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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 [24] had the largest ratio of [.2500]

Table 2.1:Rubi specific breakdown of results for each integral
# 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 1 1.00 21 0.048
2 A 2 1 1.00 23 0.043
3 A 2 1 1.00 25 0.040
4 A 2 1 1.00 27 0.037
5 A 2 1 1.00 29 0.034
6 A 2 1 1.00 17 0.059
7 A 3 2 1.00 22 0.091
8 A 6 5 1.00 25 0.200
9 A 5 5 1.00 25 0.200
10 A 4 4 1.00 23 0.174
11 A 4 4 1.00 18 0.222
12 A 6 4 1.00 25 0.160
13 A 6 4 1.00 25 0.160
14 A 7 5 1.00 25 0.200
15 A 6 5 1.00 25 0.200
16 A 5 5 1.00 25 0.200
17 A 4 4 1.00 23 0.174
18 A 4 4 1.00 18 0.222
19 A 6 5 1.00 25 0.200
20 A 6 5 1.00 25 0.200
21 A 7 6 1.00 25 0.240
22 A 8 6 1.00 26 0.231
23 A 7 6 1.00 26 0.231
24 A 6 6 1.00 24 0.250
25 A 4 4 1.00 23 0.174
26 A 5 5 1.00 26 0.192
27 A 3 3 1.00 26 0.115
28 A 4 4 1.00 26 0.154
29 A 5 4 1.00 26 0.154
30 A 6 4 1.00 26 0.154
31 A 4 4 1.00 24 0.167
32 A 5 5 1.00 36 0.139
33 A 2 1 1.00 23 0.043
34 A 3 3 1.00 29 0.103
35 A 4 3 1.00 29 0.103
36 A 3 3 0.99 29 0.103
37 A 3 3 0.99 24 0.125
38 A 4 4 1.00 31 0.129
39 A 4 4 1.00 30 0.133
40 A 7 7 1.00 33 0.212
41 A 7 7 1.00 33 0.212
42 A 6 6 1.00 33 0.182
43 A 5 5 1.74 30 0.167
44 B 5 5 2.60 29 0.172
45 B 8 8 2.45 32 0.250
46 B 8 8 2.45 32 0.250
47 A 6 6 1.55 32 0.188
48 A 7 7 1.47 32 0.219

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