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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 [51] had the largest ratio of [1.41667000000000010]

# 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 10 1.00 13 0.769
2 A 11 10 1.05 13 0.769
3 A 7 7 1.00 13 0.538
4 A 5 5 1.00 13 0.385
5 A 2 2 1.00 11 0.182
6 A 3 3 1.00 12 0.250
7 A 8 8 1.04 11 0.727
8 A 9 9 1.02 13 0.692
9 A 11 10 0.98 13 0.769
10 A 13 12 1.02 13 0.923
11 A 7 7 1.07 12 0.583
12 A 10 10 1.11 12 0.833
13 A 10 9 1.06 10 0.900
14 A 7 6 1.00 10 0.600
15 A 4 3 1.00 10 0.300
16 A 8 7 1.00 10 0.700
17 A 11 10 1.07 10 1.000
18 A 14 13 1.12 10 1.300
19 A 4 3 1.00 25 0.120
20 A 4 3 1.00 28 0.107
21 A 6 5 1.05 25 0.200
22 A 5 4 1.00 25 0.160
23 A 6 5 1.05 25 0.200
24 A 8 7 0.99 25 0.280
25 A 7 6 1.01 25 0.240
26 A 8 7 1.00 25 0.280
27 A 9 8 0.99 25 0.320
28 A 4 3 1.00 23 0.130
29 A 5 4 1.00 24 0.167
30 A 10 9 1.01 21 0.429
31 A 8 7 1.00 21 0.333
32 A 6 5 1.00 19 0.263
33 A 6 5 1.00 12 0.417
34 A 6 5 1.00 19 0.263
35 A 6 5 1.00 21 0.238
36 A 5 5 1.07 12 0.417
37 A 3 3 1.03 12 0.250
38 A 7 6 1.00 12 0.500
39 A 18 17 1.24 13 1.308
40 A 14 13 1.25 13 1.000
41 A 12 11 1.23 13 0.846
42 A 10 9 1.17 13 0.692
43 A 7 6 1.22 11 0.545
44 A 7 6 1.16 12 0.500
45 A 11 10 1.20 11 0.909
46 A 14 13 1.26 13 1.000
47 A 17 16 1.24 13 1.231
48 A 19 18 1.24 13 1.385
49 A 12 11 1.31 12 0.917
50 A 15 14 1.32 12 1.167
51 A 18 17 1.31 12 1.417
52 A 4 4 1.32 12 0.333
53 A 7 6 0.74 12 0.500
54 A 9 8 1.00 21 0.381
55 A 7 6 1.00 21 0.286
56 A 5 4 1.00 19 0.211
57 N/A 2 0 1.00 12 0.000
58 N/A 2 0 1.00 19 0.000
59 N/A 2 0 1.00 21 0.000

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