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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 [61] had the largest ratio of [.368420999999999998]

# 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 11 11 0.92 37 0.297
2 A 9 9 0.95 37 0.243
3 A 7 7 1.01 35 0.200
4 A 6 6 0.96 30 0.200
5 A 9 8 1.04 37 0.216
6 A 7 6 1.13 37 0.162
7 A 6 5 1.06 37 0.135
8 A 11 11 1.06 37 0.297
9 A 9 9 1.07 37 0.243
10 A 6 6 1.08 35 0.171
11 A 5 5 1.03 30 0.167
12 A 9 8 1.04 37 0.216
13 A 7 6 1.13 37 0.162
14 A 6 5 1.06 37 0.135
15 A 7 7 1.20 31 0.226
16 A 5 5 1.03 30 0.167
17 A 10 9 1.00 33 0.273
18 A 9 8 1.00 33 0.242
19 A 8 7 1.04 33 0.212
20 A 14 13 0.87 40 0.325
21 A 11 10 0.88 40 0.250
22 A 9 8 0.95 38 0.211
23 A 7 6 0.69 33 0.182
24 A 10 9 0.84 40 0.225
25 A 9 8 0.96 40 0.200
26 A 7 6 0.98 40 0.150
27 A 14 13 0.96 40 0.325
28 A 11 10 0.98 40 0.250
29 A 8 7 1.01 38 0.184
30 A 6 5 0.66 33 0.152
31 A 10 9 0.84 40 0.225
32 A 9 8 0.96 40 0.200
33 A 7 6 0.98 40 0.150
34 A 9 8 1.57 30 0.267
35 A 4 4 1.35 29 0.138
36 A 10 9 1.62 32 0.281
37 A 9 8 1.62 32 0.250
38 A 7 6 1.23 32 0.188
39 A 8 7 1.15 32 0.219
40 A 7 6 1.16 32 0.188
41 A 10 9 0.60 36 0.250
42 A 8 7 0.64 34 0.206
43 A 8 7 0.75 29 0.241
44 A 11 10 1.07 36 0.278
45 A 11 10 1.05 36 0.278
46 A 11 10 1.06 36 0.278
47 A 9 8 0.75 36 0.222
48 A 7 6 0.78 34 0.176
49 A 7 6 0.85 29 0.207
50 A 9 8 1.08 36 0.222
51 A 9 8 1.09 36 0.222
52 A 9 8 1.10 36 0.222
53 A 9 8 1.05 36 0.222
54 A 8 7 1.02 36 0.194
55 A 6 5 1.03 34 0.147
56 A 6 5 1.02 29 0.172
57 A 7 6 1.09 36 0.167
58 A 7 6 1.18 36 0.167
59 A 7 6 1.05 36 0.167
60 A 9 8 1.05 36 0.222
61 A 14 14 1.03 38 0.368
62 A 12 12 1.02 38 0.316
63 A 12 12 1.03 38 0.316
64 A 12 12 1.01 38 0.316
65 A 12 12 1.03 38 0.316
66 A 14 14 1.03 38 0.368
67 A 14 14 1.03 38 0.368
68 A 12 12 1.03 38 0.316
69 A 10 10 1.03 38 0.263
70 A 10 10 1.03 38 0.263
71 A 10 10 1.06 38 0.263
72 A 12 12 1.04 38 0.316
73 A 12 12 1.02 38 0.316
74 A 10 10 1.03 38 0.263
75 A 8 8 1.02 38 0.211
76 A 8 8 1.05 38 0.211
77 A 10 10 1.05 38 0.263
78 A 12 12 1.05 38 0.316

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