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2.2.7 Integrals 601 to 641

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 601

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

27 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.037 0.156 0.005 0.000 0.000 0.000 0.000 0.000

Problem 602

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

25 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.029 0.187 0.005 0.000 0.000 0.000 0.000 0.000

Problem 603

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.023 0.086 0.004 0.000 0.000 0.000 0.000 0.000

Problem 604

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

27 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.036 0.126 0.004 0.000 0.000 0.000 0.000 0.000

Problem 605

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

27 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.037 0.105 0.005 0.000 0.000 0.000 0.000 0.000

Problem 606

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

631 631 344 0 538 1263 0 514 -1

N.S.

1 1.00 0.55 0.00 0.85 2.00 0.00 0.81 -0.00

time (sec)

N/A 0.588 0.322 0.064 0.512 0.439 0.000 5.656 0.000

Problem 607

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

603 603 316 0 517 1254 0 431 -1

N.S.

1 1.00 0.52 0.00 0.86 2.08 0.00 0.71 -0.00

time (sec)

N/A 0.535 0.307 0.018 0.516 0.400 0.000 3.140 0.000

Problem 608

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

588 588 271 0 495 1339 0 443 -1

N.S.

1 1.00 0.46 0.00 0.84 2.28 0.00 0.75 -0.00

time (sec)

N/A 0.479 0.284 0.021 0.522 0.391 0.000 4.399 0.000

Problem 609

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

620 620 309 0 512 1393 0 478 -1

N.S.

1 1.00 0.50 0.00 0.83 2.25 0.00 0.77 -0.00

time (sec)

N/A 0.520 0.118 0.017 0.525 0.445 0.000 3.095 0.000

Problem 610

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

641 641 100 0 526 1408 0 488 -1

N.S.

1 1.00 0.16 0.00 0.82 2.20 0.00 0.76 -0.00

time (sec)

N/A 0.562 0.050 0.029 0.512 0.422 0.000 5.446 0.000

Problem 611

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

1002 1002 588 0 847 2326 0 820 -1

N.S.

1 1.00 0.59 0.00 0.85 2.32 0.00 0.82 -0.00

time (sec)

N/A 0.877 0.896 0.262 0.523 21.958 0.000 4.019 0.000

Problem 612

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

949 949 436 0 793 2334 0 649 -1

N.S.

1 1.00 0.46 0.00 0.84 2.46 0.00 0.68 -0.00

time (sec)

N/A 0.811 0.576 0.236 0.534 5.424 0.000 6.280 0.000

Problem 613

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

932 932 503 0 786 2347 0 638 -1

N.S.

1 1.00 0.54 0.00 0.84 2.52 0.00 0.68 -0.00

time (sec)

N/A 0.780 0.648 0.194 0.527 0.476 0.000 3.321 0.000

Problem 614

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

935 935 340 0 767 2420 0 660 -1

N.S.

1 1.00 0.36 0.00 0.82 2.59 0.00 0.71 -0.00

time (sec)

N/A 0.777 0.633 0.243 0.527 6.228 0.000 4.904 0.000

Problem 615

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

968 968 294 0 795 2436 0 674 -1

N.S.

1 1.00 0.30 0.00 0.82 2.52 0.00 0.70 -0.00

time (sec)

N/A 0.804 0.170 0.217 0.549 0.483 0.000 5.683 0.000

Problem 616

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

1680 1680 1471 0 0 0 0 0 -1

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 2.031 0.913 0.307 0.000 0.000 0.000 0.000 0.000

Problem 617

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

1361 1361 1297 0 0 0 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.171 0.280 0.305 0.000 0.000 0.000 0.000 0.000

Problem 618

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

1659 1659 1336 0 0 0 0 0 -1

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.656 1.032 0.304 0.000 0.000 0.000 0.000 0.000

Problem 619

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 33 191 0 37 0 0 -1

N.S.

1 1.00 1.00 5.79 0.00 1.12 0.00 0.00 -0.03

time (sec)

N/A 0.017 0.011 0.449 0.000 0.367 0.000 0.000 0.000

Problem 620

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 220 1373 0 108 0 0 -1

N.S.

1 1.00 2.93 18.31 0.00 1.44 0.00 0.00 -0.01

time (sec)

N/A 0.074 0.175 0.919 0.000 0.358 0.000 0.000 0.000

Problem 621

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 659 0 0 423 0 0 -1

N.S.

