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Integrals 101 to 145

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 A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 81 73 66 66 90 80 71 69

N.S.

1 1.00 0.90 0.81 0.81 1.11 0.99 0.88 0.85

time (sec)

N/A 0.087 0.022 0.063 0.266 0.244 0.078 0.433 0.033

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

74 74 66 62 59 85 73 66 65

N.S.

1 1.00 0.89 0.84 0.80 1.15 0.99 0.89 0.88

time (sec)

N/A 0.081 0.021 0.079 0.267 0.251 0.076 0.523 0.027

Problem 103

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

65 65 61 56 54 80 68 54 60

N.S.

1 1.00 0.94 0.86 0.83 1.23 1.05 0.83 0.92

time (sec)

N/A 0.069 0.020 0.071 0.279 0.251 0.078 0.470 8.608

Problem 104

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

58 58 58 51 49 70 60 49 69

N.S.

1 1.00 1.00 0.88 0.84 1.21 1.03 0.84 1.19

time (sec)

N/A 0.043 0.016 0.054 0.272 0.249 0.076 0.460 0.030

Problem 105

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

66 66 72 58 55 84 65 62 59

N.S.

1 1.00 1.09 0.88 0.83 1.27 0.98 0.94 0.89

time (sec)

N/A 0.069 0.067 0.068 0.267 0.255 0.083 0.451 8.656

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 101 63 66 105 76 66 68

N.S.

1 1.00 1.42 0.89 0.93 1.48 1.07 0.93 0.96

time (sec)

N/A 0.087 0.045 0.073 0.270 0.246 0.097 0.438 0.037

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

80 80 82 68 71 110 80 79 72

N.S.

1 1.00 1.02 0.85 0.89 1.38 1.00 0.99 0.90

time (sec)

N/A 0.088 0.068 0.072 0.285 0.252 0.095 0.438 0.038

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 114 73 76 115 85 84 78

N.S.

1 1.00 1.31 0.84 0.87 1.32 0.98 0.97 0.90

time (sec)

N/A 0.097 0.055 0.072 0.275 0.241 0.112 0.441 8.641

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 248 145 79 0 215 71 585 171

N.S.

1 1.00 0.58 0.32 0.00 0.87 0.29 2.36 0.69

time (sec)

N/A 0.230 0.126 0.174 0.000 0.249 0.344 0.594 0.075

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

237 237 132 72 0 210 1205 576 164

N.S.

1 1.00 0.56 0.30 0.00 0.89 5.08 2.43 0.69

time (sec)

N/A 0.196 0.105 0.087 0.000 0.247 0.739 0.628 8.618

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

232 232 129 69 0 205 60 573 162

N.S.

1 1.00 0.56 0.30 0.00 0.88 0.26 2.47 0.70

time (sec)

N/A 0.183 0.105 0.081 0.000 0.251 0.329 0.593 0.072

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

225 225 121 64 0 222 51 566 156

N.S.

1 1.00 0.54 0.28 0.00 0.99 0.23 2.52 0.69

time (sec)

N/A 0.196 0.109 0.076 0.000 0.270 0.330 0.611 0.089

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

224 224 115 61 0 217 1185 565 153

N.S.

1 1.00 0.51 0.27 0.00 0.97 5.29 2.52 0.68

time (sec)

N/A 0.157 0.189 0.075 0.000 0.256 0.694 0.582 8.652

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

229 229 126 63 0 230 1192 572 159

N.S.

1 1.00 0.55 0.28 0.00 1.00 5.21 2.50 0.69

time (sec)

N/A 0.200 0.121 0.099 0.000 0.253 0.765 0.577 0.101

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

238 238 131 68 0 245 60 579 165

N.S.

1 1.00 0.55 0.29 0.00 1.03 0.25 2.43 0.69

time (sec)

N/A 0.184 0.210 0.099 0.000 0.246 0.353 0.595 0.099

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 245 140 73 0 252 1202 584 171

N.S.

1 1.00 0.57 0.30 0.00 1.03 4.91 2.38 0.70

time (sec)

N/A 0.206 0.207 0.106 0.000 0.257 0.772 0.625 8.765

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

243 243 156 82 0 282 1204 588 184

N.S.

1 1.00 0.64 0.34 0.00 1.16 4.95 2.42 0.76

time (sec)

N/A 0.212 0.154 0.095 0.000 0.257 0.754 0.729 0.083

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

242 242 155 79 0 279 82 585 182

N.S.

1 1.00 0.64 0.33 0.00 1.15 0.34 2.42 0.75

time (sec)

N/A 0.206 0.136 0.076 0.000 0.252 0.369 0.751 8.896

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

235 235 138 74 0 272 71 580 176

N.S.

1 1.00 0.59 0.31 0.00 1.16 0.30 2.47 0.75

time (sec)

N/A 0.203 0.222 0.077 0.000 0.248 0.344 0.722 8.853

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

238 238 129 71 0 267 1198 577 173

N.S.

1 1.00 0.54 0.30 0.00 1.12 5.03 2.42 0.73

time (sec)

N/A 0.185 0.204 0.075 0.000 0.256 0.697 0.874 0.127

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

246 246 133 71 0 277 1200 577 174

N.S.

1 1.00 0.54 0.29 0.00 1.13 4.88 2.35 0.71

time (sec)

N/A 0.196 0.201 0.079 0.000 0.250 0.721 0.754 0.111

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 248 129 71 0 277 1195 577 173

N.S.

1 1.00 0.52 0.29 0.00 1.12 4.82 2.33 0.70

time (sec)

N/A 0.172 0.192 0.070 0.000 0.251 0.701 0.720 8.700

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

253 253 140 73 0 290 75 582 179

N.S.

