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 [45] had the largest ratio of [22]

# 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 3 3 1.00 12 0.250
2 A 4 4 1.00 12 0.333
3 A 2 2 1.00 10 0.200
4 A 3 3 1.00 8 0.375
5 A 3 3 1.00 12 0.250
6 A 4 4 1.00 12 0.333
7 A 5 5 1.00 12 0.417
8 A 3 3 1.00 14 0.214
9 A 6 5 1.00 14 0.357
10 A 3 3 1.00 12 0.250
11 A 5 4 1.00 10 0.400
12 A 5 4 1.00 14 0.286
13 A 6 6 1.00 14 0.429
14 A 7 6 1.00 14 0.429
15 A 4 4 1.00 14 0.286
16 A 10 5 1.00 14 0.357
17 A 3 2 1.00 12 0.167
18 A 8 4 1.00 10 0.400
19 A 8 4 1.00 14 0.286
20 A 9 5 1.00 14 0.357
21 A 12 6 1.00 14 0.429
22 A 3 2 1.00 12 0.167
23 A 2 2 1.00 8 0.250
24 A 2 2 1.00 8 0.250
25 A 5 5 1.00 8 0.625
26 A 3 3 1.00 12 0.250
27 A 2 2 1.00 12 0.167
28 A 3 3 1.00 12 0.250
29 A 4 3 1.00 12 0.250
30 A 5 5 1.00 8 0.625
31 A 3 3 1.00 12 0.250
32 A 4 4 1.00 12 0.333
33 A 2 2 1.00 12 0.167
34 A 5 5 1.00 12 0.417
35 A 3 2 1.00 8 0.250
36 A 3 3 1.00 12 0.250
37 A 5 3 1.00 10 0.300
38 A 5 4 1.00 14 0.286
39 A 8 3 1.00 10 0.300
40 A 8 4 1.00 14 0.286
41 A 0 0 0.00 0 0.000
42 A 0 0 0.00 0 0.000
43 A 3 3 1.00 20 0.150
44 A 0 0 0.00 0 0.000
45 A 5 5 1.00 22 0.227
46 A 0 0 0.00 0 0.000
47 A 3 2 1.00 12 0.167
48 A 5 3 1.00 14 0.214
49 A 8 3 1.00 14 0.214
50 A 5 5 1.00 16 0.312
51 A 7 6 1.00 18 0.333
52 A 12 6 1.00 18 0.333
53 A 4 4 1.00 18 0.222
54 A 12 9 1.00 12 0.750
55 A 8 7 1.00 10 0.700
56 A 4 4 1.00 8 0.500
57 A 0 0 0.00 0 0.000
58 A 0 0 0.00 0 0.000
59 A 16 4 1.00 18 0.222
60 A 10 4 1.00 16 0.250
61 A 4 4 1.00 14 0.286
62 A 10 5 1.00 18 0.278
63 A 11 6 1.00 18 0.333
64 A 23 6 1.00 18 0.333
65 A 13 5 1.00 16 0.312
66 A 5 4 1.00 14 0.286
67 A 13 5 1.00 18 0.278
68 A 14 6 1.00 18 0.333