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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 [16] had the largest ratio of [.200000000000000011]

# 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 3 3 0.84 25 0.120
2 A 3 3 0.91 23 0.130
3 A 2 2 0.87 21 0.095
4 A 5 4 0.91 25 0.160
5 A 5 4 0.93 25 0.160
6 A 2 2 0.90 25 0.080
7 A 2 2 0.92 23 0.087
8 A 2 2 1.68 21 0.095
9 A 2 2 0.80 25 0.080
10 A 2 2 0.81 25 0.080
11 A 2 2 0.76 25 0.080
12 A 2 2 0.76 23 0.087
13 A 2 2 1.83 21 0.095
14 A 2 2 0.78 25 0.080
15 A 2 2 1.08 25 0.080
16 A 3 3 1.00 15 0.200
17 A 3 3 1.00 15 0.200
18 A 2 2 1.17 17 0.118
19 A 2 2 1.00 23 0.087
20 A 2 2 1.00 23 0.087
21 A 2 2 1.00 21 0.095
22 A 2 2 1.00 19 0.105
23 A 2 2 1.00 23 0.087
24 A 2 2 1.00 23 0.087
25 A 2 2 1.00 23 0.087
26 A 3 3 0.84 25 0.120
27 A 3 3 0.91 25 0.120
28 A 2 2 1.00 23 0.087
29 A 2 2 0.79 21 0.095
30 A 5 4 0.93 25 0.160
31 A 6 5 0.84 25 0.200
32 A 2 2 0.93 25 0.080
33 A 2 2 0.94 25 0.080
34 A 2 2 0.80 23 0.087
35 A 2 2 0.80 21 0.095
36 A 2 2 0.93 25 0.080
37 A 2 2 0.92 25 0.080
38 A 2 2 0.78 25 0.080
39 A 2 2 0.79 25 0.080
40 A 2 2 0.78 25 0.080
41 A 2 2 1.11 23 0.087
42 A 2 2 1.30 21 0.095
43 A 2 2 1.00 27 0.074
44 A 4 4 1.00 42 0.095
45 A 4 4 1.00 42 0.095
46 A 4 4 1.00 40 0.100
47 A 4 4 1.00 39 0.103
48 A 4 4 1.00 42 0.095
49 A 4 4 1.00 42 0.095
50 A 4 4 1.00 42 0.095
51 B 4 4 2.46 39 0.103
52 B 4 4 2.39 35 0.114

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