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2.2.6 Integrals 501 to 547

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 Mupad

grade

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

verified

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

size

32 32 34 28 30 0 29 30 30

N.S.

1 1.00 1.06 0.88 0.94 0.00 0.91 0.94 0.94

time (sec)

N/A 0.430 1.201 0.162 11.047 0.000 1.381 2.238 1.329

Problem 502

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 28 30 0 29 30 30

N.S.

1 1.00 1.06 0.88 0.94 0.00 0.91 0.94 0.94

time (sec)

N/A 0.448 1.711 0.161 11.013 0.000 17.419 1.412 1.365

Problem 503

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 28 30 0 29 30 30

N.S.

1 1.00 1.06 0.88 0.94 0.00 0.91 0.94 0.94

time (sec)

N/A 0.261 3.996 0.176 11.081 0.000 1.061 0.369 1.314

Problem 504

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 28 30 0 31 30 30

N.S.

1 1.00 1.06 0.88 0.94 0.00 0.97 0.94 0.94

time (sec)

N/A 0.263 0.207 0.168 11.028 0.000 3.851 0.354 1.344

Problem 505

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 32 34 28 30 0 31 30 30

N.S.

1 1.00 1.06 0.88 0.94 0.00 0.97 0.94 0.94

time (sec)

N/A 0.266 0.090 0.188 11.197 0.000 51.955 0.418 1.403

Problem 506

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

99 99 86 0 0 0 0 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.330 0.080 0.000 0.000 0.000 0.000 0.000 0.000

Problem 507

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

28 28 30 28 30 30 24 30 30

N.S.

1 1.00 1.07 1.00 1.07 1.07 0.86 1.07 1.07

time (sec)

N/A 0.216 0.234 0.195 0.930 0.273 13.569 0.352 1.182

Problem 508

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 28 30 28 176 54 0 30 30

N.S.

1 1.00 1.07 1.00 6.29 1.93 0.00 1.07 1.07

time (sec)

N/A 0.216 1.998 0.198 1.204 0.307 0.000 0.440 1.251

Problem 509

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 56 0 30 30

N.S.

1 1.00 1.07 0.93 1.00 1.87 0.00 1.00 1.00

time (sec)

N/A 0.259 15.262 0.204 11.313 0.296 0.000 3.232 1.326

Problem 510

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 30 0 30 30

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.241 0.056 0.177 11.183 0.305 0.000 0.989 1.255

Problem 511

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

30 30 32 28 30 30 27 30 30

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.90 1.00 1.00

time (sec)

N/A 0.247 10.606 0.207 10.975 0.332 5.938 0.348 1.273

Problem 512

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 30 32 28 30 74 0 30 30

N.S.

1 1.00 1.07 0.93 1.00 2.47 0.00 1.00 1.00

time (sec)

N/A 0.258 13.559 0.197 11.257 0.360 0.000 0.424 1.563

Problem 513

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 28 30 28 0 30 0 0 30

N.S.

1 1.00 1.07 1.00 0.00 1.07 0.00 0.00 1.07

time (sec)

N/A 0.208 0.322 0.285 0.000 0.340 0.000 0.000 1.267

Problem 514

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

432 432 326 0 0 0 0 0 0

N.S.

1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.440 0.606 0.000 0.000 0.000 0.000 0.000 0.000

Problem 515

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

281 281 227 0 0 0 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.931 0.178 0.000 0.000 0.000 0.000 0.000 0.000

Problem 516

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

131 135 131 0 0 80 0 0 0

N.S.

1 1.03 1.00 0.00 0.00 0.61 0.00 0.00 0.00

time (sec)

N/A 0.442 0.097 0.000 0.000 0.082 0.000 0.000 0.000

Problem 517

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 28 30 28 0 30 24 30 30

N.S.

1 1.00 1.07 1.00 0.00 1.07 0.86 1.07 1.07

time (sec)

N/A 0.218 0.233 0.213 0.000 0.351 6.080 0.554 1.302

Problem 518

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

249 249 190 0 0 0 0 0 0

N.S.

1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.706 0.095 0.000 0.000 0.000 0.000 0.000 0.000

Problem 519

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

335 318 284 0 0 0 0 0 0

N.S.

1 0.95 0.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.339 0.144 0.000 0.000 0.000 0.000 0.000 0.000

Problem 520

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

515 354 0 0 0 0 0 0 0

N.S.

1 0.69 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.537 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 521

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

287 300 257 0 0 0 0 0 0

N.S.

1 1.05 0.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.481 0.129 0.000 0.000 0.000 0.000 0.000 0.000

Problem 522

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

519 341 637 0 0 0 0 0 0

N.S.

