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2.2.4 Integrals 301 to 348

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 301

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 81 361 96 0 214 1923 95 318

N.S.

1 1.16 5.16 1.37 0.00 3.06 27.47 1.36 4.54

time (sec)

N/A 0.407 0.942 0.217 0.000 0.307 114.137 0.323 5.224

Problem 302

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

737 667 2452 0 0 2684 0 0 0

N.S.

1 0.91 3.33 0.00 0.00 3.64 0.00 0.00 0.00

time (sec)

N/A 3.345 5.928 0.000 0.000 0.478 0.000 0.000 0.000

Problem 303

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

548 483 2283 0 0 1779 0 0 0

N.S.

1 0.88 4.17 0.00 0.00 3.25 0.00 0.00 0.00

time (sec)

N/A 2.262 3.291 0.000 0.000 0.473 0.000 0.000 0.000

Problem 304

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

351 318 816 1750 0 1037 0 0 0

N.S.

1 0.91 2.32 4.99 0.00 2.95 0.00 0.00 0.00

time (sec)

N/A 1.312 2.417 1.271 0.000 0.435 0.000 0.000 0.000

Problem 305

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 54 54 54 55 53 0 56 55

N.S.

1 0.89 0.89 0.89 0.90 0.87 0.00 0.92 0.90

time (sec)

N/A 0.243 0.063 0.208 0.196 0.296 0.000 0.346 0.101

Problem 306

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

937 814 2496 0 0 3069 0 0 0

N.S.

1 0.87 2.66 0.00 0.00 3.28 0.00 0.00 0.00

time (sec)

N/A 2.889 6.876 0.000 0.000 0.622 0.000 0.000 0.000

Problem 307

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

667 591 1461 0 0 2035 0 0 0

N.S.

1 0.89 2.19 0.00 0.00 3.05 0.00 0.00 0.00

time (sec)

N/A 2.090 3.786 0.000 0.000 0.570 0.000 0.000 0.000

Problem 308

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

413 386 1185 846 0 1181 0 0 0

N.S.

1 0.93 2.87 2.05 0.00 2.86 0.00 0.00 0.00

time (sec)

N/A 1.335 9.047 0.487 0.000 0.494 0.000 0.000 0.000

Problem 309

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 80 64 71 64 62 0 71 69

N.S.

1 1.07 0.85 0.95 0.85 0.83 0.00 0.95 0.92

time (sec)

N/A 0.274 0.046 0.210 0.190 0.277 0.000 0.337 0.230

Problem 310

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

923 774 1438 0 0 4116 0 0 0

N.S.

1 0.84 1.56 0.00 0.00 4.46 0.00 0.00 0.00

time (sec)

N/A 3.346 8.246 0.000 0.000 0.725 0.000 0.000 0.000

Problem 311

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

659 561 1122 0 0 2659 0 0 0

N.S.

1 0.85 1.70 0.00 0.00 4.03 0.00 0.00 0.00

time (sec)

N/A 2.556 7.645 0.000 0.000 0.579 0.000 0.000 0.000

Problem 312

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

349 324 906 2035 0 1267 0 0 0

N.S.

1 0.93 2.60 5.83 0.00 3.63 0.00 0.00 0.00

time (sec)

N/A 1.519 8.062 0.729 0.000 0.459 0.000 0.000 0.000

Problem 313

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 90 152 112 0 305 0 107 149

N.S.

1 1.07 1.81 1.33 0.00 3.63 0.00 1.27 1.77

time (sec)

N/A 0.345 0.429 0.232 0.000 0.280 0.000 0.306 5.712

Problem 314

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 30 30 26 30 30

N.S.

1 1.00 1.07 1.00 1.07 1.07 0.93 1.07 1.07

time (sec)

N/A 0.231 12.397 0.132 0.834 0.254 6.160 0.305 5.778

Problem 315

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

26 26 28 26 28 28 24 28 28

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.92 1.08 1.08

time (sec)

N/A 0.208 8.652 0.066 0.484 0.263 1.966 0.297 5.487

Problem 316

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

20 20 22 20 22 22 17 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.85 1.10 1.10

time (sec)

N/A 0.219 0.043 0.004 0.394 0.258 0.942 0.311 0.003

Problem 317

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

26 26 28 26 28 28 24 28 30

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.92 1.08 1.15

time (sec)

N/A 0.206 105.758 0.084 2.765 0.250 16.540 0.310 5.717

Problem 318

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 30 30 26 30 30

N.S.