1 1.00 4.09 0.00 0.00 2.63 0.00 0.00 -0.01

time (sec)

N/A 0.146 0.182 0.082 0.000 0.364 0.000 0.000 0.000

Problem 622

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 456 0 0 286 0 0 -1

N.S.

1 1.00 3.45 0.00 0.00 2.17 0.00 0.00 -0.01

time (sec)

N/A 0.119 0.160 0.037 0.000 0.391 0.000 0.000 0.000

Problem 623

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F A F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 265 0 0 165 0 0 -1

N.S.

1 1.00 2.60 0.00 0.00 1.62 0.00 0.00 -0.01

time (sec)

N/A 0.094 0.125 0.028 0.000 0.431 0.000 0.000 0.000

Problem 624

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 49 189 0 72 0 0 -1

N.S.

1 1.00 1.00 3.86 0.00 1.47 0.00 0.00 -0.02

time (sec)

N/A 0.034 0.010 1.457 0.000 0.353 0.000 0.000 0.000

Problem 625

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

42 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.196 0.387 0.025 0.000 0.000 0.000 0.000 0.000

Problem 626

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

64 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.076 1.768 0.027 0.000 0.000 0.000 0.000 0.000

Problem 627

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

69 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.074 7.952 0.029 0.000 0.000 0.000 0.000 0.000

Problem 628

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 65 0 0 0 0 0 -1

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.031 0.020 0.058 0.000 0.000 0.000 0.000 0.000

Problem 629

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 147 154 0 1346 0 265 192

N.S.

1 1.00 0.87 0.91 0.00 7.96 0.00 1.57 1.14

time (sec)

N/A 0.141 0.073 0.723 0.000 1.130 0.000 6.349 0.280

Problem 630

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 63 115 101 190 235 96 82

N.S.

1 1.00 1.00 1.83 1.60 3.02 3.73 1.52 1.30

time (sec)

N/A 0.035 0.025 0.310 0.518 0.344 104.352 7.278 0.134

Problem 631

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

35 35 44 57 57 50 80 69 46

N.S.

1 1.00 1.26 1.63 1.63 1.43 2.29 1.97 1.31

time (sec)

N/A 0.011 0.022 0.223 0.303 0.349 0.370 5.047 0.307

Problem 632

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 56 71 67 70 102 172 67

N.S.

1 1.00 1.24 1.58 1.49 1.56 2.27 3.82 1.49

time (sec)

N/A 0.019 0.035 0.053 0.290 0.343 0.655 8.945 0.177

Problem 633

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 61 129 101 288 0 137 163

N.S.

1 1.00 1.03 2.19 1.71 4.88 0.00 2.32 2.76

time (sec)

N/A 0.026 0.037 0.128 0.546 0.403 0.000 4.181 0.522

Problem 634

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 66 168 0 1424 0 319 499

N.S.

1 1.00 0.40 1.02 0.00 8.63 0.00 1.93 3.02

time (sec)

N/A 0.114 0.079 0.059 0.000 1.110 0.000 52.543 0.633

Problem 635

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

25 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.004 0.260 0.080 0.000 0.000 0.000 0.000 0.000

Problem 636

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

221 221 739 0 0 0 0 0 -1

N.S.

1 1.00 3.34 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.181 0.709 0.046 0.000 0.000 0.000 0.000 0.000

Problem 637

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

168 168 415 0 0 0 0 0 -1

N.S.

1 1.00 2.47 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.123 0.321 0.005 0.000 0.000 0.000 0.000 0.000

Problem 638

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 219 0 0 0 0 0 -1

N.S.

1 1.00 1.90 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.062 0.181 0.044 0.000 0.000 0.000 0.000 0.000

Problem 639

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 70 81 72 80 107 177 61

N.S.

1 1.00 1.40 1.62 1.44 1.60 2.14 3.54 1.22

time (sec)

N/A 0.026 0.027 0.030 0.387 0.401 0.569 5.627 0.419

Problem 640

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

25 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.004 0.368 0.039 0.000 0.000 0.000 0.000 0.000

Problem 641

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

25 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.004 0.580 0.044 0.000 0.000 0.000 0.000 0.000

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