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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 [.2667]

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 24 0.042
2 A 2 1 1.00 24 0.042
3 A 2 1 1.00 24 0.042
4 A 2 1 1.00 22 0.045
5 A 3 3 1.00 24 0.125
6 A 3 3 1.00 24 0.125
7 A 3 3 1.00 24 0.125
8 A 4 4 1.00 24 0.167
9 A 2 1 1.00 26 0.038
10 A 2 1 1.00 26 0.038
11 A 2 1 1.00 24 0.042
12 A 4 3 1.00 26 0.115
13 A 4 4 1.00 26 0.154
14 A 4 3 1.00 26 0.115
15 A 4 3 1.00 26 0.115
16 A 2 1 1.00 26 0.038
17 A 2 1 1.00 26 0.038
18 A 2 1 1.00 24 0.042
19 A 5 3 1.00 26 0.115
20 A 5 4 1.00 26 0.154
21 A 5 4 1.00 26 0.154
22 A 5 3 1.00 26 0.115
23 A 6 6 1.00 28 0.214
24 A 14 8 1.00 30 0.267
25 A 9 7 1.00 30 0.233
26 A 5 5 1.00 28 0.179
27 A 2 2 1.00 21 0.095
28 A 5 3 1.00 30 0.100
29 A 7 5 1.00 30 0.167
30 A 4 4 1.00 28 0.143

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