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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 [65] had the largest ratio of [.454544999999999977]

# 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 6 5 0.80 21 0.238
2 A 8 8 0.96 21 0.381
3 A 6 5 0.89 21 0.238
4 A 6 6 0.97 21 0.286
5 A 6 5 1.00 21 0.238
6 A 4 4 1.00 19 0.211
7 A 1 1 1.00 12 0.083
8 A 4 4 1.00 19 0.211
9 A 3 3 1.00 21 0.143
10 A 6 5 1.00 21 0.238
11 A 5 5 0.97 21 0.238
12 A 7 6 0.94 21 0.286
13 A 7 7 0.96 21 0.333
14 A 2 2 1.00 29 0.069
15 A 2 2 1.00 28 0.071
16 A 8 8 0.98 25 0.320
17 A 8 8 0.95 25 0.320
18 A 6 6 1.00 25 0.240
19 A 6 6 1.00 25 0.240
20 A 6 6 1.00 25 0.240
21 A 6 6 1.00 25 0.240
22 A 8 8 1.01 25 0.320
23 A 8 8 1.01 25 0.320
24 A 2 2 1.00 23 0.087
25 A 2 2 1.00 24 0.083
26 A 2 2 1.00 21 0.095
27 A 2 2 1.00 21 0.095
28 A 2 2 1.00 21 0.095
29 A 2 2 1.00 21 0.095
30 A 2 2 1.00 19 0.105
31 A 5 4 1.00 10 0.400
32 A 3 3 1.00 8 0.375
33 A 2 2 1.00 19 0.105
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 12 11 1.06 28 0.393
38 A 10 9 1.02 28 0.321
39 A 10 9 1.02 26 0.346
40 A 1 1 1.00 19 0.053
41 A 6 6 1.00 26 0.231
42 A 5 5 1.00 28 0.179
43 A 7 7 1.03 28 0.250
44 A 9 8 1.02 28 0.286
45 A 11 10 1.07 28 0.357
46 A 11 10 1.01 28 0.357
47 A 13 13 1.07 32 0.406
48 A 11 11 1.09 32 0.344
49 A 11 11 1.05 32 0.344
50 A 9 9 1.00 32 0.281
51 A 11 11 1.03 32 0.344
52 A 11 11 1.05 32 0.344
53 A 13 13 1.09 32 0.406
54 A 13 12 0.98 29 0.414
55 A 11 10 0.98 29 0.345
56 A 11 10 1.01 29 0.345
57 A 9 8 1.00 27 0.296
58 A 1 1 1.00 20 0.050
59 A 7 7 1.00 27 0.259
60 A 6 6 1.00 29 0.207
61 A 10 9 1.04 29 0.310
62 A 10 9 0.98 29 0.310
63 A 13 12 1.03 29 0.414
64 A 12 11 0.94 29 0.379
65 A 15 15 1.01 33 0.455
66 A 13 13 1.05 33 0.394
67 A 11 11 1.00 33 0.333
68 A 11 11 1.00 33 0.333
69 A 13 13 1.03 33 0.394
70 A 15 15 1.03 33 0.455

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