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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 [7] had the largest ratio of [1.11111000000000004]

# 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 2 2 1.00 9 0.222
2 A 2 2 1.00 9 0.222
3 A 2 2 1.00 9 0.222
4 A 1 1 1.00 7 0.143
5 A 9 8 1.49 9 0.889
6 A 10 9 1.49 9 1.000
7 A 11 10 1.49 9 1.111
8 A 3 3 1.00 12 0.250
9 A 4 4 1.05 12 0.333
10 A 3 3 1.00 12 0.250
11 A 2 2 1.00 12 0.167
12 A 3 3 1.00 12 0.250
13 A 4 4 1.08 12 0.333
14 A 3 3 1.04 11 0.273
15 A 2 2 1.00 11 0.182
16 A 1 1 1.00 11 0.091
17 A 2 2 1.00 11 0.182
18 A 3 3 1.06 11 0.273
19 A 4 4 1.18 11 0.364
20 A 3 3 1.12 11 0.273
21 A 2 2 1.00 11 0.182
22 A 1 1 1.00 11 0.091
23 A 2 2 1.00 11 0.182
24 A 3 3 1.12 11 0.273
25 A 4 4 1.12 9 0.444
26 A 3 3 1.07 9 0.333
27 A 2 2 1.00 9 0.222
28 A 1 1 1.00 9 0.111
29 A 2 2 1.00 9 0.222
30 A 3 3 1.07 9 0.333
31 A 7 6 1.05 11 0.545
32 A 6 5 1.05 11 0.455
33 A 5 4 1.00 11 0.364
34 A 1 1 1.00 11 0.091
35 A 2 2 1.00 11 0.182
36 A 3 3 1.14 11 0.273
37 A 4 4 1.21 11 0.364
38 A 8 7 1.07 11 0.636
39 A 7 6 1.05 11 0.545
40 A 6 5 1.00 11 0.455
41 A 5 4 1.00 11 0.364
42 A 6 5 1.00 11 0.455
43 A 7 6 1.08 11 0.545
44 A 8 7 1.13 11 0.636
45 A 11 10 1.41 12 0.833
46 A 10 9 1.45 12 0.750
47 A 1 1 1.00 12 0.083
48 A 2 2 1.00 12 0.167
49 A 3 3 1.13 12 0.250
50 A 6 5 1.00 12 0.417
51 A 5 4 1.00 12 0.333
52 A 6 5 1.00 12 0.417

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