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2.2.2 Integrals 101 to 175

Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

4 4 4 4 3 3 15 3 3

N.S.

1 1.00 1.00 1.00 0.75 0.75 3.75 0.75 0.75

time (sec)

N/A 0.134 0.013 0.029 0.272 0.240 0.054 0.266 0.102

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 33 27 25 19 28 19 21 22

N.S.

1 1.22 1.00 0.93 0.70 1.04 0.70 0.78 0.81

time (sec)

N/A 0.181 0.013 0.063 0.202 0.251 1.997 0.274 0.137

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 58 67 61 49 38 0 36 49

N.S.

1 1.38 1.60 1.45 1.17 0.90 0.00 0.86 1.17

time (sec)

N/A 0.140 0.062 0.087 0.260 0.237 0.000 0.317 0.070

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A A A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 75 68 0 80 114 61 0

N.S.

1 1.00 1.06 0.96 0.00 1.13 1.61 0.86 0.00

time (sec)

N/A 0.179 0.114 0.187 0.000 0.245 1.077 0.291 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A C B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 55 28 0 43 71 61 0

N.S.

1 1.00 1.72 0.88 0.00 1.34 2.22 1.91 0.00

time (sec)

N/A 0.144 0.033 0.106 0.000 0.246 0.901 0.312 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 14 13 13 12 15 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 0.80 1.00 0.87

time (sec)

N/A 0.134 0.003 0.053 0.182 0.234 0.041 0.262 0.054

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 14 13 13 14 15 13

N.S.

1 1.00 1.00 0.74 0.68 0.68 0.74 0.79 0.68

time (sec)

N/A 0.135 0.003 0.052 0.181 0.230 0.047 0.278 0.040

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 20 19 19 19 21 19

N.S.

1 1.00 1.00 0.87 0.83 0.83 0.83 0.91 0.83

time (sec)

N/A 0.181 0.003 0.062 0.200 0.241 0.056 0.275 0.046

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 18 17 17 17 20 19

N.S.

1 1.00 1.00 0.78 0.74 0.74 0.74 0.87 0.83

time (sec)

N/A 0.183 0.005 0.030 0.192 0.259 0.069 0.269 0.205

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 22 19 18 26 19 24 18

N.S.

1 1.00 0.92 0.79 0.75 1.08 0.79 1.00 0.75

time (sec)

N/A 0.146 0.007 0.051 0.184 0.229 0.070 0.275 0.051

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 29 28 29 28 28 3 29 57

N.S.

1 1.04 1.00 1.04 1.00 1.00 0.11 1.04 2.04

time (sec)

N/A 0.176 0.021 0.062 0.287 0.246 0.064 0.307 0.192

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 61 37 36 51 14 37 53

N.S.

1 1.00 1.24 0.76 0.73 1.04 0.29 0.76 1.08

time (sec)

N/A 0.230 0.023 0.066 0.266 0.251 0.079 0.293 0.123

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 24 19 39 38 39 37 21

N.S.

1 1.00 1.14 0.90 1.86 1.81 1.86 1.76 1.00

time (sec)

N/A 0.152 0.018 0.114 0.269 0.247 0.239 0.313 0.339

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 17 14 55 48 14 87

N.S.

1 1.00 1.00 1.06 0.88 3.44 3.00 0.88 5.44

time (sec)

N/A 0.202 0.012 0.115 0.184 0.232 1.343 0.326 0.160

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 9 9 9 9 8 11 9

N.S.

1 1.00 0.82 0.82 0.82 0.82 0.73 1.00 0.82

time (sec)

N/A 0.124 0.003 0.041 0.182 0.233 0.036 0.282 0.050

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 20 19 19 20 22 19

N.S.

1 1.00 1.00 0.87 0.83 0.83 0.87 0.96 0.83

time (sec)

N/A 0.133 0.004 0.054 0.185 0.244 0.052 0.262 0.124

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 28 21 20 27 22 22 18

N.S.

1 1.00 0.93 0.70 0.67 0.90 0.73 0.73 0.60

time (sec)

N/A 0.158 0.006 0.027 0.191 0.234 0.035 0.253 0.043

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 27 24 23 23 20 26 30

N.S.

1 1.00 1.00 0.89 0.85 0.85 0.74 0.96 1.11

time (sec)

N/A 0.188 0.004 0.030 0.207 0.235 0.062 0.275 0.095

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 24 16 20 32 17 16 15

N.S.

1 1.00 1.04 0.70 0.87 1.39 0.74 0.70 0.65

time (sec)

N/A 0.170 0.007 0.040 0.181 0.228 0.048 0.260 0.093

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 14 14 14 15 14

N.S.

