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Integrals 201 to 242

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 201

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

374 949 418 1341 1972 0 0 0 469 0

N.S.

1 2.54 1.12 3.59 5.27 0.00 0.00 0.00 1.25 0.00

time (sec)

N/A 5.926 0.748 19.236 0.665 0.000 0.000 0.000 0.187 0.000

Problem 202

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

304 611 351 1264 1579 0 0 0 374 0

N.S.

1 2.01 1.15 4.16 5.19 0.00 0.00 0.00 1.23 0.00

time (sec)

N/A 4.133 0.535 16.195 0.595 0.000 0.000 0.000 0.175 0.000

Problem 203

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

234 356 285 1145 1184 0 0 0 276 0

N.S.

1 1.52 1.22 4.89 5.06 0.00 0.00 0.00 1.18 0.00

time (sec)

N/A 2.182 0.367 15.424 0.515 0.000 0.000 0.000 0.179 0.000

Problem 204

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

142 170 201 5673 0 0 0 0 183 0

N.S.

1 1.20 1.42 39.95 0.00 0.00 0.00 0.00 1.29 0.00

time (sec)

N/A 1.052 0.188 14.079 0.000 0.000 0.000 0.000 0.173 0.000

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

224 262 423 1363 0 0 0 0 60 0

N.S.

1 1.17 1.89 6.08 0.00 0.00 0.00 0.00 0.27 0.00

time (sec)

N/A 1.203 0.325 14.581 0.000 0.000 0.000 0.000 0.190 0.000

Problem 206

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

142 151 230 4700 528 0 0 0 237 0

N.S.

1 1.06 1.62 33.10 3.72 0.00 0.00 0.00 1.67 0.00

time (sec)

N/A 1.059 0.218 15.121 1.018 0.000 0.000 0.000 0.174 0.000

Problem 207

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

234 306 333 1219 703 0 0 0 318 0

N.S.

1 1.31 1.42 5.21 3.00 0.00 0.00 0.00 1.36 0.00

time (sec)

N/A 2.009 0.488 16.687 1.168 0.000 0.000 0.000 0.182 0.000

Problem 208

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

38 35 31 35 24 36 121 170 31 24

N.S.

1 0.92 0.82 0.92 0.63 0.95 3.18 4.47 0.82 0.63

time (sec)

N/A 0.216 0.013 0.112 0.030 0.087 0.793 0.118 0.174 3.237

Problem 209

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

31 28 25 30 19 31 0 121 24 0

N.S.

1 0.90 0.81 0.97 0.61 1.00 0.00 3.90 0.77 0.00

time (sec)

N/A 0.207 0.010 0.076 0.043 0.087 0.000 0.123 0.200 0.000

Problem 210

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

20 20 20 17 16 25 87 72 20 14

N.S.

1 1.00 1.00 0.85 0.80 1.25 4.35 3.60 1.00 0.70

time (sec)

N/A 0.180 0.006 0.097 0.025 0.090 0.205 0.111 0.175 3.268

Problem 211

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 24 29 18 37 126 72 34 22

N.S.

1 1.00 1.00 1.21 0.75 1.54 5.25 3.00 1.42 0.92

time (sec)

N/A 0.188 0.015 0.138 0.026 0.091 0.375 0.117 0.179 3.250

Problem 212

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

160 212 222 194 172 2039 0 227 120 231

N.S.

1 1.32 1.39 1.21 1.08 12.74 0.00 1.42 0.75 1.44

time (sec)

N/A 0.456 0.053 0.178 0.109 0.880 0.000 0.195 0.178 16.649

Problem 213

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

49 54 75 55 58 64 0 97 43 110

N.S.

1 1.10 1.53 1.12 1.18 1.31 0.00 1.98 0.88 2.24

time (sec)

N/A 0.252 0.028 0.356 0.027 0.090 0.000 0.124 0.183 4.416

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

160 200 222 194 172 1488 0 0 117 247

N.S.

