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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 [21] had the largest ratio of [62]

# 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 9 8 1.00 40 0.200
2 A 8 7 1.00 38 0.184
3 A 6 5 1.00 33 0.152
4 A 9 7 1.00 40 0.175
5 A 12 10 1.00 40 0.250
6 A 10 10 0.99 42 0.238
7 A 7 7 1.00 42 0.167
8 A 5 5 1.00 42 0.119
9 A 7 7 1.00 42 0.167
10 A 8 7 1.00 42 0.167
11 A 10 10 1.00 49 0.204
12 A 5 5 1.00 49 0.102
13 A 5 5 1.00 49 0.102
14 A 7 7 1.00 49 0.143
15 A 8 7 1.00 49 0.143
16 A 8 7 1.00 58 0.121
17 A 7 6 1.00 53 0.113
18 A 7 6 1.00 60 0.100
19 A 10 8 1.00 60 0.133
20 A 13 11 1.00 60 0.183
21 A 9 9 1.00 62 0.145
22 A 8 8 1.00 62 0.129
23 A 6 6 1.00 62 0.097
24 A 8 8 1.00 62 0.129
25 A 9 8 0.99 62 0.129
26 A 9 8 0.99 42 0.190
27 A 8 7 1.00 40 0.175
28 A 7 6 1.00 35 0.171
29 A 11 9 1.00 42 0.214
30 A 12 10 1.00 42 0.238
31 A 10 10 0.99 44 0.227
32 A 9 9 1.00 44 0.204
33 A 8 8 1.00 44 0.182
34 A 9 9 1.00 44 0.204
35 A 8 8 1.00 44 0.182

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