 1.12 25 0.560
218 A 13 12 1.11 25 0.480
219 A 11 10 1.06 25 0.400
220 A 9 8 1.08 25 0.320
221 A 9 8 1.06 25 0.320
222 A 9 8 1.05 25 0.320
223 A 8 7 1.08 25 0.280
224 A 9 8 1.07 25 0.320
225 A 11 10 1.09 25 0.400
226 A 12 11 1.12 25 0.440
227 A 14 13 1.10 25 0.520
228 A 2 2 1.00 23 0.087
229 A 2 2 1.00 23 0.087
230 A 2 2 1.00 21 0.095
231 A 2 2 0.88 23 0.087
232 A 4 4 0.93 23 0.174
233 A 4 3 1.00 25 0.120
234 A 4 3 1.00 25 0.120
235 A 4 3 1.00 25 0.120
236 A 4 3 1.00 25 0.120
237 A 4 3 1.00 25 0.120
238 A 4 3 1.00 25 0.120
239 A 4 3 1.00 23 0.130
240 A 6 6 1.14 21 0.286
241 A 4 4 1.19 21 0.190
242 A 2 2 1.21 19 0.105
243 A 2 2 1.30 18 0.111
244 A 5 4 1.16 21 0.190
245 A 7 6 1.15 21 0.286
246 A 9 8 1.14 21 0.381

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