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Integrals 101 to 143

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 Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

62 62 57 38 50 62 60 50 39 64

N.S.

1 1.00 0.92 0.61 0.81 1.00 0.97 0.81 0.63 1.03

time (sec)

N/A 0.252 0.027 0.057 0.105 0.065 0.086 0.163 0.172 18.667

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

88 102 97 42 0 54 54 66 44 130

N.S.

1 1.16 1.10 0.48 0.00 0.61 0.61 0.75 0.50 1.48

time (sec)

N/A 0.258 0.112 0.070 0.000 0.074 0.123 0.178 0.165 0.127

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

55 59 53 33 45 56 53 45 34 59

N.S.

1 1.07 0.96 0.60 0.82 1.02 0.96 0.82 0.62 1.07

time (sec)

N/A 0.241 0.016 0.043 0.105 0.062 0.066 0.161 0.170 0.133

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

77 99 75 34 0 45 49 47 18 117

N.S.

1 1.29 0.97 0.44 0.00 0.58 0.64 0.61 0.23 1.52

time (sec)

N/A 0.211 0.032 0.060 0.000 0.071 0.109 0.146 0.163 18.898

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

47 46 38 19 31 43 42 31 18 30

N.S.

1 0.98 0.81 0.40 0.66 0.91 0.89 0.66 0.38 0.64

time (sec)

N/A 0.199 0.009 0.040 0.107 0.061 0.060 0.155 0.161 18.876

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

75 80 74 34 0 45 49 41 16 125

N.S.

1 1.07 0.99 0.45 0.00 0.60 0.65 0.55 0.21 1.67

time (sec)

N/A 0.192 0.027 0.051 0.000 0.076 0.109 0.138 0.158 0.059

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

57 74 55 35 51 58 58 51 14 42

N.S.

1 1.30 0.96 0.61 0.89 1.02 1.02 0.89 0.25 0.74

time (sec)

N/A 0.260 0.025 0.051 0.105 0.063 0.084 0.167 0.171 0.193

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F A A A F B

verified

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

size

88 104 65 42 0 67 56 68 51 130

N.S.

1 1.18 0.74 0.48 0.00 0.76 0.64 0.77 0.58 1.48

time (sec)

N/A 0.234 0.016 0.069 0.000 0.075 0.137 0.167 0.159 18.859

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

83 85 60 42 56 76 65 63 16 49

N.S.

1 1.02 0.72 0.51 0.67 0.92 0.78 0.76 0.19 0.59

time (sec)

N/A 0.316 0.023 0.056 0.111 0.063 0.095 0.149 0.164 0.111

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F A A A F B

verified

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

size

99 111 73 48 0 74 65 77 56 136

N.S.

1 1.12 0.74 0.48 0.00 0.75 0.66 0.78 0.57 1.37

time (sec)

N/A 0.263 0.015 0.073 0.000 0.074 0.148 0.163 0.168 18.856

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F A A A F B

verified

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

size

342 480 58 46 0 350 29 240 38 216

N.S.

1 1.40 0.17 0.13 0.00 1.02 0.08 0.70 0.11 0.63

time (sec)

N/A 0.762 0.015 0.043 0.000 0.074 1.152 0.198 0.160 18.969

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F A A A F B

verified

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

size

320 463 41 40 0 385 26 239 18 149

N.S.

1 1.45 0.13 0.12 0.00 1.20 0.08 0.75 0.06 0.47

time (sec)

N/A 0.668 0.012 0.042 0.000 0.074 1.036 0.198 0.158 0.251

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F A A A F B

verified

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

size

335 479 39 40 0 301 24 239 18 454

N.S.

1 1.43 0.12 0.12 0.00 0.90 0.07 0.71 0.05 1.36

time (sec)

N/A 0.677 0.011 0.043 0.000 0.075 0.988 0.190 0.176 0.238

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F A A A F B

verified

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

size

320 451 40 40 0 385 26 239 18 275

N.S.

1 1.41 0.12 0.12 0.00 1.20 0.08 0.75 0.06 0.86

time (sec)

N/A 0.652 0.010 0.043 0.000 0.077 1.033 0.201 0.160 18.829

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F A A A F B

verified

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

size

304 466 42 37 0 349 26 239 14 403

N.S.

