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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 [9] had the largest ratio of [.1875]

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 32 0.031
2 A 2 1 1.00 32 0.031
3 A 2 1 1.00 30 0.033
4 A 2 1 1.00 25 0.040
5 A 4 3 1.00 32 0.094
6 A 5 4 1.00 32 0.125
7 A 5 5 1.00 32 0.156
8 A 5 5 1.00 32 0.156
9 A 6 6 1.00 32 0.188
10 A 2 1 1.00 32 0.031
11 A 2 1 1.00 32 0.031
12 A 2 1 1.00 30 0.033
13 A 2 1 1.00 25 0.040
14 A 6 4 1.00 32 0.125
15 A 5 4 1.00 32 0.125
16 A 5 5 1.00 32 0.156
17 A 6 6 1.00 32 0.188
18 A 2 1 1.00 32 0.031
19 A 2 1 1.00 32 0.031
20 A 2 1 1.00 30 0.033
21 A 2 1 1.00 25 0.040
22 A 4 3 1.00 32 0.094
23 A 5 4 1.00 32 0.125
24 A 6 5 1.00 32 0.156
25 A 2 1 1.00 30 0.033
26 A 2 1 1.00 30 0.033
27 A 2 1 1.00 28 0.036
28 A 2 1 1.00 23 0.043

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