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 [3] had the largest ratio of [.190476000000000006]

grade

number of

steps

used

number of

unique

rules

normalized

antiderivative

leaf size

integrand

leaf size

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

1.15

0.080

1.18

0.087

0.94

0.190

1.00

0.080

1.32

0.080

1.27

0.080

0.97

0.080

1.15

0.087

1.00

0.190

0.99

0.080

1.08

0.080

1.18

0.080

1.00

0.087

1.00

0.190

1.12

0.080

0.86

0.080

0.46

0.080

0.42

0.087

0.48

0.095

0.73

0.080

0.69

0.080

0.55

0.080

0.55

0.087

0.79

0.095

0.71

0.080

0.75

0.080

0.74

0.080

1.02

0.087

0.92

0.095

0.87

0.080

0.80

0.080

0.78

0.080

0.84

0.087

1.04

0.095

0.79

0.080

0.94

0.080

0.97

0.080

1.12

0.087

1.23

0.095

0.97

0.080

0.88

0.080

1.52

0.080

1.76

0.087

1.57

0.095

1.13

0.080

1.03

0.080

0.47

0.080

0.43

0.087

0.47

0.095

0.53

0.080

0.48

0.080

0.46

0.080

0.51

0.087

0.77

0.095

0.55

0.080

0.43

0.080

0.65

0.080

0.97

0.087

0.85

0.095

0.65

0.080

0.53

0.080

1.00

0.043

2.3 Detailed conclusion table speciﬁc for Rubi results