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Integrals 501 to 537

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 501

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

57 59 69 57 65 65 73 266 84 60

N.S.

1 1.04 1.21 1.00 1.14 1.14 1.28 4.67 1.47 1.05

time (sec)

N/A 0.280 0.018 0.141 0.030 0.088 0.276 0.125 0.177 3.541

Problem 502

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

429 439 662 364 406 0 0 0 94 0

N.S.

1 1.02 1.54 0.85 0.95 0.00 0.00 0.00 0.22 0.00

time (sec)

N/A 0.820 1.222 3.101 0.198 0.000 0.000 0.000 0.164 0.000

Problem 503

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

590 618 746 1951 550 0 0 0 1167 0

N.S.

1 1.05 1.26 3.31 0.93 0.00 0.00 0.00 1.98 0.00

time (sec)

N/A 1.313 4.812 8.625 0.178 0.000 0.000 0.000 0.180 0.000

Problem 504

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

657 682 1541 4047 1087 0 0 0 0 0

N.S.

1 1.04 2.35 6.16 1.65 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.323 9.091 2.289 0.221 0.000 0.000 0.000 0.224 0.000

Problem 505

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

171 181 576 160 180 0 0 0 77 0

N.S.

1 1.06 3.37 0.94 1.05 0.00 0.00 0.00 0.45 0.00

time (sec)

N/A 0.537 0.628 3.117 0.028 0.000 0.000 0.000 0.174 0.000

Problem 506

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

17 17 17 14 23 22 14 48 15 15

N.S.

1 1.00 1.00 0.82 1.35 1.29 0.82 2.82 0.88 0.88

time (sec)

N/A 0.219 0.114 0.432 0.032 0.079 0.239 0.118 0.168 3.659

Problem 507

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 14 16 16 15 16 15 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 0.94 1.00

time (sec)

N/A 0.201 4.546 1.218 0.427 0.090 0.565 0.133 0.195 3.436

Problem 508

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 14 16 16 15 16 17 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.06 1.00

time (sec)

N/A 0.208 2.676 0.609 0.429 0.104 0.485 0.158 0.177 3.508

Problem 509

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

62 62 119 0 153 356 0 71 33 0

N.S.

1 1.00 1.92 0.00 2.47 5.74 0.00 1.15 0.53 0.00

time (sec)

N/A 0.299 0.074 0.000 0.064 0.111 0.000 0.145 0.188 0.000

Problem 510

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

128 130 226 0 223 730 0 135 52 0

N.S.

1 1.02 1.77 0.00 1.74 5.70 0.00 1.05 0.41 0.00

time (sec)

N/A 0.352 0.187 0.000 0.124 0.120 0.000 0.151 0.210 0.000

Problem 511

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

200 194 329 0 401 1280 0 218 71 0

N.S.

1 0.97 1.64 0.00 2.00 6.40 0.00 1.09 0.36 0.00

time (sec)

N/A 1.120 0.359 0.000 0.129 0.168 0.000 0.154 0.234 0.000

Problem 512

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

283 281 431 0 639 2006 0 349 90 0

N.S.

1 0.99 1.52 0.00 2.26 7.09 0.00 1.23 0.32 0.00

time (sec)

N/A 1.344 0.558 0.000 0.141 0.254 0.000 0.158 0.239 0.000

Problem 513

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

186 139 97 229 0 0 0 0 16 0

N.S.

1 0.75 0.52 1.23 0.00 0.00 0.00 0.00 0.09 0.00

time (sec)

N/A 0.414 0.271 1.653 0.000 0.000 0.000 0.000 0.179 0.000

Problem 514

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

144 99 90 210 0 0 0 0 20 0

N.S.

1 0.69 0.62 1.46 0.00 0.00 0.00 0.00 0.14 0.00

time (sec)

N/A 0.304 0.134 0.594 0.000 0.000 0.000 0.000 0.171 0.000

Problem 515

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

37 37 30 47 63 42 0 54 39 0

N.S.

1 1.00 0.81 1.27 1.70 1.14 0.00 1.46 1.05 0.00

time (sec)

N/A 0.222 0.045 0.786 0.110 0.085 0.000 0.139 0.172 0.000

Problem 516

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

83 86 45 85 67 62 0 86 49 0

N.S.

1 1.04 0.54 1.02 0.81 0.75 0.00 1.04 0.59 0.00

time (sec)

N/A 0.318 0.053 0.978 0.036 0.095 0.000 0.142 0.169 0.000

Problem 517

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

124 135 55 95 99 82 0 118 65 0

N.S.

1 1.09 0.44 0.77 0.80 0.66 0.00 0.95 0.52 0.00

time (sec)

N/A 0.456 0.059 0.866 0.036 0.092 0.000 0.147 0.176 0.000

Problem 518

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

258 258 0 434 0 0 0 0 78 0

N.S.

1 1.00 0.00 1.68 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 0.941 0.000 1.566 0.000 0.000 0.000 0.000 0.179 0.000

Problem 519

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

107 137 95 135 245 118 0 0 238 223

N.S.

1 1.28 0.89 1.26 2.29 1.10 0.00 0.00 2.22 2.08

time (sec)

N/A 0.944 0.159 0.892 0.037 0.086 0.000 0.000 0.175 4.391

Problem 520

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

107 137 96 135 245 118 0 0 238 223

N.S.