1 1.00 1.00 0.94 0.88 0.88 0.88 0.94 0.88

time (sec)

N/A 0.145 0.003 0.047 0.270 0.233 0.037 0.280 0.044

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 13 12 12 14 12 12

N.S.

1 1.00 1.00 0.72 0.67 0.67 0.78 0.67 0.67

time (sec)

N/A 0.136 0.005 0.049 0.261 0.238 0.063 0.268 0.039

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 11 11 8 13 11

N.S.

1 1.00 1.00 1.09 1.00 1.00 0.73 1.18 1.00

time (sec)

N/A 0.129 0.002 0.040 0.196 0.227 0.039 0.277 0.104

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 21 24 32 19 29 20

N.S.

1 1.00 1.00 0.88 1.00 1.33 0.79 1.21 0.83

time (sec)

N/A 0.134 0.006 0.054 0.192 0.237 0.040 0.277 0.037

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 44 39 46 83 46 52 45

N.S.

1 1.00 0.96 0.85 1.00 1.80 1.00 1.13 0.98

time (sec)

N/A 0.150 0.012 0.053 0.183 0.242 0.087 0.268 0.097

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 11 10 16 8 11 10

N.S.

1 1.00 1.00 1.10 1.00 1.60 0.80 1.10 1.00

time (sec)

N/A 0.121 0.003 0.033 0.185 0.227 0.027 0.291 0.030

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 19 17 14 17 13 10 16 13

N.S.

1 1.12 1.00 0.82 1.00 0.76 0.59 0.94 0.76

time (sec)

N/A 0.130 0.003 0.052 0.186 0.244 0.037 0.283 0.122

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 15 14 14 17 16 14

N.S.

1 1.00 1.00 0.75 0.70 0.70 0.85 0.80 0.70

time (sec)

N/A 0.135 0.003 0.063 0.188 0.234 0.045 0.291 0.054

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 12 13 12 16 8 13 12

N.S.

1 1.00 0.75 0.81 0.75 1.00 0.50 0.81 0.75

time (sec)

N/A 0.135 0.003 0.053 0.191 0.236 0.038 0.275 0.037

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 20 14 15 14 17 10 14 14

N.S.

1 1.43 1.00 1.07 1.00 1.21 0.71 1.00 1.00

time (sec)

N/A 0.148 0.006 0.242 0.281 0.240 0.078 0.300 0.093

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 21 18 17 17 20 20 17

N.S.

1 1.00 1.00 0.86 0.81 0.81 0.95 0.95 0.81

time (sec)

N/A 0.150 0.005 0.029 0.207 0.240 0.080 0.262 0.083

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 27 23 23 34 20 25 17

N.S.

1 1.00 1.29 1.10 1.10 1.62 0.95 1.19 0.81

time (sec)

N/A 0.116 0.005 0.053 0.195 0.237 0.054 0.255 0.102

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 17 16 16 17 17 16

N.S.

1 1.00 1.00 0.77 0.73 0.73 0.77 0.77 0.73

time (sec)

N/A 0.142 0.003 0.052 0.275 0.240 0.037 0.291 0.172

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 18 10 11 14 18 8 14 10

N.S.

1 1.80 1.00 1.10 1.40 1.80 0.80 1.40 1.00

time (sec)

N/A 0.146 0.004 0.037 0.190 0.243 0.068 0.271 0.030

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 31 21 19 25 19 21 16

N.S.

1 1.00 1.00 0.68 0.61 0.81 0.61 0.68 0.52

time (sec)

N/A 0.144 0.002 0.049 0.196 0.229 0.051 0.318 0.045

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 17 16 16 15 17 24

N.S.

1 1.00 1.00 0.94 0.89 0.89 0.83 0.94 1.33

time (sec)

N/A 0.162 0.004 0.046 0.330 0.247 0.066 0.364 0.041

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 25 10 17 17 17 19 9

N.S.

1 1.00 1.92 0.77 1.31 1.31 1.31 1.46 0.69

time (sec)

N/A 0.116 0.003 0.067 0.271 0.255 0.066 0.277 0.029

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 90 64 22 72 61 73 72 33

N.S.

1 1.06 0.75 0.26 0.85 0.72 0.86 0.85 0.39

time (sec)

N/A 0.225 0.013 0.054 0.263 0.246 0.073 0.289 0.118

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 15 16 15 26 14 15 15

N.S.

