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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 [27] had the largest ratio of [1.10000000000000009]

# 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 1.00 12 0.417
2 A 7 6 0.98 14 0.429
3 A 8 7 0.99 14 0.500
4 A 6 6 1.10 16 0.375
5 A 4 4 1.11 16 0.250
6 A 4 4 1.15 14 0.286
7 A 1 1 1.00 8 0.125
8 A 6 5 1.00 16 0.312
9 A 4 3 1.00 16 0.188
10 A 5 4 1.01 16 0.250
11 A 7 6 1.09 16 0.375
12 A 3 3 1.05 18 0.167
13 A 3 3 1.10 18 0.167
14 A 3 3 1.16 16 0.188
15 A 3 3 1.09 10 0.300
16 A 7 6 0.98 18 0.333
17 A 11 10 0.91 18 0.556
18 A 15 14 0.95 18 0.778
19 A 4 3 0.96 18 0.167
20 A 4 3 0.95 18 0.167
21 A 4 3 0.95 16 0.188
22 A 9 8 0.91 10 0.800
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 16 0.125
27 C 12 11 1.05 10 1.100
28 N/A 1 0 1.00 18 0.000
29 N/A 1 0 1.00 18 0.000
30 N/A 2 0 1.00 18 0.000
31 A 4 3 1.00 16 0.188
32 N/A 1 0 1.00 18 0.000
33 N/A 1 0 1.00 18 0.000
34 A 3 3 0.59 30 0.100
35 A 3 3 0.60 30 0.100
36 A 3 3 0.62 28 0.107
37 A 7 7 0.69 30 0.233
38 A 7 7 0.73 30 0.233
39 A 3 3 0.56 30 0.100
40 A 3 3 0.58 30 0.100
41 A 3 3 0.57 28 0.107
42 A 3 3 0.66 30 0.100
43 A 3 3 0.54 30 0.100
44 A 3 3 0.56 30 0.100
45 A 3 3 0.55 28 0.107
46 A 3 3 0.63 30 0.100
47 A 3 3 0.63 30 0.100
48 A 3 3 0.64 30 0.100
49 A 3 3 0.74 28 0.107
50 A 1 1 1.00 23 0.043
51 A 10 9 0.73 30 0.300
52 A 14 13 0.75 30 0.433
53 N/A 1 0 1.00 34 0.000
54 A 9 8 0.97 34 0.235
55 A 8 7 0.99 32 0.219
56 A 8 7 0.99 24 0.292
57 N/A 1 0 1.00 34 0.000

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