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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 [90] had the largest ratio of [27]

# 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 2 2 1.00 15 0.133
2 A 5 3 1.00 23 0.130
3 A 4 3 1.00 23 0.130
4 A 3 3 1.00 23 0.130
5 A 2 2 1.00 23 0.087
6 A 3 3 1.00 23 0.130
7 A 4 3 1.00 23 0.130
8 A 16 12 1.00 25 0.480
9 A 15 12 1.00 25 0.480
10 A 15 12 1.00 25 0.480
11 A 14 11 1.00 25 0.440
12 A 13 10 1.00 25 0.400
13 A 14 11 1.00 25 0.440
14 A 14 11 1.00 25 0.440
15 A 7 5 1.00 25 0.200
16 A 6 5 1.00 25 0.200
17 A 5 5 1.00 25 0.200
18 A 4 4 1.00 25 0.160
19 A 4 4 1.00 25 0.160
20 A 4 4 1.00 25 0.160
21 A 5 5 1.00 25 0.200
22 A 6 5 1.00 25 0.200
23 A 7 6 1.00 25 0.240
24 A 6 6 1.00 25 0.240
25 A 6 5 1.00 25 0.200
26 A 6 6 1.00 25 0.240
27 A 7 6 1.00 25 0.240
28 A 10 10 1.00 25 0.400
29 A 17 14 1.00 25 0.560
30 A 18 15 1.00 25 0.600
31 A 17 14 1.00 25 0.560
32 A 18 15 1.00 25 0.600
33 A 18 15 1.00 25 0.600
34 A 20 16 1.00 25 0.640
35 A 8 8 1.00 25 0.320
36 A 8 7 1.00 25 0.280
37 A 8 8 1.00 25 0.320
38 A 8 7 1.00 25 0.280
39 A 9 8 1.00 25 0.320
40 A 10 8 1.00 25 0.320
41 A 12 9 1.00 13 0.692
42 A 6 5 1.00 11 0.454
43 A 8 7 1.00 13 0.538
44 A 14 9 1.00 11 0.818
45 A 12 8 1.00 13 0.615
46 A 5 4 1.00 11 0.364
47 A 6 5 1.00 13 0.385
48 A 13 10 1.00 11 0.909
49 A 8 7 1.00 13 0.538
50 A 13 9 1.00 11 0.818
51 A 12 8 1.00 23 0.348
52 A 11 8 1.00 23 0.348
53 A 10 7 1.00 23 0.304
54 A 11 8 1.00 23 0.348
55 A 12 8 1.00 23 0.348
56 A 13 9 1.00 25 0.360
57 A 12 9 1.00 25 0.360
58 A 11 8 1.00 25 0.320
59 A 11 8 1.00 25 0.320
60 A 12 9 1.00 25 0.360
61 A 13 9 1.00 25 0.360
62 A 14 10 1.00 25 0.400
63 A 13 10 1.00 25 0.400
64 A 12 9 1.00 25 0.360
65 A 12 9 1.00 25 0.360
66 A 12 9 1.00 25 0.360
67 A 13 10 1.00 25 0.400
68 A 14 10 1.00 25 0.400
69 A 15 12 1.00 25 0.480
70 A 14 11 1.00 25 0.440
71 A 14 11 1.00 25 0.440
72 A 14 11 1.00 25 0.440
73 A 15 12 1.00 25 0.480
74 A 16 13 1.00 25 0.520
75 A 16 13 1.00 25 0.520
76 A 15 12 1.00 25 0.480
77 A 15 12 1.00 25 0.480
78 A 15 12 1.00 25 0.480
79 A 15 12 1.00 25 0.480
80 A 16 13 1.00 25 0.520
81 A 17 14 1.00 25 0.560
82 A 16 13 1.00 25 0.520
83 A 16 13 1.00 25 0.520
84 A 16 13 1.00 25 0.520
85 A 16 13 1.00 25 0.520
86 A 16 13 1.00 25 0.520
87 A 17 13 1.00 25 0.520
88 A 5 3 1.00 12 0.250
89 A 8 5 1.00 23 0.217
90 A 3 3 1.00 27 0.111
91 A 3 3 1.00 27 0.111
92 A 2 2 1.00 23 0.087
93 A 3 3 1.00 23 0.130
94 A 4 3 1.00 23 0.130
95 A 10 5 1.00 25 0.200
96 A 9 5 1.00 25 0.200
97 A 8 5 1.00 25 0.200
98 A 10 7 1.00 27 0.259
99 A 13 9 1.00 27 0.333
100 A 13 9 1.00 27 0.333
101 A 7 4 1.00 25 0.160
102 A 8 5 1.00 25 0.200
103 A 9 5 1.00 25 0.200
104 A 7 4 1.00 27 0.148
105 A 8 5 1.00 27 0.185
106 A 9 5 1.00 27 0.185

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