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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 [65] had the largest ratio of [33]

# 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 3 2 1.00 21 0.095
2 A 4 3 1.00 21 0.143
3 A 3 2 1.00 21 0.095
4 A 3 3 1.00 21 0.143
5 A 3 3 1.00 21 0.143
6 A 2 2 1.00 19 0.105
7 A 3 2 1.00 12 0.167
8 A 2 2 1.00 19 0.105
9 A 2 2 1.00 21 0.095
10 A 3 2 1.00 21 0.095
11 A 3 3 1.00 21 0.143
12 A 4 3 1.00 21 0.143
13 A 4 3 1.00 21 0.143
14 A 1 1 1.00 29 0.034
15 A 1 1 1.00 28 0.036
16 A 4 4 1.00 25 0.160
17 A 4 4 1.00 25 0.160
18 A 3 3 1.00 25 0.120
19 A 3 3 1.00 25 0.120
20 A 3 3 1.00 25 0.120
21 A 3 3 1.00 25 0.120
22 A 4 4 1.00 25 0.160
23 A 4 4 1.00 25 0.160
24 A 1 1 1.00 23 0.043
25 A 1 1 1.00 24 0.042
26 A 1 1 1.00 21 0.048
27 A 1 1 1.00 21 0.048
28 A 1 1 1.00 21 0.048
29 A 1 1 1.00 21 0.048
30 A 1 1 1.00 19 0.053
31 A 2 2 1.00 10 0.200
32 A 1 1 1.00 8 0.125
33 A 1 1 1.00 19 0.053
34 A 1 1 1.00 21 0.048
35 A 1 1 1.00 21 0.048
36 A 1 1 1.00 21 0.048
37 A 7 5 1.00 28 0.179
38 A 6 5 1.00 28 0.179
39 A 6 6 1.00 26 0.231
40 A 4 3 1.00 19 0.158
41 A 4 4 1.00 26 0.154
42 A 3 3 1.00 28 0.107
43 A 5 5 1.00 28 0.179
44 A 6 5 1.00 28 0.179
45 A 7 5 1.00 28 0.179
46 A 7 5 1.00 28 0.179
47 A 10 7 1.00 32 0.219
48 A 9 7 1.00 32 0.219
49 A 8 7 1.00 32 0.219
50 A 7 6 1.00 32 0.188
51 A 8 7 1.00 32 0.219
52 A 9 7 1.00 32 0.219
53 A 10 7 1.00 32 0.219
54 A 7 5 1.00 29 0.172
55 A 6 5 1.00 29 0.172
56 A 6 6 1.00 29 0.207
57 A 5 5 1.00 27 0.185
58 A 4 3 1.00 20 0.150
59 A 4 4 1.00 27 0.148
60 A 4 4 1.00 29 0.138
61 A 6 5 1.00 29 0.172
62 A 6 5 1.00 29 0.172
63 A 8 6 1.00 29 0.207
64 A 7 5 1.00 29 0.172
65 A 8 6 1.00 33 0.182
66 A 7 6 1.00 33 0.182
67 A 6 5 1.00 33 0.152
68 A 6 5 1.00 33 0.152
69 A 7 6 1.00 33 0.182
70 A 8 6 1.00 33 0.182

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