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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 [57] had the largest ratio of [.650000000000000022]

# 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 16 0.125
2 N/A 2 0 1.00 16 0.000
3 A 2 2 1.00 14 0.143
4 N/A 1 0 1.00 12 0.000
5 N/A 2 0 1.00 16 0.000
6 N/A 2 0 1.00 16 0.000
7 A 5 4 0.95 18 0.222
8 N/A 1 0 1.00 18 0.000
9 A 6 5 0.96 16 0.312
10 N/A 1 0 1.00 14 0.000
11 N/A 1 0 1.00 18 0.000
12 N/A 1 0 1.00 18 0.000
13 A 7 6 1.07 18 0.333
14 N/A 1 0 1.00 18 0.000
15 A 6 5 0.96 16 0.312
16 N/A 1 0 1.00 14 0.000
17 N/A 1 0 1.00 18 0.000
18 N/A 1 0 1.00 18 0.000
19 A 9 8 1.05 18 0.444
20 N/A 1 0 1.00 18 0.000
21 A 8 7 1.12 16 0.438
22 N/A 1 0 1.00 14 0.000
23 N/A 1 0 1.00 18 0.000
24 N/A 1 0 1.00 18 0.000
25 A 2 2 1.00 18 0.111
26 A 2 2 1.00 18 0.111
27 A 2 2 1.00 16 0.125
28 A 1 1 1.00 14 0.071
29 N/A 2 0 1.00 18 0.000
30 N/A 2 0 1.00 18 0.000
31 A 5 4 1.01 20 0.200
32 A 5 4 1.03 18 0.222
33 A 5 4 1.04 16 0.250
34 N/A 1 0 1.00 20 0.000
35 N/A 1 0 1.00 20 0.000
36 A 13 12 1.03 20 0.600
37 A 11 10 1.05 20 0.500
38 A 9 8 1.05 18 0.444
39 A 7 6 1.11 16 0.375
40 N/A 1 0 1.00 20 0.000
41 N/A 1 0 1.00 20 0.000
42 A 5 4 1.05 20 0.200
43 A 5 4 1.05 18 0.222
44 A 9 8 1.08 16 0.500
45 N/A 1 0 1.00 20 0.000
46 N/A 1 0 1.00 20 0.000
47 A 2 2 1.00 18 0.111
48 A 2 2 1.00 16 0.125
49 A 1 1 1.00 14 0.071
50 N/A 2 0 1.00 18 0.000
51 N/A 2 0 1.00 18 0.000
52 A 5 4 1.00 20 0.200
53 A 5 4 1.01 18 0.222
54 A 5 4 1.04 16 0.250
55 N/A 1 0 1.00 20 0.000
56 N/A 1 0 1.00 20 0.000
57 A 14 13 1.04 20 0.650
58 A 11 10 1.03 18 0.556
59 A 8 7 1.07 16 0.438
60 N/A 1 0 1.00 20 0.000
61 N/A 1 0 1.00 20 0.000
62 A 5 4 1.05 20 0.200
63 A 5 4 1.05 18 0.222
64 A 5 4 1.06 16 0.250
65 N/A 1 0 1.00 20 0.000
66 N/A 1 0 1.00 20 0.000

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