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2.2.6 Integrals 501 to 525

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

232 229 114 213 0 20298 0 3690 0

N.S.

1 0.99 0.49 0.92 0.00 87.49 0.00 15.91 0.00

time (sec)

N/A 0.395 0.412 1.731 0.000 1.779 0.000 24.122 0.000

Problem 502

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 162 82 213 0 10506 0 1981 0

N.S.

1 0.99 0.50 1.31 0.00 64.45 0.00 12.15 0.00

time (sec)

N/A 0.324 0.091 0.785 0.000 0.746 0.000 8.262 0.000

Problem 503

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 107 60 173 0 4200 0 0 0

N.S.

1 1.08 0.61 1.75 0.00 42.42 0.00 0.00 0.00

time (sec)

N/A 0.280 0.060 0.496 0.000 0.414 0.000 0.000 0.000

Problem 504

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 87 49 65 0 3084 0 0 0

N.S.

1 1.05 0.59 0.78 0.00 37.16 0.00 0.00 0.00

time (sec)

N/A 0.278 0.043 0.477 0.000 0.371 0.000 0.000 0.000

Problem 505

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 131 69 73 0 7594 0 0 0

N.S.

1 0.92 0.48 0.51 0.00 53.10 0.00 0.00 0.00

time (sec)

N/A 0.312 0.214 0.738 0.000 0.589 0.000 0.000 0.000

Problem 506

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

208 185 117 73 0 15102 0 0 0

N.S.

1 0.89 0.56 0.35 0.00 72.61 0.00 0.00 0.00

time (sec)

N/A 0.373 0.295 1.687 0.000 1.294 0.000 0.000 0.000

Problem 507

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

333 417 252 661 0 15718 0 0 0

N.S.

1 1.25 0.76 1.98 0.00 47.20 0.00 0.00 0.00

time (sec)

N/A 0.556 2.861 4.485 0.000 0.790 0.000 0.000 0.000

Problem 508

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

274 344 215 797 0 8226 0 0 0

N.S.

1 1.26 0.78 2.91 0.00 30.02 0.00 0.00 0.00

time (sec)

N/A 0.475 2.297 3.085 0.000 0.319 0.000 0.000 0.000

Problem 509

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

251 258 190 406 0 5442 0 0 0

N.S.

1 1.03 0.76 1.62 0.00 21.68 0.00 0.00 0.00

time (sec)

N/A 1.260 0.971 1.248 0.000 0.215 0.000 0.000 0.000

Problem 510

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

351 412 226 640 0 7847 0 0 0

N.S.

1 1.17 0.64 1.82 0.00 22.36 0.00 0.00 0.00

time (sec)

N/A 0.584 2.378 3.041 0.000 0.288 0.000 0.000 0.000

Problem 511

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

385 471 247 923 0 13823 0 0 0

N.S.

1 1.22 0.64 2.40 0.00 35.90 0.00 0.00 0.00

time (sec)

N/A 0.695 2.358 4.114 0.000 0.601 0.000 0.000 0.000

Problem 512

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

122 149 0 0 0 0 0 0 0

N.S.

1 1.22 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.389 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 513

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

110 110 90 0 0 0 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.283 0.176 0.000 0.000 0.000 0.000 0.000 0.000

Problem 514

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

63 63 65 0 0 0 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.238 0.054 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 F F(-1) F F(-1)

verified

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

size

54 54 54 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.245 0.044 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 F F(-1) F F(-1)

verified

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

size

94 91 71 0 0 0 0 0 0

N.S.

1 0.97 0.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.265 0.274 0.000 0.000 0.000 0.000 0.000 0.000

Problem 517

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

103 103 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.302 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 518

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

103 103 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.299 0.000 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 F F F F F(-1) F F(-1)

verified

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

size

99 99 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.284 0.000 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(-1) F F(-1)

verified

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

size

103 103 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.287 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 C F C F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 152 136 91 0 1432 0 209 1129

N.S.

1 1.00 0.89 0.60 0.00 9.42 0.00 1.38 7.43

time (sec)

N/A 0.455 0.241 5.239 0.000 0.949 0.000 0.276 0.998

Problem 522

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 28 28 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.254 0.018 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 B F F F(-1)

verified

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

size

45 45 45 0 0 1663 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 36.96 0.00 0.00 0.00

time (sec)

N/A 0.275 0.017 0.000 0.000 1.451 0.000 0.000 0.000

Problem 524

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 29 24 0 113 0 0 0

N.S.

1 1.00 1.00 0.83 0.00 3.90 0.00 0.00 0.00

time (sec)

N/A 0.273 0.019 0.258 0.000 0.280 0.000 0.000 0.000

Problem 525

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 45 45 38 0 156 0 0 0

N.S.

1 0.96 0.96 0.81 0.00 3.32 0.00 0.00 0.00

time (sec)

N/A 0.275 0.017 0.212 0.000 0.264 0.000 0.000 0.000

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