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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 [.866666999999999965]

# 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 18 17 0.92 25 0.680
2 A 1 1 1.00 12 0.083
3 A 5 4 1.09 14 0.286
4 A 5 4 1.01 14 0.286
5 A 6 5 1.00 14 0.357
6 A 7 6 1.21 14 0.429
7 A 8 7 1.23 14 0.500
8 A 7 6 1.09 10 0.600
9 A 6 5 1.00 10 0.500
10 A 6 5 1.17 10 0.500
11 A 8 7 1.11 12 0.583
12 A 7 6 1.14 12 0.500
13 A 6 5 1.14 12 0.417
14 A 11 10 1.29 17 0.588
15 A 10 9 0.71 17 0.529
16 A 9 8 1.00 15 0.533
17 A 12 11 1.25 15 0.733
18 A 9 8 0.79 17 0.471
19 A 10 9 1.09 17 0.529
20 A 9 8 1.10 15 0.533
21 A 9 8 1.08 15 0.533
22 A 9 8 1.04 17 0.471
23 A 8 7 1.00 12 0.583
24 A 8 7 1.00 17 0.412
25 A 9 8 1.04 17 0.471
26 A 11 10 1.08 17 0.588
27 A 11 10 1.07 17 0.588
28 A 10 9 1.12 15 0.600
29 A 10 9 1.07 15 0.600
30 A 10 9 1.00 17 0.529
31 A 10 9 1.00 16 0.562
32 A 9 8 0.98 16 0.500
33 A 8 7 0.97 16 0.438
34 A 5 4 1.00 16 0.250
35 A 6 5 0.99 16 0.312
36 A 8 7 1.07 16 0.438
37 A 9 8 1.13 16 0.500
38 A 8 7 1.06 12 0.583
39 A 7 6 1.00 12 0.500
40 A 5 4 1.00 12 0.333
41 A 9 8 1.05 10 0.800
42 A 8 7 1.00 10 0.700
43 A 5 4 1.00 10 0.400
44 A 9 8 1.08 17 0.471
45 A 8 7 1.00 17 0.412
46 A 8 7 1.00 15 0.467
47 A 9 8 1.08 15 0.533
48 A 8 7 1.00 17 0.412
49 A 9 8 1.08 17 0.471
50 A 6 5 1.00 17 0.294
51 A 9 8 1.09 15 0.533
52 A 10 9 1.30 15 0.600
53 A 8 7 1.10 17 0.412
54 A 10 9 1.17 17 0.529
55 A 8 7 1.12 17 0.412
56 A 10 9 1.19 15 0.600
57 A 12 11 1.35 15 0.733
58 A 9 8 1.14 17 0.471
59 A 5 4 1.16 8 0.500
60 A 12 11 0.96 15 0.733
61 A 14 13 1.03 15 0.867
62 A 8 7 1.00 15 0.467
63 A 11 10 0.99 15 0.667
64 A 12 11 1.11 15 0.733

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