1 1.28 0.90 1.26 2.29 1.10 0.00 0.00 2.22 2.08

time (sec)

N/A 0.945 0.081 0.668 0.037 0.087 0.000 0.000 0.166 3.951

Problem 521

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

263 286 236 296 317 251 338 313 308 599

N.S.

1 1.09 0.90 1.13 1.21 0.95 1.29 1.19 1.17 2.28

time (sec)

N/A 1.139 0.086 6.273 0.044 0.102 1.863 0.263 0.169 6.733

Problem 522

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

225 222 192 249 271 196 279 0 244 851

N.S.

1 0.99 0.85 1.11 1.20 0.87 1.24 0.00 1.08 3.78

time (sec)

N/A 0.567 0.081 3.657 0.034 0.096 1.303 0.000 0.165 4.248

Problem 523

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

206 223 183 229 252 200 258 244 243 515

N.S.

1 1.08 0.89 1.11 1.22 0.97 1.25 1.18 1.18 2.50

time (sec)

N/A 0.924 0.071 3.060 0.038 0.112 0.903 0.250 0.172 5.401

Problem 524

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

140 140 129 174 171 139 202 209 173 557

N.S.

1 1.00 0.92 1.24 1.22 0.99 1.44 1.49 1.24 3.98

time (sec)

N/A 0.418 0.060 2.141 0.031 0.083 0.676 0.218 0.178 4.092

Problem 525

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

104 116 144 141 178 132 148 165 161 385

N.S.

1 1.12 1.38 1.36 1.71 1.27 1.42 1.59 1.55 3.70

time (sec)

N/A 0.917 0.023 1.859 0.039 0.091 0.415 0.179 0.176 4.494

Problem 526

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

216 190 0 1227 152 0 0 0 174 0

N.S.

1 0.88 0.00 5.68 0.70 0.00 0.00 0.00 0.81 0.00

time (sec)

N/A 1.234 0.000 11.179 0.129 0.000 0.000 0.000 0.180 0.000

Problem 527

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

105 85 332 0 0 0 0 0 155 0

N.S.

1 0.81 3.16 0.00 0.00 0.00 0.00 0.00 1.48 0.00

time (sec)

N/A 0.785 0.124 0.000 0.000 0.000 0.000 0.000 0.167 0.000

Problem 528

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

157 146 152 0 0 0 0 0 112 0

N.S.

1 0.93 0.97 0.00 0.00 0.00 0.00 0.00 0.71 0.00

time (sec)

N/A 0.401 0.103 0.000 0.000 0.000 0.000 0.000 0.171 0.000

Problem 529

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

197 178 460 0 0 0 0 0 164 0

N.S.

1 0.90 2.34 0.00 0.00 0.00 0.00 0.00 0.83 0.00

time (sec)

N/A 1.596 0.210 0.000 0.000 0.000 0.000 0.000 0.179 0.000

Problem 530

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

244 234 299 0 0 0 0 0 134 0

N.S.

1 0.96 1.23 0.00 0.00 0.00 0.00 0.00 0.55 0.00

time (sec)

N/A 0.554 0.086 0.000 0.000 0.000 0.000 0.000 0.188 0.000

Problem 531

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

256 293 0 0 0 0 0 0 324 0

N.S.

1 1.14 0.00 0.00 0.00 0.00 0.00 0.00 1.27 0.00

time (sec)

N/A 2.600 0.000 0.000 0.000 0.000 0.000 0.000 0.181 0.000

Problem 532

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

512 504 1145 970 0 0 0 0 254 0

N.S.

1 0.98 2.24 1.89 0.00 0.00 0.00 0.00 0.50 0.00

time (sec)

N/A 1.083 4.763 14.128 0.000 0.000 0.000 0.000 0.183 0.000

Problem 533

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 No No TBD TBD TBD TBD TBD TBD

size

599 609 1251 3550 0 0 0 0 367 0

N.S.

1 1.02 2.09 5.93 0.00 0.00 0.00 0.00 0.61 0.00

time (sec)

N/A 1.859 2.295 18.317 0.000 0.000 0.000 0.000 0.180 0.000

Problem 534

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

24 24 26 24 77 37 22 26 148 26

N.S.

1 1.00 1.08 1.00 3.21 1.54 0.92 1.08 6.17 1.08

time (sec)

N/A 0.831 0.141 0.782 0.185 0.091 116.602 0.128 0.209 4.942

Problem 535

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

613 602 1226 0 0 0 0 0 115 0

N.S.

1 0.98 2.00 0.00 0.00 0.00 0.00 0.00 0.19 0.00

time (sec)

N/A 1.528 2.419 0.000 0.000 0.000 0.000 0.000 0.190 0.000

Problem 536

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

511 487 1211 961 0 0 0 0 1230 0

N.S.

1 0.95 2.37 1.88 0.00 0.00 0.00 0.00 2.41 0.00

time (sec)

N/A 1.081 5.062 12.714 0.000 0.000 0.000 0.000 0.226 0.000

Problem 537

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

78 102 70 73 226 74 0 93 137 67

N.S.

1 1.31 0.90 0.94 2.90 0.95 0.00 1.19 1.76 0.86

time (sec)

N/A 0.580 0.108 0.789 0.085 0.085 0.000 0.129 0.176 3.964

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