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Integrals 501 to 538

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 A F F F F F F(-1)

verified

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

size

73 73 57 0 0 0 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.053 0.292 0.000 0.000 0.000 0.000 0.000 0.000

Problem 502

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

73 73 63 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.053 0.281 0.000 0.000 0.000 0.000 0.000 0.000

Problem 503

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

76 76 104 0 0 0 0 0 0

N.S.

1 1.00 1.37 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.071 31.911 0.000 0.000 0.000 0.000 0.000 0.000

Problem 504

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

76 76 75 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 0.059 10.377 0.000 0.000 0.000 0.000 0.000 0.000

Problem 505

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

76 76 72 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.061 10.423 0.000 0.000 0.000 0.000 0.000 0.000

Problem 506

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

78 78 73 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.078 10.500 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 A A C F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 100 67 252 0 95 0 0 0

N.S.

1 1.00 0.67 2.52 0.00 0.95 0.00 0.00 0.00

time (sec)

N/A 0.051 0.268 1.019 0.000 0.119 0.000 0.000 0.000

Problem 508

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 62 248 0 93 0 0 0

N.S.

1 1.00 0.83 3.31 0.00 1.24 0.00 0.00 0.00

time (sec)

N/A 0.034 0.173 0.890 0.000 0.108 0.000 0.000 0.000

Problem 509

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 55 233 0 82 0 0 0

N.S.

1 1.00 0.76 3.24 0.00 1.14 0.00 0.00 0.00

time (sec)

N/A 0.036 0.180 0.875 0.000 0.101 0.000 0.000 0.000

Problem 510

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 43 314 0 59 0 0 0

N.S.

1 1.00 0.98 7.14 0.00 1.34 0.00 0.00 0.00

time (sec)

N/A 0.021 0.050 0.947 0.000 0.100 0.000 0.000 0.000

Problem 511

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 42 120 0 55 0 0 63

N.S.

1 1.00 0.98 2.79 0.00 1.28 0.00 0.00 1.47

time (sec)

N/A 0.014 0.043 0.753 0.000 0.092 0.000 0.000 0.382

Problem 512

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 57 409 0 80 0 0 0

N.S.

1 1.00 0.84 6.01 0.00 1.18 0.00 0.00 0.00

time (sec)

N/A 0.028 0.111 0.918 0.000 0.091 0.000 0.000 0.000

Problem 513

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 55 227 0 96 0 0 0

N.S.

1 1.00 0.74 3.07 0.00 1.30 0.00 0.00 0.00

time (sec)

N/A 0.027 0.151 0.851 0.000 0.122 0.000 0.000 0.000

Problem 514

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 100 68 430 0 128 0 0 0

N.S.

1 1.00 0.68 4.30 0.00 1.28 0.00 0.00 0.00

time (sec)

N/A 0.041 0.167 0.931 0.000 0.107 0.000 0.000 0.000

Problem 515

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 68 186 0 99 0 0 0

N.S.

1 1.00 0.66 1.81 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 0.053 0.226 1.260 0.000 0.105 0.000 0.000 0.000

Problem 516

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 62 249 0 98 0 0 0

N.S.

1 1.00 0.81 3.23 0.00 1.27 0.00 0.00 0.00

time (sec)

N/A 0.041 0.221 1.007 0.000 0.106 0.000 0.000 0.000

Problem 517

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 56 159 0 85 0 0 0

N.S.

1 1.00 0.75 2.12 0.00 1.13 0.00 0.00 0.00

time (sec)

N/A 0.035 0.110 0.892 0.000 0.103 0.000 0.000 0.000

Problem 518

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 45 316 0 61 0 0 0

N.S.

1 1.00 0.98 6.87 0.00 1.33 0.00 0.00 0.00

time (sec)

N/A 0.025 0.011 0.918 0.000 0.100 0.000 0.000 0.000

Problem 519

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 43 121 0 57 0 0 0

N.S.

1 1.00 0.98 2.75 0.00 1.30 0.00 0.00 0.00

time (sec)

N/A 0.019 0.006 0.782 0.000 0.106 0.000 0.000 0.000

Problem 520

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 54 413 0 83 0 0 0

N.S.

1 1.00 0.76 5.82 0.00 1.17 0.00 0.00 0.00

time (sec)

N/A 0.026 0.007 0.839 0.000 0.105 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 F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 58 227 0 99 0 0 0

N.S.

