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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 [3] had the largest ratio of [1.62500000000000000]

# 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 9 8 1.02 10 0.800
2 A 6 5 1.00 10 0.500
3 A 14 13 0.99 8 1.625
4 C 17 16 1.39 10 1.600
5 A 9 8 1.14 10 0.800
6 A 17 16 1.25 10 1.600
7 A 6 5 0.95 20 0.250
8 A 6 5 0.96 20 0.250
9 A 6 5 1.03 18 0.278
10 C 9 8 0.99 12 0.667
11 C 16 15 1.20 20 0.750
12 A 6 5 1.03 20 0.250
13 A 6 5 0.98 20 0.250
14 A 4 4 0.69 10 0.400
15 A 4 4 0.76 10 0.400
16 A 4 4 0.86 8 0.500
17 A 2 2 1.00 6 0.333
18 C 11 10 1.26 10 1.000
19 A 6 5 0.86 10 0.500
20 A 7 6 0.86 10 0.600
21 A 8 7 0.85 10 0.700
22 A 3 3 1.00 4 0.750
23 C 11 10 1.26 10 1.000
24 C 11 10 1.26 10 1.000
25 C 11 10 1.26 10 1.000
26 A 5 4 1.00 10 0.400
27 A 4 4 1.00 10 0.400
28 A 8 7 1.07 10 0.700
29 A 3 3 1.00 10 0.300
30 A 7 6 0.98 8 0.750
31 A 6 5 1.46 6 0.833
32 A 7 6 1.18 10 0.600
33 A 6 5 1.10 10 0.500
34 A 3 3 1.00 10 0.300
35 A 7 6 1.14 10 0.600
36 A 6 5 1.10 10 0.500
37 A 5 4 1.00 12 0.333
38 A 10 9 1.03 12 0.750
39 A 7 6 0.98 12 0.500
40 A 6 5 1.02 12 0.417
41 A 7 6 1.00 10 0.600
42 A 9 8 1.08 8 1.000
43 A 7 6 1.02 12 0.500
44 A 6 5 1.02 12 0.417
45 A 7 6 1.17 12 0.500
46 A 9 8 1.02 12 0.667
47 A 3 3 1.00 12 0.250
48 A 3 3 1.00 12 0.250
49 A 3 3 1.00 12 0.250
50 A 3 3 1.00 12 0.250
51 A 3 3 1.00 12 0.250
52 A 3 3 1.00 10 0.300
53 A 3 3 1.00 8 0.375
54 A 3 3 1.00 12 0.250
55 A 5 4 0.97 12 0.333
56 A 3 3 1.00 12 0.250
57 A 3 3 1.00 12 0.250
58 A 3 3 1.00 12 0.250
59 A 5 4 1.00 23 0.174
60 A 9 8 1.11 21 0.381
61 A 7 6 1.07 21 0.286
62 A 8 7 1.08 21 0.333
63 A 3 3 1.00 21 0.143
64 A 6 5 1.00 19 0.263
65 A 8 7 1.15 18 0.389
66 A 4 4 1.10 21 0.190
67 A 8 7 1.35 21 0.333
68 A 8 7 1.26 21 0.333
69 C 12 11 1.20 19 0.579
70 A 7 6 0.83 12 0.500
71 A 7 6 0.87 14 0.429

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