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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 [44] had the largest ratio of [.769230999999999998]

# 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 1.01 16 0.188
2 A 3 3 0.98 16 0.188
3 A 3 3 1.03 16 0.188
4 A 3 3 1.01 14 0.214
5 A 5 4 1.00 16 0.250
6 A 3 3 0.96 16 0.188
7 A 3 3 0.95 16 0.188
8 A 3 3 0.98 16 0.188
9 A 2 2 1.01 18 0.111
10 A 2 2 1.05 18 0.111
11 A 2 2 1.11 16 0.125
12 A 1 1 1.00 18 0.056
13 A 2 2 0.97 18 0.111
14 A 2 2 0.94 18 0.111
15 A 2 2 0.99 18 0.111
16 A 2 2 1.04 18 0.111
17 A 2 2 1.06 16 0.125
18 A 1 1 1.00 18 0.056
19 A 2 2 0.94 18 0.111
20 A 2 2 0.94 18 0.111
21 A 5 4 1.63 17 0.235
22 A 5 4 1.23 15 0.267
23 A 5 4 1.00 10 0.400
24 A 3 3 1.04 18 0.167
25 A 3 3 0.89 18 0.167
26 A 3 3 0.88 16 0.188
27 A 3 3 1.00 18 0.167
28 A 3 3 1.01 18 0.167
29 A 3 3 0.99 18 0.167
30 A 2 2 1.00 18 0.111
31 N/A 1 0 1.00 20 0.000
32 N/A 1 0 1.00 20 0.000
33 A 3 3 1.09 18 0.167
34 A 3 3 1.19 16 0.188
35 A 3 3 0.99 18 0.167
36 A 3 3 0.99 18 0.167
37 A 18 17 1.54 26 0.654
38 A 14 13 1.36 26 0.500
39 A 10 9 1.22 24 0.375
40 A 6 5 1.14 23 0.217
41 A 6 5 1.09 26 0.192
42 A 10 9 1.05 26 0.346
43 A 15 14 1.18 26 0.538
44 A 21 20 1.36 26 0.769
45 A 12 11 1.00 23 0.478
46 A 8 7 1.03 21 0.333
47 A 4 3 1.03 20 0.150
48 A 5 4 1.04 23 0.174
49 A 9 8 1.04 23 0.348
50 A 14 13 0.98 23 0.565

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