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Integrals 601 to 641

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 601

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

24 24 26 22 24 42 0 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.75 0.00 1.00 1.00

time (sec)

N/A 0.044 0.174 0.046 0.337 0.345 0.000 2.230 1.454

Problem 602

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

22 22 24 20 22 40 0 22 22

N.S.

1 1.00 1.09 0.91 1.00 1.82 0.00 1.00 1.00

time (sec)

N/A 0.033 0.202 0.044 0.377 0.326 0.000 2.273 1.561

Problem 603

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

20 20 22 18 20 38 0 20 20

N.S.

1 1.00 1.10 0.90 1.00 1.90 0.00 1.00 1.00

time (sec)

N/A 0.025 0.036 0.043 0.343 0.323 0.000 1.784 1.444

Problem 604

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

24 24 26 22 24 42 0 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.75 0.00 1.00 1.00

time (sec)

N/A 0.044 0.149 0.046 0.329 0.377 0.000 2.329 1.539

Problem 605

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

24 24 26 22 24 42 0 24 24

N.S.

1 1.00 1.08 0.92 1.00 1.75 0.00 1.00 1.00

time (sec)

N/A 0.041 0.137 0.049 0.352 0.321 0.000 2.297 1.455

Problem 606

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

631 631 373 0 754 1196 0 556 0

N.S.

1 1.00 0.59 0.00 1.19 1.90 0.00 0.88 0.00

time (sec)

N/A 0.650 0.241 0.000 0.287 0.344 0.000 0.389 0.000

Problem 607

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

603 603 332 0 731 1162 0 448 0

N.S.

1 1.00 0.55 0.00 1.21 1.93 0.00 0.74 0.00

time (sec)

N/A 0.526 0.319 0.000 0.292 0.368 0.000 0.385 0.000

Problem 608

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

588 588 271 0 707 1236 0 471 0

N.S.

1 1.00 0.46 0.00 1.20 2.10 0.00 0.80 0.00

time (sec)

N/A 0.488 0.290 0.000 0.289 0.399 0.000 0.384 0.000

Problem 609

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

620 620 235 0 723 1348 0 494 0

N.S.

1 1.00 0.38 0.00 1.17 2.17 0.00 0.80 0.00

time (sec)

N/A 0.529 0.161 0.000 0.297 0.381 0.000 0.398 0.000

Problem 610

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

641 641 100 0 739 1369 0 511 0

N.S.

1 1.00 0.16 0.00 1.15 2.14 0.00 0.80 0.00

time (sec)

N/A 0.550 0.052 0.000 0.327 0.412 0.000 0.418 0.000

Problem 611

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1002 1002 628 0 1165 2178 0 885 0

N.S.

1 1.00 0.63 0.00 1.16 2.17 0.00 0.88 0.00

time (sec)

N/A 0.863 0.564 0.000 0.319 0.428 0.000 0.389 0.000

Problem 612

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

949 949 478 0 1119 2118 0 577 0

N.S.

1 1.00 0.50 0.00 1.18 2.23 0.00 0.61 0.00

time (sec)

N/A 0.830 0.622 0.000 0.315 0.460 0.000 0.431 0.000

Problem 613

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

932 932 527 0 1102 2112 0 641 0

N.S.

1 1.00 0.57 0.00 1.18 2.27 0.00 0.69 0.00

time (sec)

N/A 0.809 0.647 0.000 0.303 0.440 0.000 0.440 0.000

Problem 614

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

935 935 340 0 1088 2205 0 675 0

N.S.

1 1.00 0.36 0.00 1.16 2.36 0.00 0.72 0.00

time (sec)

N/A 0.790 0.637 0.000 0.313 0.461 0.000 0.426 0.000

Problem 615

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

968 968 294 0 1110 2283 0 688 0

N.S.

1 1.00 0.30 0.00 1.15 2.36 0.00 0.71 0.00

time (sec)

N/A 0.800 0.183 0.000 0.312 0.434 0.000 0.438 0.000

Problem 616

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

1680 1680 1506 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 2.279 0.911 0.000 0.000 0.000 0.000 0.000 0.000

Problem 617

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

1361 1361 1297 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 1.333 0.296 0.000 0.000 0.000 0.000 0.000 0.000

Problem 618

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

1659 1659 1336 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 1.759 1.055 0.000 0.000 0.000 0.000 0.000 0.000

Problem 619

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

33 33 33 148 0 35 0 0 0

N.S.

1 1.00 1.00 4.48 0.00 1.06 0.00 0.00 0.00

time (sec)

N/A 0.020 0.012 2.543 0.000 0.352 0.000 0.000 0.000

Problem 620

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

75 75 220 496 0 105 0 0 0

N.S.

1 1.00 2.93 6.61 0.00 1.40 0.00 0.00 0.00

time (sec)

N/A 0.079 0.176 1.418 0.000 0.338 0.000 0.000 0.000

Problem 621

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

161 161 659 0 0 417 0 0 0

N.S.

