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 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

73 73 57 0 0 0 0 0 23 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.32 0.00

time (sec)

N/A 0.505 0.476 0.000 0.000 0.000 0.000 0.000 0.167 0.000

Problem 502

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

73 73 63 0 0 0 0 0 23 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.32 0.00

time (sec)

N/A 0.511 0.448 0.000 0.000 0.000 0.000 0.000 0.200 0.000

Problem 503

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

76 76 104 0 0 0 0 0 31 0

N.S.

1 1.00 1.37 0.00 0.00 0.00 0.00 0.00 0.41 0.00

time (sec)

N/A 0.613 33.014 0.000 0.000 0.000 0.000 0.000 0.208 0.000

Problem 504

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

76 76 75 0 0 0 0 0 24 0

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 0.32 0.00

time (sec)

N/A 0.531 10.601 0.000 0.000 0.000 0.000 0.000 0.206 0.000

Problem 505

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

76 76 72 0 0 0 0 0 35 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.46 0.00

time (sec)

N/A 0.541 10.668 0.000 0.000 0.000 0.000 0.000 0.187 0.000

Problem 506

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

78 78 73 0 0 0 0 0 35 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.45 0.00

time (sec)

N/A 0.557 10.773 0.000 0.000 0.000 0.000 0.000 0.259 0.000

Problem 507

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

100 117 67 153 0 95 0 0 21 0

N.S.

1 1.17 0.67 1.53 0.00 0.95 0.00 0.00 0.21 0.00

time (sec)

N/A 0.841 0.424 1.003 0.000 0.116 0.000 0.000 0.176 0.000

Problem 508

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

75 81 62 248 0 93 0 0 21 0

N.S.

1 1.08 0.83 3.31 0.00 1.24 0.00 0.00 0.28 0.00

time (sec)

N/A 0.646 0.290 0.950 0.000 0.097 0.000 0.000 0.169 0.000

Problem 509

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 81 55 141 0 82 0 0 21 0

N.S.

1 1.12 0.76 1.96 0.00 1.14 0.00 0.00 0.29 0.00

time (sec)

N/A 0.608 0.290 0.776 0.000 0.116 0.000 0.000 0.175 0.000

Problem 510

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

44 44 43 237 0 59 0 0 19 0

N.S.

1 1.00 0.98 5.39 0.00 1.34 0.00 0.00 0.43 0.00

time (sec)

N/A 0.430 0.079 0.891 0.000 0.112 0.000 0.000 0.169 0.000

Problem 511

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

43 43 42 120 0 55 0 0 12 63

N.S.

1 1.00 0.98 2.79 0.00 1.28 0.00 0.00 0.28 1.47

time (sec)

N/A 0.379 0.071 0.648 0.000 0.121 0.000 0.000 0.204 25.560

Problem 512

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

68 75 57 155 0 80 0 0 19 0

N.S.

1 1.10 0.84 2.28 0.00 1.18 0.00 0.00 0.28 0.00

time (sec)

N/A 0.583 0.177 0.719 0.000 0.123 0.000 0.000 0.166 0.000

Problem 513

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 79 55 135 0 96 0 0 21 0

N.S.

1 1.07 0.74 1.82 0.00 1.30 0.00 0.00 0.28 0.00

time (sec)

N/A 0.577 0.231 0.751 0.000 0.095 0.000 0.000 0.168 0.000

Problem 514

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

100 109 68 246 0 128 0 0 21 0

N.S.

1 1.09 0.68 2.46 0.00 1.28 0.00 0.00 0.21 0.00

time (sec)

N/A 0.766 0.269 0.841 0.000 0.109 0.000 0.000 0.160 0.000

Problem 515

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 117 68 154 0 99 0 0 28 0

N.S.

1 1.14 0.66 1.50 0.00 0.96 0.00 0.00 0.27 0.00

time (sec)

N/A 0.812 0.366 1.006 0.000 0.095 0.000 0.000 0.170 0.000

Problem 516

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

77 81 62 249 0 98 0 0 28 0

N.S.

1 1.05 0.81 3.23 0.00 1.27 0.00 0.00 0.36 0.00

time (sec)

N/A 0.608 0.424 0.956 0.000 0.090 0.000 0.000 0.181 0.000

Problem 517

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

75 81 56 141 0 85 0 0 28 0

N.S.

1 1.08 0.75 1.88 0.00 1.13 0.00 0.00 0.37 0.00

time (sec)

N/A 0.613 0.178 0.800 0.000 0.094 0.000 0.000 0.182 0.000

Problem 518

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 46 45 238 0 61 0 0 28 0

N.S.

1 1.00 0.98 5.17 0.00 1.33 0.00 0.00 0.61 0.00

time (sec)

N/A 0.441 0.018 0.809 0.000 0.096 0.000 0.000 0.170 0.000

Problem 519

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

44 44 43 121 0 57 0 0 26 0

N.S.

1 1.00 0.98 2.75 0.00 1.30 0.00 0.00 0.59 0.00

time (sec)

N/A 0.418 0.010 0.674 0.000 0.118 0.000 0.000 0.172 0.000

Problem 520

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

71 71 54 156 0 83 0 0 20 0

N.S.

