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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 [29] had the largest ratio of [1]

# 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 4 4 1.00 10 0.400
2 A 8 7 1.07 10 0.700
3 A 3 3 1.00 10 0.300
4 A 7 6 0.98 8 0.750
5 A 6 5 1.46 6 0.833
6 A 7 6 1.18 10 0.600
7 A 6 5 1.10 10 0.500
8 A 3 3 1.00 10 0.300
9 A 7 6 1.14 10 0.600
10 A 6 5 1.10 10 0.500
11 A 3 3 1.00 12 0.250
12 A 3 3 1.00 12 0.250
13 A 3 3 1.00 12 0.250
14 A 3 3 1.00 10 0.300
15 A 3 3 1.00 8 0.375
16 A 3 3 1.00 12 0.250
17 A 5 4 0.97 12 0.333
18 A 3 3 1.00 12 0.250
19 A 3 3 1.00 12 0.250
20 A 3 3 1.00 12 0.250
21 A 3 3 1.00 12 0.250
22 A 5 4 1.00 10 0.400
23 C 6 5 53.00 12 0.417
24 C 3 3 64.00 12 0.250
25 A 10 9 1.03 12 0.750
26 A 7 6 0.98 12 0.500
27 A 6 5 1.02 12 0.417
28 A 7 6 1.00 10 0.600
29 A 9 8 1.08 8 1.000
30 A 7 6 1.02 12 0.500
31 A 6 5 1.02 12 0.417
32 A 7 6 1.17 12 0.500
33 A 9 8 1.02 12 0.667
34 A 3 3 1.00 12 0.250
35 A 5 4 1.00 12 0.333
36 C 5 4 52.00 10 0.400
37 A 5 4 1.00 23 0.174
38 A 9 8 1.11 21 0.381
39 A 7 6 1.07 21 0.286
40 A 8 7 1.08 21 0.333
41 A 3 3 1.00 21 0.143
42 A 6 5 1.00 19 0.263
43 A 8 7 1.15 18 0.389
44 A 4 4 1.10 21 0.190
45 A 8 7 1.35 21 0.333
46 A 8 7 1.26 21 0.333

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