1 1.00 4.09 0.00 0.00 2.59 0.00 0.00 0.00

time (sec)

N/A 0.144 0.202 0.000 0.000 0.383 0.000 0.000 0.000

Problem 622

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

132 132 456 0 0 281 0 0 0

N.S.

1 1.00 3.45 0.00 0.00 2.13 0.00 0.00 0.00

time (sec)

N/A 0.123 0.157 0.000 0.000 0.318 0.000 0.000 0.000

Problem 623

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

102 102 265 0 0 161 0 0 0

N.S.

1 1.00 2.60 0.00 0.00 1.58 0.00 0.00 0.00

time (sec)

N/A 0.094 0.148 0.000 0.000 0.327 0.000 0.000 0.000

Problem 624

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

49 49 49 180 0 69 0 0 0

N.S.

1 1.00 1.00 3.67 0.00 1.41 0.00 0.00 0.00

time (sec)

N/A 0.038 0.009 2.135 0.000 0.309 0.000 0.000 0.000

Problem 625

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 44 30 24 30 30

N.S.

1 1.00 1.07 1.00 1.57 1.07 0.86 1.07 1.07

time (sec)

N/A 0.197 0.441 0.079 0.376 0.302 53.375 0.333 1.720

Problem 626

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

28 28 30 28 91 30 0 30 30

N.S.

1 1.00 1.07 1.00 3.25 1.07 0.00 1.07 1.07

time (sec)

N/A 0.082 2.150 0.085 0.319 0.315 0.000 0.332 1.799

Problem 627

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

28 28 30 28 238 30 0 30 30

N.S.

1 1.00 1.07 1.00 8.50 1.07 0.00 1.07 1.07

time (sec)

N/A 0.078 8.834 0.063 0.315 0.308 0.000 0.341 2.000

Problem 628

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 65 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 0.033 0.020 0.000 0.000 0.000 0.000 0.000 0.000

Problem 629

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 169 147 132 0 1134 0 261 192

N.S.

1 1.00 0.87 0.78 0.00 6.71 0.00 1.54 1.14

time (sec)

N/A 0.136 0.079 1.463 0.000 1.067 0.000 0.445 1.619

Problem 630

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 63 63 105 0 206 235 92 82

N.S.

1 1.00 1.00 1.67 0.00 3.27 3.73 1.46 1.30

time (sec)

N/A 0.035 0.027 0.762 0.000 0.323 95.181 0.338 0.142

Problem 631

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 47 47 54 46 80 64 46

N.S.

1 1.00 1.34 1.34 1.54 1.31 2.29 1.83 1.31

time (sec)

N/A 0.012 0.030 0.518 0.230 0.332 0.287 0.353 1.418

Problem 632

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 56 65 65 65 102 171 67

N.S.

1 1.00 1.24 1.44 1.44 1.44 2.27 3.80 1.49

time (sec)

N/A 0.020 0.040 0.306 0.226 0.350 0.775 0.346 1.440

Problem 633

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 79 111 0 287 0 139 163

N.S.

1 1.00 1.34 1.88 0.00 4.86 0.00 2.36 2.76

time (sec)

N/A 0.027 0.096 0.927 0.000 0.338 0.000 0.533 1.847

Problem 634

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 165 66 138 0 1169 0 319 499

N.S.

1 1.00 0.40 0.84 0.00 7.08 0.00 1.93 3.02

time (sec)

N/A 0.118 0.349 1.964 0.000 1.060 0.000 0.743 1.689

Problem 635

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

22 22 24 22 24 30 19 24 24

N.S.

1 1.00 1.09 1.00 1.09 1.36 0.86 1.09 1.09

time (sec)

N/A 0.005 0.264 0.095 1.330 0.345 18.083 0.433 2.070

Problem 636

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

221 221 743 0 0 0 0 0 0

N.S.

1 1.00 3.36 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.208 0.921 0.000 0.000 0.000 0.000 0.000 0.000

Problem 637

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

168 168 441 0 0 0 0 0 0

N.S.

1 1.00 2.62 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.141 0.432 0.000 0.000 0.000 0.000 0.000 0.000

Problem 638

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

115 115 219 0 0 0 0 0 0

N.S.

1 1.00 1.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.067 0.169 0.000 0.000 0.000 0.000 0.000 0.000

Problem 639

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 70 77 70 76 107 176 61

N.S.

1 1.00 1.40 1.54 1.40 1.52 2.14 3.52 1.22

time (sec)

N/A 0.035 0.034 0.201 0.211 0.323 0.757 0.321 1.500

Problem 640

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

22 22 24 22 24 30 19 24 24

N.S.

1 1.00 1.09 1.00 1.09 1.36 0.86 1.09 1.09

time (sec)

N/A 0.006 0.315 0.078 0.348 0.304 1.148 1.038 1.484

Problem 641

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

22 22 24 22 148 62 20 24 24

N.S.

1 1.00 1.09 1.00 6.73 2.82 0.91 1.09 1.09

time (sec)

N/A 0.005 0.394 0.076 0.397 0.356 3.460 0.481 1.601

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