1 1.00 0.81 3.15 0.00 1.38 0.00 0.00 0.00

time (sec)

N/A 0.031 0.142 0.937 0.000 0.091 0.000 0.000 0.000

Problem 522

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 68 431 0 138 0 0 0

N.S.

1 1.00 0.66 4.18 0.00 1.34 0.00 0.00 0.00

time (sec)

N/A 0.044 0.266 0.980 0.000 0.102 0.000 0.000 0.000

Problem 523

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 102 70 246 0 98 0 0 0

N.S.

1 1.00 0.69 2.41 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 0.050 0.179 1.148 0.000 0.113 0.000 0.000 0.000

Problem 524

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 57 442 0 96 0 0 0

N.S.

1 1.00 0.79 6.14 0.00 1.33 0.00 0.00 0.00

time (sec)

N/A 0.035 0.136 1.003 0.000 0.119 0.000 0.000 0.000

Problem 525

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 64 233 0 85 0 0 0

N.S.

1 1.00 0.86 3.15 0.00 1.15 0.00 0.00 0.00

time (sec)

N/A 0.034 0.066 0.945 0.000 0.091 0.000 0.000 0.000

Problem 526

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 42 297 0 62 0 0 0

N.S.

1 1.00 0.98 6.91 0.00 1.44 0.00 0.00 0.00

time (sec)

N/A 0.017 0.014 0.979 0.000 0.093 0.000 0.000 0.000

Problem 527

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 45 125 0 58 0 0 0

N.S.

1 1.00 0.98 2.72 0.00 1.26 0.00 0.00 0.00

time (sec)

N/A 0.019 0.006 0.930 0.000 0.096 0.000 0.000 0.000

Problem 528

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 52 415 0 83 0 0 0

N.S.

1 1.00 0.74 5.93 0.00 1.19 0.00 0.00 0.00

time (sec)

N/A 0.030 0.172 0.956 0.000 0.090 0.000 0.000 0.000

Problem 529

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 60 250 0 99 0 0 0

N.S.

1 1.00 0.78 3.25 0.00 1.29 0.00 0.00 0.00

time (sec)

N/A 0.029 0.113 0.957 0.000 0.097 0.000 0.000 0.000

Problem 530

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 103 70 281 0 98 0 0 0

N.S.

1 1.00 0.68 2.73 0.00 0.95 0.00 0.00 0.00

time (sec)

N/A 0.052 0.121 1.068 0.000 0.103 0.000 0.000 0.000

Problem 531

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 60 445 0 96 0 0 0

N.S.

1 1.00 0.81 6.01 0.00 1.30 0.00 0.00 0.00

time (sec)

N/A 0.035 0.073 0.998 0.000 0.101 0.000 0.000 0.000

Problem 532

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 63 262 0 85 0 0 0

N.S.

1 1.00 0.82 3.40 0.00 1.10 0.00 0.00 0.00

time (sec)

N/A 0.034 0.008 1.056 0.000 0.099 0.000 0.000 0.000

Problem 533

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 45 303 0 62 0 0 0

N.S.

1 1.00 0.98 6.59 0.00 1.35 0.00 0.00 0.00

time (sec)

N/A 0.017 0.012 1.166 0.000 0.093 0.000 0.000 0.000

Problem 534

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 45 131 0 58 0 0 0

N.S.

1 1.00 0.98 2.85 0.00 1.26 0.00 0.00 0.00

time (sec)

N/A 0.017 0.007 0.944 0.000 0.097 0.000 0.000 0.000

Problem 535

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 55 421 0 83 0 0 0

N.S.

1 1.00 0.75 5.77 0.00 1.14 0.00 0.00 0.00

time (sec)

N/A 0.030 0.145 0.922 0.000 0.107 0.000 0.000 0.000

Problem 536

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 60 254 0 99 0 0 0

N.S.

1 1.00 0.78 3.30 0.00 1.29 0.00 0.00 0.00

time (sec)

N/A 0.025 0.143 0.960 0.000 0.100 0.000 0.000 0.000

Problem 537

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 105 73 453 0 134 0 0 0

N.S.

1 1.00 0.70 4.31 0.00 1.28 0.00 0.00 0.00

time (sec)

N/A 0.044 0.212 1.014 0.000 0.100 0.000 0.000 0.000

Problem 538

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

87 87 102 0 0 0 0 0 0

N.S.

1 1.00 1.17 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.043 8.100 0.000 0.000 0.000 0.000 0.000 0.000

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