1 1.00 0.65 0.70 0.65 1.13 0.61 0.65 0.65

time (sec)

N/A 0.137 0.006 0.117 0.295 0.258 0.041 0.284 0.089

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 11 11 8 11 11

N.S.

1 1.00 1.00 1.09 1.00 1.00 0.73 1.00 1.00

time (sec)

N/A 0.131 0.005 0.042 0.185 0.243 0.045 0.280 0.062

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 26 23 20 23 36 39 47 21

N.S.

1 0.58 0.51 0.44 0.51 0.80 0.87 1.04 0.47

time (sec)

N/A 0.171 0.027 0.168 0.274 0.255 0.228 0.276 0.100

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 31 30 0 111 110 53 28

N.S.

1 1.00 0.84 0.81 0.00 3.00 2.97 1.43 0.76

time (sec)

N/A 0.171 0.024 0.109 0.000 0.281 1.449 0.265 0.339

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 20 20 16 37 50 36 35 15

N.S.

1 0.36 0.36 0.29 0.66 0.89 0.64 0.62 0.27

time (sec)

N/A 0.149 0.015 0.070 0.267 0.250 0.165 0.301 0.271

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 20 16 19 23 32 40 32

N.S.

1 1.00 0.65 0.52 0.61 0.74 1.03 1.29 1.03

time (sec)

N/A 0.158 0.013 0.090 0.274 0.255 0.133 0.264 0.224

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 18 18 17 14 33 248 48 26

N.S.

1 0.50 0.50 0.47 0.39 0.92 6.89 1.33 0.72

time (sec)

N/A 0.206 0.105 0.143 0.264 0.287 24.438 0.285 0.212

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 16 15 43 71839 26 15

N.S.

1 1.00 1.00 1.07 1.00 2.87 4789.27 1.73 1.00

time (sec)

N/A 0.172 0.042 0.855 0.262 0.273 18.580 0.286 0.460

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 14 14 39 602 13 29

N.S.

1 1.00 1.00 0.82 0.82 2.29 35.41 0.76 1.71

time (sec)

N/A 0.152 0.027 0.304 0.181 0.259 134.571 0.278 0.649

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 22 20 41 11 22 25 34

N.S.

1 1.00 0.73 0.67 1.37 0.37 0.73 0.83 1.13

time (sec)

N/A 0.210 0.053 0.253 0.300 0.253 0.147 0.312 0.319

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 41 23 22 29 24 22 22

N.S.

1 1.00 1.41 0.79 0.76 1.00 0.83 0.76 0.76

time (sec)

N/A 0.123 0.045 0.335 0.277 0.243 0.088 0.279 0.037

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 12 11 11 8 11 11

N.S.

1 1.00 1.00 0.92 0.85 0.85 0.62 0.85 0.85

time (sec)

N/A 0.112 0.001 0.059 0.186 0.240 0.071 0.273 0.194

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 43 33 30 41 40 87 47 35

N.S.

1 1.16 0.89 0.81 1.11 1.08 2.35 1.27 0.95

time (sec)

N/A 0.135 0.033 0.171 0.270 0.254 0.910 0.273 0.224

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 42 22 25 25 0 26 21

N.S.

1 1.00 1.91 1.00 1.14 1.14 0.00 1.18 0.95

time (sec)

N/A 0.135 0.034 0.158 0.188 0.253 0.000 0.273 0.090

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 33 21 20 25 24 25 20

N.S.

1 1.00 1.22 0.78 0.74 0.93 0.89 0.93 0.74

time (sec)

N/A 0.119 0.019 0.147 0.283 0.240 0.099 0.268 0.087

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 33 21 22 27 26 27 23

N.S.

1 1.00 1.22 0.78 0.81 1.00 0.96 1.00 0.85

time (sec)

N/A 0.139 0.044 0.429 0.283 0.237 0.250 0.272 0.054

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 39 7 15 17 15 33 11

N.S.

1 1.00 2.79 0.50 1.07 1.21 1.07 2.36 0.79

time (sec)

N/A 0.119 0.022 0.080 0.195 0.238 0.214 0.270 0.203

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 72 76 60 59 92 0 168 73

N.S.

1 1.06 1.12 0.88 0.87 1.35 0.00 2.47 1.07

time (sec)

N/A 0.200 0.110 0.296 0.265 0.254 0.000 0.283 0.094

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A F C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 13 12 0 73 0 13

N.S.

1 1.00 1.00 1.00 0.92 0.00 5.62 0.00 1.00

time (sec)

N/A 0.149 0.003 0.062 0.190 0.000 0.990 0.000 0.033

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 15 2 2 15 2 2

N.S.