1 1.53 0.14 0.12 0.00 1.15 0.09 0.79 0.05 1.33

time (sec)

N/A 0.679 0.010 0.043 0.000 0.073 1.101 0.146 0.162 0.083

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F A A A F B

verified

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

size

340 468 61 42 0 395 32 244 48 292

N.S.

1 1.38 0.18 0.12 0.00 1.16 0.09 0.72 0.14 0.86

time (sec)

N/A 0.687 0.014 0.061 0.000 0.072 1.064 0.194 0.159 20.142

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C C F A A A F B

verified

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

size

348 486 65 40 0 379 34 244 49 492

N.S.

1 1.40 0.19 0.11 0.00 1.09 0.10 0.70 0.14 1.41

time (sec)

N/A 0.717 0.015 0.059 0.000 0.073 1.063 0.176 0.157 20.264

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

62 62 56 38 50 62 58 53 123 64

N.S.

1 1.00 0.90 0.61 0.81 1.00 0.94 0.85 1.98 1.03

time (sec)

N/A 0.236 0.019 0.045 0.113 0.061 0.077 0.143 0.171 0.132

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B B A F B

verified

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

size

88 102 103 67 92 114 170 97 77 90

N.S.

1 1.16 1.17 0.76 1.05 1.30 1.93 1.10 0.88 1.02

time (sec)

N/A 0.238 0.040 0.044 0.105 0.068 0.235 0.153 0.169 0.108

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

55 59 53 33 45 57 53 48 118 59

N.S.

1 1.07 0.96 0.60 0.82 1.04 0.96 0.87 2.15 1.07

time (sec)

N/A 0.235 0.014 0.032 0.107 0.060 0.075 0.156 0.163 0.112

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B B B B F B

verified

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

size

76 99 91 62 87 109 165 92 72 77

N.S.

1 1.30 1.20 0.82 1.14 1.43 2.17 1.21 0.95 1.01

time (sec)

N/A 0.216 0.026 0.041 0.105 0.070 0.228 0.148 0.177 0.112

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

47 46 38 19 31 43 42 33 118 30

N.S.

1 0.98 0.81 0.40 0.66 0.91 0.89 0.70 2.51 0.64

time (sec)

N/A 0.203 0.007 0.032 0.103 0.061 0.060 0.142 0.164 19.085

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B B B B F B

verified

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

size

75 80 91 62 87 107 165 92 16 83

N.S.

1 1.07 1.21 0.83 1.16 1.43 2.20 1.23 0.21 1.11

time (sec)

N/A 0.198 0.022 0.041 0.102 0.066 0.211 0.130 0.158 20.301

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

57 71 55 64 51 59 58 54 14 42

N.S.

1 1.25 0.96 1.12 0.89 1.04 1.02 0.95 0.25 0.74

time (sec)

N/A 0.234 0.019 0.046 0.105 0.064 0.089 0.122 0.167 20.466

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B B A F B

verified

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

size

88 104 103 67 92 125 172 97 16 88

N.S.

1 1.18 1.17 0.76 1.05 1.42 1.95 1.10 0.18 1.00

time (sec)

N/A 0.234 0.040 0.049 0.103 0.066 0.240 0.129 0.172 19.405

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A F B

verified

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

size

73 78 61 71 56 76 66 66 16 49

N.S.

1 1.07 0.84 0.97 0.77 1.04 0.90 0.90 0.22 0.67

time (sec)

N/A 0.248 0.027 0.047 0.107 0.065 0.095 0.136 0.164 19.324

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B B B F B

verified

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

size

99 111 111 72 99 130 199 104 16 95

N.S.

1 1.12 1.12 0.73 1.00 1.31 2.01 1.05 0.16 0.96

time (sec)

N/A 0.264 0.049 0.055 0.107 0.082 0.265 0.134 0.160 0.127

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

178 178 160 69 0 200 58 148 170 246

N.S.

