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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 [36] 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 7 6 1.00 37 0.162
2 A 6 6 1.00 37 0.162
3 A 5 5 1.01 35 0.143
4 A 5 5 1.00 30 0.167
5 A 6 6 1.00 37 0.162
6 A 6 6 1.00 37 0.162
7 A 5 5 1.00 37 0.135
8 A 6 5 1.00 37 0.135
9 A 5 5 1.00 37 0.135
10 A 4 4 1.02 35 0.114
11 A 4 4 1.00 30 0.133
12 A 6 6 1.00 37 0.162
13 A 6 6 1.00 37 0.162
14 A 5 5 1.00 37 0.135
15 A 4 4 1.00 31 0.129
16 A 4 4 1.00 30 0.133
17 A 7 7 1.00 33 0.212
18 A 7 7 1.00 33 0.212
19 A 6 6 1.00 33 0.182
20 A 8 7 0.99 40 0.175
21 A 7 7 1.00 40 0.175
22 A 6 6 0.99 38 0.158
23 A 6 6 1.00 33 0.182
24 A 7 7 1.00 40 0.175
25 A 7 7 1.00 40 0.175
26 A 5 5 0.99 40 0.125
27 A 7 6 0.99 40 0.150
28 A 6 6 1.00 40 0.150
29 A 5 5 1.01 38 0.132
30 A 5 5 1.00 33 0.152
31 A 7 7 1.00 40 0.175
32 A 7 7 1.00 40 0.175
33 A 5 5 0.99 40 0.125
34 A 5 5 1.74 30 0.167
35 B 5 5 2.60 29 0.172
36 B 8 8 2.45 32 0.250
37 B 8 8 2.45 32 0.250
38 A 6 6 1.55 32 0.188
39 A 7 7 1.47 32 0.219
40 A 5 5 1.22 32 0.156
41 A 8 7 1.00 36 0.194
42 A 7 6 1.00 34 0.176
43 A 7 6 1.00 29 0.207
44 A 9 8 1.01 36 0.222
45 A 9 8 1.00 36 0.222
46 A 9 9 1.00 36 0.250
47 A 7 7 1.00 36 0.194
48 A 6 6 1.00 34 0.176
49 A 6 6 1.00 29 0.207
50 A 8 8 1.00 36 0.222
51 A 8 8 1.00 36 0.222
52 A 8 8 1.00 36 0.222
53 A 6 6 1.00 36 0.167
54 A 6 6 1.00 36 0.167
55 A 5 5 0.99 34 0.147
56 A 5 5 1.00 29 0.172
57 A 7 7 1.00 36 0.194
58 A 7 7 1.00 36 0.194
59 A 5 5 1.00 36 0.139
60 A 6 5 1.00 36 0.139

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