1 1.00 1.00 1.00 0.13 0.13 1.00 0.13 0.13

time (sec)

N/A 0.199 0.010 0.223 0.186 0.235 0.073 0.276 0.125

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2 2 2 8 2 2 2 2 2

N.S.

1 1.00 1.00 4.00 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.118 0.009 0.036 0.221 0.229 0.387 0.294 0.008

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

4 4 4 9 4 4 3 4 4

N.S.

1 1.00 1.00 2.25 1.00 1.00 0.75 1.00 1.00

time (sec)

N/A 0.124 0.010 0.033 0.209 0.234 0.405 0.276 0.013

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 16 5 13 7 13 14

N.S.

1 1.00 1.00 1.45 0.45 1.18 0.64 1.18 1.27

time (sec)

N/A 0.150 0.011 0.033 0.221 0.240 0.599 0.274 0.025

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 15 9 13 10 18 9

N.S.

1 1.00 1.00 1.07 0.64 0.93 0.71 1.29 0.64

time (sec)

N/A 0.158 0.004 0.038 0.207 0.234 0.622 0.255 0.018

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 17 16 14 0 14 14

N.S.

1 1.00 1.00 1.13 1.07 0.93 0.00 0.93 0.93

time (sec)

N/A 0.144 0.029 0.068 0.228 0.234 0.000 0.265 0.029

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 14 13 10 0 10 10

N.S.

1 1.00 1.00 1.08 1.00 0.77 0.00 0.77 0.77

time (sec)

N/A 0.225 0.051 0.052 0.218 0.235 0.000 0.269 0.128

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 22 16 23 0 80 17

N.S.

1 1.00 1.00 1.16 0.84 1.21 0.00 4.21 0.89

time (sec)

N/A 0.162 0.040 0.039 0.226 0.231 0.000 0.263 0.125

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 19 18 19 0 16 0

N.S.

1 1.00 1.00 1.06 1.00 1.06 0.00 0.89 0.00

time (sec)

N/A 0.158 0.008 0.035 0.222 0.240 0.000 0.272 0.000

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 11 10 9 9 7 9 9

N.S.

1 1.00 0.69 0.62 0.56 0.56 0.44 0.56 0.56

time (sec)

N/A 0.141 0.009 0.018 0.188 0.228 0.031 0.303 0.019

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 29 16 15 14 14 12 14 14

N.S.

1 1.12 0.62 0.58 0.54 0.54 0.46 0.54 0.54

time (sec)

N/A 0.178 0.011 0.020 0.207 0.233 0.033 0.295 0.029

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 42 21 20 19 19 17 19 19

N.S.

1 1.17 0.58 0.56 0.53 0.53 0.47 0.53 0.53

time (sec)

N/A 0.211 0.012 0.027 0.203 0.237 0.039 0.304 0.022

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 39 66 181 60 360 77 2034

N.S.

1 1.00 0.81 1.38 3.77 1.25 7.50 1.60 42.38

time (sec)

N/A 0.195 0.150 0.513 0.282 0.268 0.409 0.298 10.335

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2 2 2 9 3 2 2 3 2

N.S.

1 1.00 1.00 4.50 1.50 1.00 1.00 1.50 1.00

time (sec)

N/A 0.115 0.053 0.014 0.234 0.232 0.184 0.298 0.010

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 17 6 14 7 11 10

N.S.

1 1.00 1.00 1.70 0.60 1.40 0.70 1.10 1.00

time (sec)

N/A 0.134 0.004 0.021 0.232 0.249 0.172 0.288 0.035

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A C A F B

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

22 22 22 0 22 18 24 0 22

N.S.

1 1.00 1.00 0.00 1.00 0.82 1.09 0.00 1.00

time (sec)

N/A 0.156 0.019 0.000 0.071 0.076 0.274 0.000 0.063

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 10 12 11 9 0 9 9

N.S.

1 1.00 0.83 1.00 0.92 0.75 0.00 0.75 0.75

time (sec)

N/A 0.133 0.038 0.043 0.218 0.233 0.000 0.298 0.015

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 23 0 20 0 20 0

N.S.

1 1.00 1.00 1.05 0.00 0.91 0.00 0.91 0.00

time (sec)

N/A 0.186 0.120 0.092 0.000 0.250 0.000 0.282 0.000

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 17 14 0 6 27 0 155

N.S.

1 1.00 0.17 0.14 0.00 0.06 0.26 0.00 1.50

time (sec)

N/A 0.159 10.020 0.153 0.000 0.069 0.411 0.000 0.281

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