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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [16] had the largest ratio of [45]

# 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 6 1.00 10 0.600
2 A 5 5 1.00 10 0.500
3 A 4 4 1.00 8 0.500
4 A 0 0 0.00 0 0.000
5 A 0 0 0.00 0 0.000
6 A 7 7 1.00 12 0.583
7 A 6 6 1.00 12 0.500
8 A 3 3 1.00 10 0.300
9 A 0 0 0.00 0 0.000
10 A 0 0 0.00 0 0.000
11 A 13 10 1.00 12 0.833
12 A 9 8 1.00 12 0.667
13 A 7 7 1.00 10 0.700
14 A 0 0 0.00 0 0.000
15 A 0 0 0.00 0 0.000
16 A 76 12 1.00 45 0.267
17 F 0 0 N/A 0. N/A
18 A 5 3 1.00 23 0.130
19 A 4 3 1.00 23 0.130
20 A 3 3 1.00 21 0.143
21 A 7 4 1.00 23 0.174
22 A 7 4 1.00 23 0.174
23 A 8 5 1.00 23 0.217
24 A 10 3 1.00 23 0.130
25 A 8 3 1.00 23 0.130
26 A 7 3 1.00 21 0.143
27 A 21 5 1.00 23 0.217
28 A 24 7 1.00 23 0.304
29 A 14 3 1.00 23 0.130
30 A 11 3 1.00 23 0.130
31 A 11 3 1.00 21 0.143
32 A 53 7 1.00 23 0.304
33 A 60 9 1.00 23 0.391
34 A 0 0 0.00 0 0.000
35 A 0 0 0.00 0 0.000
36 A 2 2 1.00 23 0.087
37 A 4 2 1.00 23 0.087
38 A 5 2 1.00 23 0.087
39 A 8 7 1.00 18 0.389
40 A 7 6 1.00 18 0.333
41 A 6 5 1.00 16 0.312
42 A 0 0 0.00 0 0.000
43 A 0 0 0.00 0 0.000
44 A 15 9 1.00 20 0.450
45 A 13 10 1.00 20 0.500
46 A 9 7 1.00 18 0.389
47 A 0 0 0.00 0 0.000
48 A 0 0 0.00 0 0.000
49 A 28 11 1.00 20 0.550
50 A 22 11 1.00 20 0.550
51 A 16 9 1.00 18 0.500
52 A 0 0 0.00 0 0.000
53 A 0 0 0.00 0 0.000
54 A 6 6 1.00 20 0.300
55 A 5 5 1.00 20 0.250
56 A 4 4 1.00 18 0.222
57 A 0 0 0.00 0 0.000
58 A 0 0 0.00 0 0.000
59 A 21 9 1.00 20 0.450
60 A 18 10 1.00 20 0.500
61 A 5 5 1.00 18 0.278
62 A 0 0 0.00 0 0.000
63 A 0 0 0.00 0 0.000

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