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Integrals 101 to 117

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 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

20 20 22 18 0 20 19 20 61 20

N.S.

1 1.00 1.10 0.90 0.00 1.00 0.95 1.00 3.05 1.00

time (sec)

N/A 0.220 4.999 2.157 0.000 0.124 9.138 0.277 0.267 0.537

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

20 20 22 18 0 20 19 0 48 20

N.S.

1 1.00 1.10 0.90 0.00 1.00 0.95 0.00 2.40 1.00

time (sec)

N/A 0.206 2.832 1.768 0.000 0.115 4.676 0.000 0.289 0.494

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

71 71 73 0 0 294 0 0 123 0

N.S.

1 1.00 1.03 0.00 0.00 4.14 0.00 0.00 1.73 0.00

time (sec)

N/A 0.267 0.079 0.000 0.000 0.163 0.000 0.000 0.289 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

146 147 190 0 0 686 0 0 276 0

N.S.

1 1.01 1.30 0.00 0.00 4.70 0.00 0.00 1.89 0.00

time (sec)

N/A 0.335 0.157 0.000 0.000 0.190 0.000 0.000 0.320 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

226 242 189 0 0 1324 0 0 461 0

N.S.

1 1.07 0.84 0.00 0.00 5.86 0.00 0.00 2.04 0.00

time (sec)

N/A 1.110 0.266 0.000 0.000 0.289 0.000 0.000 0.347 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

22 22 24 20 0 34 20 22 89 22

N.S.

1 1.00 1.09 0.91 0.00 1.55 0.91 1.00 4.05 1.00

time (sec)

N/A 0.213 16.112 1.287 0.000 0.122 8.998 0.369 0.321 0.387

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 24 20 0 34 20 0 76 22

N.S.

1 1.00 1.09 0.91 0.00 1.55 0.91 0.00 3.45 1.00

time (sec)

N/A 0.213 8.327 1.145 0.000 0.105 5.154 0.000 0.325 0.399

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 24 20 0 54 20 0 222 22

N.S.

1 1.00 1.09 0.91 0.00 2.45 0.91 0.00 10.09 1.00

time (sec)

N/A 0.217 3.074 2.135 0.000 0.134 5.033 0.000 0.340 0.366

Problem 109

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 F(-2) N/A N/A

verified

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

size

22 22 24 20 130 65 20 0 488 22

N.S.

1 1.00 1.09 0.91 5.91 2.95 0.91 0.00 22.18 1.00

time (sec)

N/A 0.221 7.822 2.062 0.384 0.153 58.250 0.000 0.371 0.401

Problem 110

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

22 22 24 20 22 22 19 22 22 22

N.S.

1 1.00 1.09 0.91 1.00 1.00 0.86 1.00 1.00 1.00

time (sec)

N/A 0.221 0.973 1.921 0.206 0.110 0.363 0.265 200.042 0.300

Problem 111

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

22 22 24 20 22 39 20 22 29 22

N.S.

1 1.00 1.09 0.91 1.00 1.77 0.91 1.00 1.32 1.00

time (sec)

N/A 0.232 0.873 1.407 0.205 0.125 0.636 0.207 0.642 0.313

Problem 112

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

22 22 24 20 22 63 20 22 63 22

N.S.

1 1.00 1.09 0.91 1.00 2.86 0.91 1.00 2.86 1.00

time (sec)

N/A 0.227 1.543 1.949 0.243 0.097 1.732 0.248 0.679 0.300

Problem 113

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

22 22 24 20 22 87 20 22 107 22

N.S.

1 1.00 1.09 0.91 1.00 3.95 0.91 1.00 4.86 1.00

time (sec)

N/A 0.244 3.519 1.971 0.257 0.118 7.646 0.286 0.883 0.300

Problem 114

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

22 22 24 20 237 36 20 22 22 22

N.S.

1 1.00 1.09 0.91 10.77 1.64 0.91 1.00 1.00 1.00

time (sec)

N/A 0.216 6.535 1.877 1.480 0.114 0.655 0.383 200.019 0.327

Problem 115

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

22 22 24 20 365 67 22 22 22 22

N.S.

1 1.00 1.09 0.91 16.59 3.05 1.00 1.00 1.00 1.00

time (sec)

N/A 0.218 12.519 1.379 1.610 0.116 1.227 0.277 200.027 0.340

Problem 116

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

22 22 24 20 456 108 22 22 22 22

N.S.

1 1.00 1.09 0.91 20.73 4.91 1.00 1.00 1.00 1.00

time (sec)

N/A 0.219 26.706 1.930 3.282 0.125 4.679 0.366 200.023 0.335

Problem 117

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

22 22 24 20 578 149 22 22 187 22

N.S.

1 1.00 1.09 0.91 26.27 6.77 1.00 1.00 8.50 1.00

time (sec)

N/A 0.220 53.527 2.057 4.439 0.129 26.584 0.415 0.782 0.325

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