1 0.66 1.23 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.876 10.981 0.000 0.000 0.000 0.000 0.000 0.000

Problem 523

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

427 427 386 0 0 0 0 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.002 0.581 0.000 0.000 0.000 0.000 0.000 0.000

Problem 524

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

258 258 231 0 0 0 0 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.734 0.189 0.000 0.000 0.000 0.000 0.000 0.000

Problem 525

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

129 129 120 0 0 0 0 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.533 0.073 0.000 0.000 0.000 0.000 0.000 0.000

Problem 526

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

68 68 67 0 0 0 0 0 0

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.396 0.003 0.000 0.000 0.000 0.000 0.000 0.000

Problem 527

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

165 165 117 0 0 0 0 0 0

N.S.

1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.666 0.045 0.000 0.000 0.000 0.000 0.000 0.000

Problem 528

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

268 268 225 0 0 0 0 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.814 0.134 0.000 0.000 0.000 0.000 0.000 0.000

Problem 529

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

425 425 363 0 0 0 0 0 0

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.083 0.261 0.000 0.000 0.000 0.000 0.000 0.000

Problem 530

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

519 519 927 0 0 0 0 0 0

N.S.

1 1.00 1.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.483 0.405 0.000 0.000 0.000 0.000 0.000 0.000

Problem 531

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

240 240 852 0 0 0 0 0 0

N.S.

1 1.00 3.55 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.860 0.233 0.000 0.000 0.000 0.000 0.000 0.000

Problem 532

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

123 117 324 0 0 0 0 0 0

N.S.

1 0.95 2.63 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.686 0.046 0.000 0.000 0.000 0.000 0.000 0.000

Problem 533

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

288 288 652 0 0 0 0 0 0

N.S.

1 1.00 2.26 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.153 0.176 0.000 0.000 0.000 0.000 0.000 0.000

Problem 534

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

463 463 654 0 0 0 0 0 0

N.S.

1 1.00 1.41 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.448 0.408 0.000 0.000 0.000 0.000 0.000 0.000

Problem 535

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

742 742 4056 0 0 0 0 0 0

N.S.

1 1.00 5.47 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.984 0.889 0.000 0.000 0.000 0.000 0.000 0.000

Problem 536

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

349 349 1769 0 0 0 0 0 0

N.S.

1 1.00 5.07 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.145 0.475 0.000 0.000 0.000 0.000 0.000 0.000

Problem 537

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

177 166 646 0 0 0 0 0 0

N.S.

1 0.94 3.65 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.885 0.098 0.000 0.000 0.000 0.000 0.000 0.000

Problem 538

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

410 410 1350 0 0 0 0 0 0

N.S.

1 1.00 3.29 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.495 0.311 0.000 0.000 0.000 0.000 0.000 0.000

Problem 539

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

659 659 1057 0 0 0 0 0 0

N.S.

1 1.00 1.60 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.035 0.733 0.000 0.000 0.000 0.000 0.000 0.000

Problem 540

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

33 33 35 33 35 41 27 35 35

N.S.

1 1.00 1.06 1.00 1.06 1.24 0.82 1.06 1.06

time (sec)

N/A 0.394 0.135 0.180 1.550 0.309 3.554 0.465 1.344

Problem 541

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

28 28 30 28 30 35 24 30 30

N.S.

1 1.00 1.07 1.00 1.07 1.25 0.86 1.07 1.07

time (sec)

N/A 0.223 0.011 0.026 0.905 0.295 1.485 0.295 1.224

Problem 542

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

35 35 37 35 37 65 29 37 37

N.S.

1 1.00 1.06 1.00 1.06 1.86 0.83 1.06 1.06

time (sec)

N/A 0.415 0.614 0.330 0.884 0.343 3.728 0.291 1.241

Problem 543

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

35 35 37 35 37 115 31 37 37

N.S.

1 1.00 1.06 1.00 1.06 3.29 0.89 1.06 1.06

time (sec)

N/A 0.447 1.966 0.309 0.912 0.290 12.189 0.310 1.262

Problem 544

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

33 33 35 33 302 77 29 35 35

N.S.

1 1.00 1.06 1.00 9.15 2.33 0.88 1.06 1.06

time (sec)

N/A 0.420 1.360 0.171 2.060 0.295 16.904 0.306 1.479

Problem 545

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

28 28 30 28 267 71 26 30 30

N.S.

1 1.00 1.07 1.00 9.54 2.54 0.93 1.07 1.07

time (sec)

N/A 0.222 0.094 0.026 1.204 0.296 5.208 0.290 1.275

Problem 546

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

35 35 37 35 701 126 31 37 37

N.S.

1 1.00 1.06 1.00 20.03 3.60 0.89 1.06 1.06

time (sec)

N/A 0.408 13.246 0.319 1.269 0.330 16.727 0.375 1.347

Problem 547

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

35 35 37 35 1039 211 32 37 37

N.S.

1 1.00 1.06 1.00 29.69 6.03 0.91 1.06 1.06

time (sec)

N/A 0.433 19.109 0.323 1.272 0.330 112.691 0.446 1.419

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