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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 [17]

# 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 3 1.00 14 0.214
2 A 4 3 1.00 14 0.214
3 A 4 3 1.00 14 0.214
4 A 4 3 1.00 14 0.214
5 A 3 3 1.00 14 0.214
6 A 5 5 1.00 14 0.357
7 A 6 6 1.00 14 0.429
8 A 7 6 1.00 14 0.429
9 A 3 3 1.00 10 0.300
10 A 3 3 1.00 12 0.250
11 A 4 4 1.00 10 0.400
12 A 4 4 1.00 12 0.333
13 A 5 5 1.00 10 0.500
14 A 3 3 1.00 12 0.250
15 A 3 3 1.00 10 0.300
16 A 6 6 1.00 17 0.353
17 A 7 6 1.00 17 0.353
18 A 5 5 1.00 15 0.333
19 A 6 5 1.00 12 0.417
20 A 7 5 1.00 15 0.333
21 A 5 5 1.00 17 0.294
22 A 7 6 1.00 17 0.353
23 A 8 7 1.00 17 0.412
24 A 6 5 1.00 15 0.333
25 A 7 6 1.00 12 0.500
26 A 8 6 1.00 15 0.400
27 A 7 6 1.00 17 0.353
28 A 5 5 1.00 10 0.500
29 A 6 5 1.00 12 0.417
30 A 6 6 1.00 10 0.600
31 A 7 6 1.00 12 0.500
32 A 5 5 1.00 17 0.294
33 A 6 5 1.00 17 0.294
34 A 4 4 1.00 15 0.267
35 A 3 3 1.00 12 0.250
36 A 7 5 1.00 15 0.333
37 A 5 5 1.00 17 0.294
38 A 5 5 1.00 17 0.294
39 A 4 4 1.00 17 0.235
40 A 5 5 1.00 15 0.333
41 A 8 6 1.00 15 0.400
42 A 6 6 1.00 17 0.353
43 A 6 6 1.00 17 0.353
44 A 6 6 1.00 17 0.353
45 A 6 5 1.00 15 0.333
46 A 9 7 1.00 15 0.467
47 A 7 7 1.00 17 0.412
48 A 3 3 1.00 10 0.300
49 A 3 3 1.00 12 0.250
50 A 6 5 1.00 8 0.625
51 A 8 7 1.00 15 0.467
52 A 4 4 1.00 15 0.267
53 A 6 6 1.00 15 0.400

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