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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 [62] had the largest ratio of [32]

# 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 19 15 1.00 12 1.250
2 A 15 13 1.00 12 1.083
3 A 12 10 1.00 10 1.000
4 A 6 6 1.00 8 0.750
5 A 2 2 1.00 12 0.167
6 A 17 15 1.00 12 1.250
7 A 21 16 1.00 12 1.333
8 A 4 5 1.00 12 0.417
9 A 6 5 1.00 21 0.238
10 A 6 5 1.00 21 0.238
11 A 5 5 1.00 19 0.263
12 A 3 3 1.00 21 0.143
13 A 7 7 1.00 21 0.333
14 A 5 5 1.00 21 0.238
15 A 13 9 1.00 23 0.391
16 A 11 10 1.00 23 0.435
17 A 8 7 1.00 21 0.333
18 A 8 7 1.00 23 0.304
19 A 6 6 1.00 23 0.261
20 A 10 9 1.00 23 0.391
21 A 10 9 1.00 23 0.391
22 A 15 10 1.00 23 0.435
23 A 14 11 1.00 23 0.478
24 A 10 10 1.00 21 0.476
25 A 10 8 1.00 23 0.348
26 A 7 8 1.00 23 0.348
27 A 9 8 1.00 23 0.348
28 A 16 13 1.00 23 0.565
29 A 3 3 1.00 12 0.250
30 A 3 3 1.00 19 0.158
31 A 7 5 1.00 18 0.278
32 A 7 5 1.00 18 0.278
33 A 7 5 1.00 16 0.312
34 A 4 3 1.00 10 0.300
35 A 5 5 1.00 18 0.278
36 A 7 5 1.00 18 0.278
37 A 5 4 1.00 18 0.222
38 A 20 15 1.00 20 0.750
39 A 16 13 1.00 20 0.650
40 A 13 10 1.00 18 0.556
41 A 6 6 1.00 12 0.500
42 A 2 2 1.00 20 0.100
43 A 21 19 1.01 20 0.950
44 A 26 18 1.00 20 0.900
45 A 21 14 1.00 20 0.700
46 A 15 11 1.00 18 0.611
47 A 6 7 1.00 12 0.583
48 A 2 2 1.00 20 0.100
49 A 30 18 1.00 20 0.900
50 A 0 0 0.00 0 0.000
51 A 0 0 0.00 0 0.000
52 A 6 4 1.00 18 0.222
53 A 23 5 1.00 16 0.312
54 A 17 5 1.00 16 0.312
55 A 5 5 1.00 14 0.357
56 A 15 7 1.00 16 0.438
57 A 25 7 1.00 16 0.438
58 A 31 7 1.00 16 0.438
59 A 31 13 1.00 18 0.722
60 A 37 16 1.00 18 0.889
61 A 12 8 1.00 19 0.421
62 A 6 5 1.00 32 0.156

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