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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 [49] had the largest ratio of [19]

# 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 7 6 1.00 10 0.600
2 A 4 3 1.00 10 0.300
3 A 4 3 1.00 10 0.300
4 A 4 3 1.00 8 0.375
5 A 3 3 1.00 6 0.500
6 A 7 6 1.00 10 0.600
7 A 5 5 1.00 10 0.500
8 A 6 5 1.00 10 0.500
9 A 5 4 1.00 10 0.400
10 A 4 4 1.00 8 0.500
11 A 3 3 1.00 6 0.500
12 A 6 6 1.00 10 0.600
13 A 5 5 1.00 10 0.500
14 A 3 3 1.00 10 0.300
15 A 6 6 1.00 10 0.600
16 A 7 6 1.00 10 0.600
17 A 9 8 1.00 10 0.800
18 A 8 7 1.00 10 0.700
19 A 7 6 1.00 10 0.600
20 A 6 6 1.00 8 0.750
21 A 5 5 1.00 6 0.833
22 A 14 8 1.00 10 0.800
23 A 6 6 1.00 10 0.600
24 A 8 8 1.00 10 0.800
25 A 9 9 1.00 10 0.900
26 A 10 9 1.00 10 0.900
27 A 20 9 1.00 12 0.750
28 A 17 9 1.00 12 0.750
29 A 11 8 1.00 10 0.800
30 A 8 6 1.00 8 0.750
31 A 17 9 1.00 12 0.750
32 A 12 8 1.00 12 0.667
33 A 25 14 1.00 12 1.167
34 A 16 12 1.00 10 1.200
35 A 10 7 1.00 8 0.875
36 A 20 10 1.00 12 0.833
37 A 14 9 1.00 12 0.750
38 A 6 6 1.00 12 0.500
39 A 6 6 1.00 14 0.429
40 A 7 7 1.00 10 0.700
41 A 6 4 1.00 10 0.400
42 A 6 4 1.00 8 0.500
43 A 5 3 1.00 6 0.500
44 A 6 5 1.00 10 0.500
45 A 3 3 1.00 10 0.300
46 A 5 4 1.00 10 0.400
47 A 6 4 1.00 10 0.400
48 A 6 4 1.00 10 0.400
49 A 8 8 1.00 19 0.421

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