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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 [88] had the largest ratio of [1.08000000000000007]

# 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 5 5 0.97 13 0.385
2 A 4 3 1.00 13 0.231
3 A 3 3 1.00 13 0.231
4 A 4 3 1.20 11 0.273
5 A 2 2 1.00 8 0.250
6 A 5 4 1.26 11 0.364
7 A 6 5 1.00 13 0.385
8 A 5 4 1.13 13 0.308
9 A 6 5 0.95 13 0.385
10 B 4 3 2.20 13 0.231
11 B 4 3 4.33 15 0.200
12 A 4 3 1.00 9 0.333
13 A 4 3 1.00 11 0.273
14 A 3 3 1.00 11 0.273
15 A 3 3 1.00 13 0.231
16 A 5 4 1.00 11 0.364
17 A 5 4 1.00 13 0.308
18 A 4 3 1.00 9 0.333
19 A 4 3 1.00 11 0.273
20 A 2 2 1.00 11 0.182
21 A 2 2 1.00 13 0.154
22 A 5 4 1.00 11 0.364
23 A 5 4 1.00 13 0.308
24 A 12 11 1.20 13 0.846
25 A 5 4 1.00 13 0.308
26 A 9 8 1.24 13 0.615
27 A 4 3 1.00 11 0.273
28 A 4 3 1.00 8 0.375
29 A 5 4 1.25 11 0.364
30 A 7 6 1.16 13 0.462
31 A 5 4 1.18 13 0.308
32 A 10 9 1.23 13 0.692
33 A 10 10 1.05 23 0.435
34 A 8 8 1.01 23 0.348
35 A 8 8 1.01 23 0.348
36 A 6 6 1.00 23 0.261
37 A 6 6 1.00 23 0.261
38 A 8 8 1.01 23 0.348
39 A 8 8 1.01 23 0.348
40 A 10 10 1.03 23 0.435
41 A 13 13 0.95 25 0.520
42 A 11 11 0.97 25 0.440
43 A 11 11 0.97 25 0.440
44 A 9 9 1.03 25 0.360
45 A 9 9 1.01 25 0.360
46 A 9 9 1.03 25 0.360
47 A 9 9 1.01 25 0.360
48 A 11 11 0.96 25 0.440
49 A 16 16 0.98 25 0.640
50 A 14 14 1.00 25 0.560
51 A 14 14 1.00 25 0.560
52 A 12 12 1.05 25 0.480
53 A 12 12 1.01 25 0.480
54 A 12 12 1.02 25 0.480
55 A 12 12 0.99 25 0.480
56 A 12 12 1.04 25 0.480
57 A 12 12 1.05 25 0.480
58 A 25 24 1.02 25 0.960
59 A 22 21 1.00 25 0.840
60 A 22 21 1.01 25 0.840
61 A 19 18 0.98 25 0.720
62 A 19 18 0.99 25 0.720
63 A 11 10 0.98 25 0.400
64 A 11 10 1.03 25 0.400
65 A 19 18 0.95 25 0.720
66 A 19 18 0.96 25 0.720
67 A 22 21 0.99 25 0.840
68 A 25 24 1.00 25 0.960
69 A 22 21 0.97 25 0.840
70 A 22 21 0.98 25 0.840
71 A 19 18 0.97 25 0.720
72 A 20 19 0.98 25 0.760
73 A 19 18 0.92 25 0.720
74 A 19 18 0.95 25 0.720
75 A 22 21 0.97 25 0.840
76 A 22 21 0.97 25 0.840
77 A 25 24 0.99 25 0.960
78 A 25 24 0.92 25 0.960
79 A 25 24 0.93 25 0.960
80 A 22 21 0.94 25 0.840
81 A 22 21 0.94 25 0.840
82 A 22 21 0.89 25 0.840
83 A 23 22 0.90 25 0.880
84 A 22 21 0.90 25 0.840
85 A 22 21 0.93 25 0.840
86 A 25 24 0.94 25 0.960
87 A 25 24 0.95 25 0.960
88 A 28 27 0.97 25 1.080
89 A 4 3 1.00 23 0.130

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