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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 [93] had the largest ratio of [.647059000000000051]

# 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 25 0.080
2 A 2 2 1.00 27 0.074
3 A 2 2 1.00 27 0.074
4 A 11 10 0.82 27 0.370
5 A 13 12 1.00 27 0.444
6 A 12 11 1.12 30 0.367
7 A 6 5 1.00 30 0.167
8 A 8 7 1.16 30 0.233
9 A 10 9 1.12 30 0.300
10 A 6 5 1.00 23 0.217
11 A 6 5 1.07 23 0.217
12 A 6 5 1.14 30 0.167
13 A 2 2 0.99 28 0.071
14 A 2 2 1.00 30 0.067
15 A 7 6 0.77 30 0.200
16 F 0 0 N/A 0.000 N/A
17 A 6 5 0.99 34 0.147
18 A 6 5 0.99 34 0.147
19 A 10 9 1.00 32 0.281
20 F 0 0 N/A 0.000 N/A
21 A 4 3 1.00 32 0.094
22 A 5 4 1.12 29 0.138
23 A 4 3 1.00 29 0.103
24 A 7 6 1.00 26 0.231
25 A 6 5 1.10 30 0.167
26 A 8 7 1.07 30 0.233
27 A 10 9 1.07 30 0.300
28 A 5 4 1.07 30 0.133
29 A 7 6 1.07 30 0.200
30 A 9 8 1.08 30 0.267
31 A 3 2 1.00 26 0.077
32 A 7 6 1.00 26 0.231
33 A 3 2 1.00 24 0.083
34 A 6 5 1.00 20 0.250
35 A 8 7 1.12 36 0.194
36 A 2 2 1.00 36 0.056
37 A 3 2 1.00 32 0.062
38 A 12 11 0.93 32 0.344
39 A 7 6 0.82 38 0.158
40 A 11 10 0.71 35 0.286
41 A 8 7 0.76 33 0.212
42 A 7 6 0.65 32 0.188
43 A 10 9 0.68 35 0.257
44 A 10 9 0.66 35 0.257
45 A 11 10 0.70 35 0.286
46 A 9 8 0.71 38 0.211
47 A 7 6 0.73 36 0.167
48 A 7 6 0.73 35 0.171
49 A 10 9 0.78 38 0.237
50 A 10 9 0.74 38 0.237
51 A 10 9 0.79 38 0.237
52 A 9 8 1.02 27 0.296
53 A 11 10 1.01 25 0.400
54 A 7 6 1.10 24 0.250
55 A 2 2 1.00 27 0.074
56 A 2 2 1.00 27 0.074
57 A 2 2 1.00 27 0.074
58 A 12 11 0.83 27 0.407
59 A 12 11 1.03 25 0.440
60 A 9 8 1.01 24 0.333
61 A 2 2 1.00 27 0.074
62 A 2 2 1.00 27 0.074
63 A 2 2 1.00 27 0.074
64 A 2 2 1.00 27 0.074
65 A 8 7 0.99 27 0.259
66 A 4 3 0.93 25 0.120
67 A 4 3 1.00 24 0.125
68 A 2 2 1.00 27 0.074
69 A 2 2 1.00 27 0.074
70 A 2 2 1.00 27 0.074
71 A 2 2 1.00 27 0.074
72 A 6 5 0.96 27 0.185
73 A 6 5 0.96 25 0.200
74 A 6 5 0.96 24 0.208
75 A 2 2 1.00 27 0.074
76 A 2 2 1.00 27 0.074
77 A 2 2 1.00 28 0.071
78 A 12 11 1.12 28 0.393
79 A 12 11 1.02 26 0.423
80 A 9 8 1.12 25 0.320
81 A 2 2 1.00 28 0.071
82 A 2 2 1.00 28 0.071
83 A 2 2 1.00 28 0.071
84 A 2 2 1.00 28 0.071
85 A 14 13 1.04 28 0.464
86 A 14 13 1.06 26 0.500
87 A 12 11 1.02 25 0.440
88 A 2 2 1.00 28 0.071
89 A 2 2 1.00 28 0.071
90 A 2 2 1.00 28 0.071
91 A 11 10 1.03 24 0.417
92 A 10 9 1.00 22 0.409
93 A 12 11 1.15 17 0.647
94 A 2 2 1.00 28 0.071
95 A 2 2 1.00 28 0.071
96 A 10 9 1.00 28 0.321
97 A 6 5 1.00 26 0.192
98 A 5 4 1.00 25 0.160
99 A 2 2 1.00 28 0.071
100 A 2 2 1.00 28 0.071
101 A 2 2 1.00 28 0.071
102 A 2 2 1.00 28 0.071
103 A 2 2 1.00 28 0.071
104 A 8 7 1.19 28 0.250
105 A 8 7 1.21 26 0.269
106 A 8 7 1.18 25 0.280
107 A 2 2 1.00 28 0.071
108 A 2 2 1.00 28 0.071
109 F 0 0 N/A 0.000 N/A
110 A 10 9 1.01 28 0.321
111 A 7 6 1.14 27 0.222
112 A 2 2 1.00 30 0.067
113 A 2 2 1.00 30 0.067
114 A 2 2 1.00 30 0.067
115 A 8 7 1.00 30 0.233
116 A 4 3 0.95 28 0.107
117 A 4 3 1.00 27 0.111
118 A 2 2 1.00 30 0.067
119 A 2 2 1.00 30 0.067
120 A 2 2 1.00 30 0.067
121 A 2 2 1.00 30 0.067
122 A 6 5 0.95 30 0.167
123 A 6 5 0.95 28 0.179
124 F 0 0 N/A 0.000 N/A
125 F 0 0 N/A 0.000 N/A
126 A 2 2 1.00 30 0.067
127 A 2 2 1.00 30 0.067
128 A 16 15 1.01 30 0.500
129 A 6 5 0.50 28 0.179
130 A 10 9 0.61 27 0.333
131 A 2 2 1.00 30 0.067
132 A 2 2 1.00 30 0.067
133 A 10 9 1.13 34 0.265
134 A 7 6 1.10 30 0.200
135 A 4 3 1.00 34 0.088
136 A 7 6 1.06 34 0.176
137 A 11 10 1.11 34 0.294
138 A 1 1 1.00 17 0.059
139 A 1 1 1.00 15 0.067
140 A 3 3 1.00 23 0.130
141 A 4 4 1.00 21 0.190
142 A 2 2 0.70 40 0.050
143 A 3 3 0.62 104 0.029

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