1 1.00 0.55 0.29 0.00 1.15 0.30 2.30 0.71

time (sec)

N/A 0.223 0.263 0.096 0.000 0.270 0.364 0.738 8.872

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

262 262 139 78 0 305 80 589 185

N.S.

1 1.00 0.53 0.30 0.00 1.16 0.31 2.25 0.71

time (sec)

N/A 0.238 0.233 0.098 0.000 0.261 0.367 0.768 8.752

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 142 151 0 486 0 144 1834

N.S.

1 1.00 0.95 1.01 0.00 3.26 0.00 0.97 12.31

time (sec)

N/A 0.187 0.075 0.256 0.000 0.335 0.000 0.638 9.001

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

594 594 721 348 0 0 0 10752 47339

N.S.

1 1.00 1.21 0.59 0.00 0.00 0.00 18.10 79.70

time (sec)

N/A 11.107 1.562 0.183 0.000 0.000 0.000 2.341 10.708

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

471 471 575 274 0 23774 0 9152 36589

N.S.

1 1.00 1.22 0.58 0.00 50.48 0.00 19.43 77.68

time (sec)

N/A 4.197 1.164 0.160 0.000 181.702 0.000 2.044 10.390

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

449 449 512 269 0 19375 0 8905 32587

N.S.

1 1.00 1.14 0.60 0.00 43.15 0.00 19.83 72.58

time (sec)

N/A 1.891 1.012 0.148 0.000 151.256 0.000 1.895 11.165

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

460 460 529 550 0 23991 0 9167 40860

N.S.

1 1.00 1.15 1.20 0.00 52.15 0.00 19.93 88.83

time (sec)

N/A 1.805 1.611 0.255 0.000 144.800 0.000 1.747 12.149

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

542 542 612 629 0 33432 0 10411 51386

N.S.

1 1.00 1.13 1.16 0.00 61.68 0.00 19.21 94.81

time (sec)

N/A 4.717 1.362 0.272 0.000 297.365 0.000 1.799 12.571

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 21 31 31 54 58 31

N.S.

1 1.00 1.00 1.05 1.55 1.55 2.70 2.90 1.55

time (sec)

N/A 0.023 0.449 0.273 0.239 0.248 158.450 0.346 8.107

Problem 132

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

210 278 149 145 295 138 367 228 287

N.S.

1 1.32 0.71 0.69 1.40 0.66 1.75 1.09 1.37

time (sec)

N/A 0.211 0.362 0.461 0.284 0.263 19.879 0.372 8.419

Problem 133

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

159 213 116 109 217 104 367 164 215

N.S.

1 1.34 0.73 0.69 1.36 0.65 2.31 1.03 1.35

time (sec)

N/A 0.138 0.271 0.423 0.281 0.261 11.903 0.324 8.289

Problem 134

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

109 149 80 73 139 71 350 102 143

N.S.

1 1.37 0.73 0.67 1.28 0.65 3.21 0.94 1.31

time (sec)

N/A 0.086 0.196 0.435 0.284 0.274 7.520 0.337 8.359

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 151 106 143 105 80 304 189 161

N.S.

1 1.62 1.14 1.54 1.13 0.86 3.27 2.03 1.73

time (sec)

N/A 0.109 0.260 0.442 0.313 0.268 18.143 0.440 9.754

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 155 85 137 123 98 0 374 422

N.S.

1 1.57 0.86 1.38 1.24 0.99 0.00 3.78 4.26

time (sec)

N/A 0.177 0.278 0.434 0.278 0.275 0.000 0.462 10.856

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 182 102 143 193 102 0 767 932

N.S.

1 1.44 0.81 1.13 1.53 0.81 0.00 6.09 7.40

time (sec)

N/A 0.185 0.304 0.444 0.290 0.268 0.000 0.607 15.498

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

212 248 141 179 271 137 0 1434 1621

N.S.

1 1.17 0.67 0.84 1.28 0.65 0.00 6.76 7.65

time (sec)

N/A 0.249 0.390 0.441 0.279 0.273 0.000 0.770 24.813

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 245 134 161 226 134 0 177 1132

N.S.

1 1.13 0.62 0.75 1.05 0.62 0.00 0.82 5.24

time (sec)

N/A 0.141 0.317 0.436 0.281 0.284 0.000 0.340 27.906

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 179 98 128 146 100 0 115 651

N.S.

1 1.40 0.77 1.00 1.14 0.78 0.00 0.90 5.09

time (sec)

N/A 0.065 0.230 0.444 0.287 0.266 0.000 0.334 17.263

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 155 86 116 94 90 0 239 306

N.S.

1 1.52 0.84 1.14 0.92 0.88 0.00 2.34 3.00

time (sec)

N/A 0.082 0.203 0.441 0.293 0.271 0.000 0.372 11.990

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 157 81 107 94 90 257 530 138

N.S.

1 1.00 0.52 0.68 0.60 0.57 1.64 3.38 0.88

time (sec)

N/A 0.092 0.196 0.440 0.278 0.282 18.200 0.414 8.747

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 160 87 82 148 76 0 1055 146

N.S.

1 1.00 0.54 0.51 0.92 0.48 0.00 6.59 0.91

time (sec)

N/A 0.104 0.166 0.447 0.279 0.269 0.000 0.528 8.491

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

226 226 124 118 226 110 0 1451 218

N.S.

1 1.00 0.55 0.52 1.00 0.49 0.00 6.42 0.96

time (sec)

N/A 0.123 0.216 0.441 0.289 0.317 0.000 0.692 8.531

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 292 158 154 304 144 0 1847 290

N.S.

1 1.00 0.54 0.53 1.04 0.49 0.00 6.33 0.99

time (sec)

N/A 0.156 0.257 0.441 0.280 0.352 0.000 0.936 8.564

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