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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 [51] had the largest ratio of [.857142999999999988]

# 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 6 5 1.03 13 0.385
2 A 7 7 1.07 13 0.538
3 A 6 5 1.04 13 0.385
4 A 7 7 1.21 11 0.636
5 A 7 7 1.12 11 0.636
6 A 5 4 1.06 13 0.308
7 A 7 7 1.08 13 0.538
8 A 6 5 1.00 13 0.385
9 A 7 7 1.00 13 0.538
10 A 6 5 1.00 13 0.385
11 A 3 3 1.00 19 0.158
12 A 8 7 1.20 19 0.368
13 A 3 3 1.00 19 0.158
14 A 8 7 1.28 19 0.368
15 A 3 3 1.00 17 0.176
16 A 3 3 1.00 17 0.176
17 A 5 4 0.92 19 0.211
18 A 3 3 1.00 19 0.158
19 A 5 4 0.86 19 0.211
20 A 3 3 1.00 19 0.158
21 A 5 4 0.84 19 0.211
22 A 7 6 1.40 21 0.286
23 A 3 3 1.00 21 0.143
24 A 8 7 1.33 21 0.333
25 A 3 3 1.00 19 0.158
26 A 3 3 1.00 19 0.158
27 A 5 4 0.95 21 0.190
28 A 3 3 1.00 21 0.143
29 A 5 4 0.92 21 0.190
30 A 3 3 1.00 21 0.143
31 A 5 4 0.92 21 0.190
32 A 3 3 1.00 21 0.143
33 A 8 7 1.21 21 0.333
34 A 3 3 1.00 19 0.158
35 A 3 3 1.00 19 0.158
36 A 5 4 0.92 21 0.190
37 A 3 3 1.00 21 0.143
38 A 5 4 0.92 21 0.190
39 A 3 3 1.00 21 0.143
40 A 5 4 0.92 21 0.190
41 A 3 3 1.00 21 0.143
42 A 8 7 1.13 21 0.333
43 A 3 3 1.00 19 0.158
44 A 3 3 1.00 19 0.158
45 A 5 4 0.90 21 0.190
46 A 3 3 1.00 21 0.143
47 A 5 4 0.91 21 0.190
48 A 3 3 1.00 21 0.143
49 A 5 4 0.92 21 0.190
50 A 3 3 1.00 21 0.143
51 A 19 18 0.92 21 0.857
52 A 15 14 0.99 21 0.667
53 A 10 9 1.00 19 0.474
54 A 5 5 1.00 19 0.263
55 A 5 5 1.00 21 0.238
56 A 8 7 1.53 21 0.333
57 A 8 7 1.55 21 0.333
58 A 5 4 0.98 21 0.190
59 A 5 4 0.95 21 0.190
60 A 5 4 0.95 21 0.190
61 A 10 9 1.36 21 0.429
62 A 7 6 1.40 21 0.286
63 A 7 6 1.40 21 0.286
64 A 5 4 0.93 21 0.190
65 A 5 4 0.94 21 0.190
66 A 5 4 0.94 21 0.190
67 A 10 9 1.30 21 0.429
68 A 7 6 1.33 21 0.286
69 A 7 6 1.31 21 0.286
70 A 5 4 0.91 21 0.190
71 A 5 4 0.93 21 0.190
72 A 5 4 0.94 21 0.190
73 A 7 6 1.27 21 0.286
74 A 7 6 1.25 21 0.286
75 A 5 4 0.89 21 0.190
76 A 5 4 0.92 21 0.190
77 A 5 4 0.93 21 0.190
78 A 5 5 1.00 9 0.556
79 A 3 3 1.00 21 0.143
80 A 3 3 1.00 21 0.143
81 A 3 3 1.00 19 0.158
82 A 7 6 0.76 21 0.286
83 N/A 8 0 1.00 21 0.000
84 A 8 7 1.09 21 0.333
85 A 8 7 1.02 21 0.333
86 A 4 3 0.98 21 0.143
87 A 6 5 1.04 21 0.238
88 N/A 8 0 1.00 21 0.000
89 N/A 7 0 1.00 19 0.000
90 N/A 7 0 1.00 19 0.000
91 N/A 8 0 1.00 21 0.000

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