1 1.00 0.90 0.39 0.00 1.12 0.33 0.83 0.96 1.38

time (sec)

N/A 0.289 0.176 0.080 0.000 0.081 0.823 0.180 0.163 0.220

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

167 185 160 68 0 193 53 147 167 147

N.S.

1 1.11 0.96 0.41 0.00 1.16 0.32 0.88 1.00 0.88

time (sec)

N/A 0.295 0.110 0.059 0.000 0.074 0.822 0.173 0.173 19.529

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

173 177 132 60 0 175 49 147 165 269

N.S.

1 1.02 0.76 0.35 0.00 1.01 0.28 0.85 0.95 1.55

time (sec)

N/A 0.265 0.130 0.063 0.000 0.076 0.844 0.190 0.162 19.505

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

145 173 131 64 0 179 53 147 18 269

N.S.

1 1.19 0.90 0.44 0.00 1.23 0.37 1.01 0.12 1.86

time (sec)

N/A 0.267 0.034 0.058 0.000 0.078 0.850 0.186 0.159 0.082

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

169 164 160 68 0 199 53 147 14 245

N.S.

1 0.97 0.95 0.40 0.00 1.18 0.31 0.87 0.08 1.45

time (sec)

N/A 0.253 0.095 0.051 0.000 0.080 0.819 0.153 0.168 0.086

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

180 190 174 73 0 203 63 152 16 250

N.S.

1 1.06 0.97 0.41 0.00 1.13 0.35 0.84 0.09 1.39

time (sec)

N/A 0.308 0.191 0.064 0.000 0.080 0.846 0.190 0.159 19.272

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

182 184 166 73 0 223 63 152 16 268

N.S.

1 1.01 0.91 0.40 0.00 1.23 0.35 0.84 0.09 1.47

time (sec)

N/A 0.288 0.170 0.069 0.000 0.088 0.942 0.175 0.169 0.233

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

173 197 189 79 0 230 73 159 16 257

N.S.

1 1.14 1.09 0.46 0.00 1.33 0.42 0.92 0.09 1.49

time (sec)

N/A 0.368 0.185 0.077 0.000 0.090 0.842 0.189 0.168 19.364

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C F A A A F B

verified

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

size

189 189 189 79 0 222 70 159 16 291

N.S.

1 1.00 1.00 0.42 0.00 1.17 0.37 0.84 0.08 1.54

time (sec)

N/A 0.328 0.209 0.081 0.000 0.075 1.070 0.199 0.167 0.241

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

21 19 21 18 17 17 15 17 59 16

N.S.

1 0.90 1.00 0.86 0.81 0.81 0.71 0.81 2.81 0.76

time (sec)

N/A 0.189 0.004 0.033 0.030 0.060 0.067 0.136 0.171 19.279

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

26 22 26 23 22 22 19 22 64 22

N.S.

1 0.85 1.00 0.88 0.85 0.85 0.73 0.85 2.46 0.85

time (sec)

N/A 0.191 0.004 0.034 0.029 0.062 0.082 0.115 0.160 0.046

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD TBD

size

163 163 82 0 0 0 0 0 20 0

N.S.

1 1.00 0.50 0.00 0.00 0.00 0.00 0.00 0.12 0.00

time (sec)

N/A 0.324 0.271 0.000 0.000 0.000 0.000 0.000 0.227 0.000

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD TBD

size

127 133 488 0 0 0 0 0 16 0

N.S.

1 1.05 3.84 0.00 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.251 1.085 0.000 0.000 0.000 0.000 0.000 0.170 0.000

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD TBD

size

127 133 79 0 0 0 0 0 18 0

N.S.

1 1.05 0.62 0.00 0.00 0.00 0.00 0.00 0.14 0.00

time (sec)

N/A 0.239 0.116 0.000 0.000 0.000 0.000 0.000 0.162 0.000

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD TBD

size

117 117 79 0 0 0 0 0 18 0

N.S.

1 1.00 0.68 0.00 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 0.261 0.120 0.000 0.000 0.000 0.000 0.000 0.167 0.000

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD TBD

size

117 117 575 0 0 0 0 0 18 0

N.S.

1 1.00 4.91 0.00 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 0.235 0.966 0.000 0.000 0.000 0.000 0.000 0.157 0.000

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