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

grade

number of

steps

used

number of

unique

rules

normalized

antiderivative

leaf size

integrand

leaf size

\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)

1.20

0.312

0.82

0.250

1.09

0.312

0.85

0.250

1.16

0.250

1.00

0.125

1.16

0.286

1.00

0.250

1.09

0.312

0.95

0.250

1.14

0.375

1.14

0.375

1.32

0.375

1.17

0.312

1.19

0.312

1.17

0.312

1.19

0.417

1.15

0.375

1.21

0.375

1.14

0.312

0.86

0.250

1.10

0.312

0.82

0.250

1.17

0.250

1.00

0.125

1.17

0.286

1.00

0.250

1.17

0.312

1.00

0.250

1.15

0.375

1.36

0.688

1.43

0.688

1.40

0.625

1.41

0.625

1.40

0.625

1.41

0.833

1.37

0.688

1.40

0.688

1.06

0.154

0.60

0.154

1.00

0.154

1.00

0.125

1.00

0.125

1.00

0.077

0.99

0.167

1.01

0.222

1.02

0.278

1.04

0.167

1.00

0.167

1.03

0.188

1.06

0.389

0.98

0.278

1.07

0.278

0.90

0.389

0.90

0.278

0.97

0.278

0.96

0.222

0.98

0.278

0.95

0.286

0.91

0.389

0.90

0.333

0.84

0.444

0.95

0.214

0.93

0.357

1.05

0.357

1.32

0.571

1.00

0.214

1.32

0.583

1.10

0.500

0.96

0.429

1.04

0.357

1.21

0.786

1.56

0.571

1.37

0.500

1.47

0.571

1.57

0.500

1.37

0.700

1.45

0.714

1.53

0.643

1.32

0.714

1.41

0.857

0.93

0.188

1.68

0.312

1.03

0.375

1.53

0.500

1.00

0.188

1.71

0.500

1.07

0.438

1.74

0.312

1.02

0.250

1.40

0.688

1.22

0.562

1.89

0.438

1.33

0.500

1.49

0.438

1.88

0.583

1.26

0.688

1.21

0.625

1.84

0.625

100

1.31

0.750

101

1.00

0.188

102

1.16

0.250

103

1.07

0.188

104

1.29

0.188

105

0.98

0.188

106

1.07

0.214

107

1.30

0.188

108

1.18

0.312

109

1.02

0.188

110

1.12

0.375

111

1.40

0.625

112

1.45

0.562

113

1.43

0.562

114

1.41

0.562

115

1.53

0.750

116

1.38

0.688

117

1.40

0.688

118

1.00

0.188

119

1.16

0.250

120

1.07

0.188

121

1.30

0.188

122

0.98

0.188

123

1.07

0.214

124

1.25

0.188

125

1.18

0.250

126

1.07

0.188

127

1.12

0.438

128

1.00

0.312

129

1.11

0.312

130

1.02

0.250

131

1.19

0.312

132

0.97

0.333

133

1.06

0.375

134

1.01

0.375

135

1.14

0.562

136

1.00

0.500

137

0.90

0.188

138

0.85

0.188

139

1.00

0.167

140

1.05

0.214

141

1.05

0.188

142

1.00

0.188

143

1.00

0.188

2.3 Detailed conclusion table speciﬁc for Rubi results