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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi only. 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 also given. The larger this ratio is, the harder the integral is to solve. In this test file, problem number [5] had the largest ratio of [.325000000000000011]

# 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 9 1.03 40 0.225
2 A 7 7 1.02 38 0.184
3 A 6 6 1.00 33 0.182
4 A 10 9 1.10 40 0.225
5 A 14 13 1.01 40 0.325
6 A 12 11 1.00 42 0.262
7 A 8 7 0.99 42 0.167
8 A 6 5 1.00 42 0.119
9 A 8 7 0.95 42 0.167
10 A 11 10 0.99 42 0.238
11 A 12 11 0.99 49 0.224
12 A 6 5 1.00 49 0.102
13 A 6 5 1.00 49 0.102
14 A 8 7 0.95 49 0.143
15 A 9 8 0.99 49 0.163
16 A 10 10 1.03 58 0.172
17 A 8 8 1.02 53 0.151
18 A 7 7 1.00 60 0.117
19 A 11 10 1.10 60 0.167
20 A 14 13 1.01 60 0.217
21 A 13 12 1.00 62 0.194
22 A 9 8 1.00 62 0.129
23 A 7 6 1.00 62 0.097
24 A 9 8 0.95 62 0.129
25 A 10 9 0.98 62 0.145
26 A 11 11 1.01 42 0.262
27 A 10 10 1.03 40 0.250
28 A 8 8 1.02 35 0.229
29 A 12 11 1.07 42 0.262
30 A 14 13 1.01 42 0.310
31 A 12 11 1.00 44 0.250
32 A 11 10 1.00 44 0.227
33 A 9 8 1.01 44 0.182
34 A 12 11 0.99 44 0.250
35 A 11 10 0.99 44 0.227

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