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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 0.99 42 0.262
7 A 8 7 0.97 42 0.167
8 A 6 5 0.98 42 0.119
9 A 8 7 1.28 42 0.167
10 A 11 10 1.45 42 0.238
11 A 12 11 0.98 49 0.224
12 A 6 5 0.67 49 0.102
13 A 6 5 0.98 49 0.102
14 A 8 7 1.28 49 0.143
15 A 9 8 1.36 49 0.163
16 A 2 2 1.00 39 0.051
17 A 10 10 1.03 58 0.172
18 A 8 8 1.02 53 0.151
19 A 7 7 1.00 60 0.117
20 A 11 10 1.10 60 0.167
21 A 14 13 1.01 60 0.217
22 A 13 12 0.99 62 0.194
23 A 9 8 0.98 62 0.129
24 A 7 6 0.98 62 0.097
25 A 9 8 1.28 62 0.129
26 A 10 9 1.45 62 0.145
27 A 11 11 1.03 42 0.262
28 A 10 10 1.04 40 0.250
29 A 8 8 1.03 35 0.229
30 A 12 11 1.07 42 0.262
31 A 14 13 1.01 42 0.310
32 A 12 11 0.99 44 0.250
33 A 11 10 1.00 44 0.227
34 A 9 8 1.00 44 0.182
35 A 12 11 1.22 44 0.250
36 A 11 10 1.45 44 0.227
37 A 13 12 1.61 44 0.273
38 A 12 11 0.98 47 0.234
39 A 11 10 0.99 47 0.213
40 A 9 8 1.00 47 0.170
41 A 11 10 1.22 47 0.213
42 A 9 8 1.50 47 0.170
43 A 11 10 1.24 47 0.213

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