1 1.25 1.39 1.21 1.08 9.30 0.00 0.00 0.73 1.54

time (sec)

N/A 0.513 0.041 0.187 0.114 0.785 0.000 0.000 0.174 15.596

Problem 215

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

140 170 114 179 158 1914 0 186 105 107

N.S.

1 1.21 0.81 1.28 1.13 13.67 0.00 1.33 0.75 0.76

time (sec)

N/A 0.663 0.108 0.197 0.108 0.854 0.000 0.139 0.185 8.189

Problem 216

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

34 42 32 57 62 0 0 0 19 0

N.S.

1 1.24 0.94 1.68 1.82 0.00 0.00 0.00 0.56 0.00

time (sec)

N/A 0.412 0.026 0.444 0.169 0.000 0.000 0.000 0.183 0.000

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

142 180 205 167 163 234 0 172 116 220

N.S.

1 1.27 1.44 1.18 1.15 1.65 0.00 1.21 0.82 1.55

time (sec)

N/A 0.579 0.044 0.162 0.115 0.104 0.000 0.212 0.189 10.402

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

158 207 220 180 168 214 0 200 145 228

N.S.

1 1.31 1.39 1.14 1.06 1.35 0.00 1.27 0.92 1.44

time (sec)

N/A 0.704 0.055 0.184 0.108 0.110 0.000 0.220 0.182 10.473

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 49 140 55 51 59 0 67 39 114

N.S.

1 1.04 2.98 1.17 1.09 1.26 0.00 1.43 0.83 2.43

time (sec)

N/A 0.307 0.035 0.176 0.036 0.091 0.000 0.146 0.185 3.922

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

101 102 122 220 186 179 0 0 143 105

N.S.

1 1.01 1.21 2.18 1.84 1.77 0.00 0.00 1.42 1.04

time (sec)

N/A 0.533 0.072 1.157 0.037 0.114 0.000 0.000 0.180 3.890

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

156 179 207 706 0 0 0 0 41 0

N.S.

1 1.15 1.33 4.53 0.00 0.00 0.00 0.00 0.26 0.00

time (sec)

N/A 0.860 0.327 18.046 0.000 0.000 0.000 0.000 0.191 0.000

Problem 222

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

96 95 210 3062 175 173 0 0 170 281

N.S.

1 0.99 2.19 31.90 1.82 1.80 0.00 0.00 1.77 2.93

time (sec)

N/A 0.622 0.094 2.239 0.042 0.105 0.000 0.000 0.197 4.687

Problem 223

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

66 66 73 0 0 0 0 0 21 0

N.S.

1 1.00 1.11 0.00 0.00 0.00 0.00 0.00 0.32 0.00

time (sec)

N/A 0.235 0.048 0.000 0.000 0.000 0.000 0.000 0.184 0.000

Problem 224

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

67 67 73 0 0 0 0 0 19 0

N.S.

1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 0.224 0.042 0.000 0.000 0.000 0.000 0.000 0.186 0.000

Problem 225

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

58 58 58 0 0 0 0 0 14 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.24 0.00

time (sec)

N/A 0.188 0.088 0.000 0.000 0.000 0.000 0.000 0.180 0.000

Problem 226

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

36 36 39 35 0 141 0 0 19 0

N.S.

1 1.00 1.08 0.97 0.00 3.92 0.00 0.00 0.53 0.00

time (sec)

N/A 0.248 0.075 0.676 0.000 0.091 0.000 0.000 0.183 0.000

Problem 227

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

67 67 66 0 0 0 0 0 23 0

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 0.34 0.00

time (sec)

N/A 0.240 0.056 0.000 0.000 0.000 0.000 0.000 0.178 0.000

Problem 228

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

70 71 73 0 0 0 0 0 27 0

N.S.