1 1.00 0.76 2.20 0.00 1.17 0.00 0.00 0.28 0.00

time (sec)

N/A 0.518 0.012 0.726 0.000 0.114 0.000 0.000 0.164 0.000

Problem 521

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 79 58 136 0 99 0 0 22 0

N.S.

1 1.10 0.81 1.89 0.00 1.38 0.00 0.00 0.31 0.00

time (sec)

N/A 0.571 0.222 0.770 0.000 0.081 0.000 0.000 0.194 0.000

Problem 522

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 109 68 247 0 138 0 0 22 0

N.S.

1 1.06 0.66 2.40 0.00 1.34 0.00 0.00 0.21 0.00

time (sec)

N/A 0.758 0.419 0.817 0.000 0.088 0.000 0.000 0.245 0.000

Problem 523

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

102 117 70 155 0 98 0 0 32 0

N.S.

1 1.15 0.69 1.52 0.00 0.96 0.00 0.00 0.31 0.00

time (sec)

N/A 0.790 0.292 1.032 0.000 0.123 0.000 0.000 0.168 0.000

Problem 524

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 81 57 254 0 96 0 0 32 0

N.S.

1 1.12 0.79 3.53 0.00 1.33 0.00 0.00 0.44 0.00

time (sec)

N/A 0.602 0.218 0.918 0.000 0.110 0.000 0.000 0.159 0.000

Problem 525

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 79 64 139 0 85 0 0 30 0

N.S.

1 1.07 0.86 1.88 0.00 1.15 0.00 0.00 0.41 0.00

time (sec)

N/A 0.583 0.103 0.757 0.000 0.091 0.000 0.000 0.166 0.000

Problem 526

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

43 43 42 243 0 62 0 0 24 0

N.S.

1 1.00 0.98 5.65 0.00 1.44 0.00 0.00 0.56 0.00

time (sec)

N/A 0.371 0.023 0.793 0.000 0.086 0.000 0.000 0.188 0.000

Problem 527

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 46 45 125 0 58 0 0 15 0

N.S.

1 1.00 0.98 2.72 0.00 1.26 0.00 0.00 0.33 0.00

time (sec)

N/A 0.411 0.010 0.727 0.000 0.101 0.000 0.000 0.159 0.000

Problem 528

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

70 75 52 161 0 83 0 0 22 0

N.S.

1 1.07 0.74 2.30 0.00 1.19 0.00 0.00 0.31 0.00

time (sec)

N/A 0.581 0.271 0.729 0.000 0.089 0.000 0.000 0.174 0.000

Problem 529

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

77 79 60 145 0 99 0 0 24 0

N.S.

1 1.03 0.78 1.88 0.00 1.29 0.00 0.00 0.31 0.00

time (sec)

N/A 0.572 0.169 0.751 0.000 0.092 0.000 0.000 0.164 0.000

Problem 530

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 117 70 158 0 98 0 0 32 0

N.S.

1 1.14 0.68 1.53 0.00 0.95 0.00 0.00 0.31 0.00

time (sec)

N/A 0.789 0.195 1.023 0.000 0.088 0.000 0.000 0.163 0.000

Problem 531

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

74 79 60 257 0 96 0 0 30 0

N.S.

1 1.07 0.81 3.47 0.00 1.30 0.00 0.00 0.41 0.00

time (sec)

N/A 0.593 0.131 0.926 0.000 0.112 0.000 0.000 0.172 0.000

Problem 532

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

77 77 63 142 0 85 0 0 24 0

N.S.

1 1.00 0.82 1.84 0.00 1.10 0.00 0.00 0.31 0.00

time (sec)

N/A 0.542 0.012 0.759 0.000 0.111 0.000 0.000 0.168 0.000

Problem 533

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 46 45 246 0 62 0 0 24 0

N.S.

1 1.00 0.98 5.35 0.00 1.35 0.00 0.00 0.52 0.00

time (sec)

N/A 0.420 0.020 0.779 0.000 0.078 0.000 0.000 0.162 0.000

Problem 534

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 46 45 128 0 58 0 0 15 0

N.S.

1 1.00 0.98 2.78 0.00 1.26 0.00 0.00 0.33 0.00

time (sec)

N/A 0.426 0.011 0.747 0.000 0.090 0.000 0.000 0.175 0.000

Problem 535

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 75 55 167 0 83 0 0 22 0

N.S.

1 1.03 0.75 2.29 0.00 1.14 0.00 0.00 0.30 0.00

time (sec)

N/A 0.573 0.228 0.749 0.000 0.124 0.000 0.000 0.167 0.000

Problem 536

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

77 79 60 148 0 99 0 0 24 0

N.S.

1 1.03 0.78 1.92 0.00 1.29 0.00 0.00 0.31 0.00

time (sec)

N/A 0.583 0.228 0.753 0.000 0.092 0.000 0.000 0.182 0.000

Problem 537

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

105 109 73 272 0 134 0 0 24 0

N.S.

1 1.04 0.70 2.59 0.00 1.28 0.00 0.00 0.23 0.00

time (sec)

N/A 0.797 0.340 0.844 0.000 0.090 0.000 0.000 0.181 0.000

Problem 538

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

87 87 102 0 0 0 0 0 26 0

N.S.

1 1.00 1.17 0.00 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 0.500 12.037 0.000 0.000 0.000 0.000 0.000 0.167 0.000