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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 [70] had the largest ratio of [21]

# 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 1 1 1.00 6 0.167
2 A 2 2 1.00 8 0.250
3 A 2 2 1.00 8 0.250
4 A 2 1 1.00 8 0.125
5 A 3 2 1.00 8 0.250
6 A 2 1 1.00 8 0.125
7 A 4 2 1.00 8 0.250
8 A 2 1 1.00 8 0.125
9 A 4 3 1.00 10 0.300
10 A 3 3 1.00 10 0.300
11 A 3 3 1.00 10 0.300
12 A 2 2 1.00 10 0.200
13 A 2 2 1.00 10 0.200
14 A 3 3 1.00 10 0.300
15 A 3 3 1.00 10 0.300
16 A 4 3 1.00 10 0.300
17 A 4 3 1.00 12 0.250
18 A 3 3 1.00 12 0.250
19 A 3 3 1.00 12 0.250
20 A 2 2 1.00 12 0.167
21 A 2 2 1.00 12 0.167
22 A 3 3 1.00 12 0.250
23 A 3 3 1.00 12 0.250
24 A 4 3 1.00 12 0.250
25 A 2 2 1.00 10 0.200
26 A 2 2 1.00 10 0.200
27 A 2 2 1.00 10 0.200
28 A 2 2 1.00 10 0.200
29 A 2 2 1.00 10 0.200
30 A 2 2 1.00 10 0.200
31 A 2 2 1.00 12 0.167
32 A 2 2 1.00 12 0.167
33 A 2 2 1.00 12 0.167
34 A 2 2 1.00 12 0.167
35 A 2 2 1.00 12 0.167
36 A 2 2 1.00 12 0.167
37 A 2 2 1.00 8 0.250
38 A 2 2 1.00 10 0.200
39 A 5 3 1.00 8 0.375
40 A 4 3 1.00 8 0.375
41 A 3 3 1.00 8 0.375
42 A 2 2 1.00 8 0.250
43 A 2 2 1.00 8 0.250
44 A 3 3 1.00 8 0.375
45 A 4 3 1.00 8 0.375
46 A 5 3 1.00 8 0.375
47 A 6 4 1.00 10 0.400
48 A 5 4 1.00 10 0.400
49 A 4 4 1.00 10 0.400
50 A 3 3 1.00 10 0.300
51 A 2 2 1.00 10 0.200
52 A 3 3 1.00 10 0.300
53 A 4 3 1.00 10 0.300
54 A 5 3 1.00 10 0.300
55 A 7 4 1.00 10 0.400
56 A 5 4 1.00 10 0.400
57 A 4 4 1.00 10 0.400
58 A 4 4 1.00 10 0.400
59 A 5 4 1.00 10 0.400
60 A 7 4 1.00 10 0.400
61 A 3 2 1.00 10 0.200
62 A 3 2 1.00 10 0.200
63 A 3 2 1.00 10 0.200
64 A 3 3 1.00 10 0.300
65 A 3 3 1.00 10 0.300
66 A 5 3 1.00 10 0.300
67 A 7 3 1.00 10 0.300
68 A 3 3 1.00 12 0.250
69 A 3 3 1.00 14 0.214
70 A 3 3 1.00 21 0.143

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