1 1.01 1.04 0.00 0.00 0.00 0.00 0.00 0.39 0.00

time (sec)

N/A 0.232 0.039 0.000 0.000 0.000 0.000 0.000 0.176 0.000

Problem 229

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 72 73 0 0 0 0 0 27 0

N.S.

1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 0.38 0.00

time (sec)

N/A 0.232 0.037 0.000 0.000 0.000 0.000 0.000 0.177 0.000

Problem 230

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

14 14 16 14 155 32 14 16 39 16

N.S.

1 1.00 1.14 1.00 11.07 2.29 1.00 1.14 2.79 1.14

time (sec)

N/A 0.194 12.172 0.037 1.292 0.088 30.205 0.408 0.193 3.460

Problem 231

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

12 12 14 12 143 28 12 14 32 14

N.S.

1 1.00 1.17 1.00 11.92 2.33 1.00 1.17 2.67 1.17

time (sec)

N/A 0.175 1.545 0.033 0.399 0.078 18.779 0.243 0.187 3.310

Problem 232

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

148 163 181 750 0 0 0 0 41 0

N.S.

1 1.10 1.22 5.07 0.00 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 0.847 0.318 13.485 0.000 0.000 0.000 0.000 0.179 0.000

Problem 233

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 154 32 15 18 46 18

N.S.

1 1.00 1.12 1.00 9.62 2.00 0.94 1.12 2.88 1.12

time (sec)

N/A 0.193 12.206 0.041 0.506 0.077 19.734 0.405 0.183 3.387

Problem 234

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 153 32 15 18 52 18

N.S.

1 1.00 1.12 1.00 9.56 2.00 0.94 1.12 3.25 1.12

time (sec)

N/A 0.200 12.120 0.034 0.498 0.079 43.166 0.387 0.180 3.379

Problem 235

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

30 28 33 29 147 129 0 0 12 0

N.S.

1 0.93 1.10 0.97 4.90 4.30 0.00 0.00 0.40 0.00

time (sec)

N/A 0.231 0.030 0.612 0.098 0.090 0.000 0.000 0.177 0.000

Problem 236

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 28 22 61 104 0 0 0 12 0

N.S.

1 1.17 0.92 2.54 4.33 0.00 0.00 0.00 0.50 0.00

time (sec)

N/A 0.228 0.011 0.345 0.036 0.000 0.000 0.000 0.179 0.000

Problem 237

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

19 19 17 16 15 22 15 101 15 15

N.S.

1 1.00 0.89 0.84 0.79 1.16 0.79 5.32 0.79 0.79

time (sec)

N/A 0.178 0.002 0.327 0.033 0.081 0.093 0.114 0.184 0.070

Problem 238

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 20 18 468 65 0 20 133 20

N.S.

1 1.00 1.11 1.00 26.00 3.61 0.00 1.11 7.39 1.11

time (sec)

N/A 0.205 6.758 0.049 1.489 0.102 0.000 0.774 0.200 3.616

Problem 239

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 20 18 265 44 0 20 88 20

N.S.

1 1.00 1.11 1.00 14.72 2.44 0.00 1.11 4.89 1.11

time (sec)

N/A 0.204 14.298 0.037 0.876 0.095 0.000 0.454 0.191 3.608

Problem 240

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

84 90 77 0 0 0 0 0 45 0

N.S.

1 1.07 0.92 0.00 0.00 0.00 0.00 0.00 0.54 0.00

time (sec)

N/A 0.308 0.077 0.000 0.000 0.000 0.000 0.000 0.179 0.000

Problem 241

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 20 20 15 20 22 20

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.83 1.11 1.22 1.11

time (sec)

N/A 0.200 0.343 0.036 0.090 0.075 36.479 0.241 0.177 3.362

Problem 242

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 20 0 169 36 0 20 38 20

N.S.

1 1.00 1.11 0.00 9.39 2.00 0.00 1.11 2.11 1.11

time (sec)

N/A 0.204 1.757 180.000 0.238 0.078 0.000 0.389 0.194 3.470

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