1 1.00 1.07 1.00 1.07 1.07 0.93 1.07 1.07

time (sec)

N/A 0.237 16.185 0.088 19.304 0.273 72.634 0.335 5.543

Problem 319

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 83 73 194 0 339 0 0 0

N.S.

1 1.08 0.95 2.52 0.00 4.40 0.00 0.00 0.00

time (sec)

N/A 0.304 0.962 1.501 0.000 0.283 0.000 0.000 0.000

Problem 320

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

280 272 311 597 0 1393 0 0 0

N.S.

1 0.97 1.11 2.13 0.00 4.98 0.00 0.00 0.00

time (sec)

N/A 0.967 2.143 1.327 0.000 0.391 0.000 0.000 0.000

Problem 321

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

418 382 446 0 0 2284 0 0 0

N.S.

1 0.91 1.07 0.00 0.00 5.46 0.00 0.00 0.00

time (sec)

N/A 1.463 1.708 0.000 0.000 0.467 0.000 0.000 0.000

Problem 322

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 128 112 349 0 625 0 0 0

N.S.

1 1.10 0.97 3.01 0.00 5.39 0.00 0.00 0.00

time (sec)

N/A 0.425 1.407 2.770 0.000 0.295 0.000 0.000 0.000

Problem 323

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

357 355 1017 937 0 2375 0 0 0

N.S.

1 0.99 2.85 2.62 0.00 6.65 0.00 0.00 0.00

time (sec)

N/A 1.284 11.331 2.615 0.000 0.459 0.000 0.000 0.000

Problem 324

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

753 672 2259 0 0 4917 0 0 0

N.S.

1 0.89 3.00 0.00 0.00 6.53 0.00 0.00 0.00

time (sec)

N/A 3.005 15.405 0.000 0.000 0.568 0.000 0.000 0.000

Problem 325

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

765 0 1194 0 0 0 0 0 0

N.S.

1 0.00 1.56 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 1.406 0.000 0.000 0.000 0.000 0.000 0.000

Problem 326

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

557 627 607 0 0 2109 0 0 0

N.S.

1 1.13 1.09 0.00 0.00 3.79 0.00 0.00 0.00

time (sec)

N/A 3.909 1.278 0.000 0.000 0.529 0.000 0.000 0.000

Problem 327

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

351 406 876 1189 0 1273 0 0 0

N.S.

1 1.16 2.50 3.39 0.00 3.63 0.00 0.00 0.00

time (sec)

N/A 2.097 6.188 0.606 0.000 0.499 0.000 0.000 0.000

Problem 328

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 87 90 94 0 262 0 94 896

N.S.

1 1.16 1.20 1.25 0.00 3.49 0.00 1.25 11.95

time (sec)

N/A 0.500 0.212 0.273 0.000 0.335 0.000 0.415 6.885

Problem 329

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

763 0 4052 0 0 0 0 0 0

N.S.

1 0.00 5.31 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 9.843 0.000 0.000 0.000 0.000 0.000 0.000

Problem 330

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

566 701 1741 0 0 2260 0 0 0

N.S.

1 1.24 3.08 0.00 0.00 3.99 0.00 0.00 0.00

time (sec)

N/A 4.477 8.600 0.000 0.000 0.532 0.000 0.000 0.000

Problem 331

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

379 463 884 1721 0 1293 0 0 0

N.S.

1 1.22 2.33 4.54 0.00 3.41 0.00 0.00 0.00

time (sec)

N/A 2.668 3.177 2.510 0.000 0.496 0.000 0.000 0.000

Problem 332

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 57 53 55 54 55 0 56 98

N.S.

1 0.97 0.90 0.93 0.92 0.93 0.00 0.95 1.66

time (sec)

N/A 0.291 0.053 0.668 0.186 0.330 0.000 0.307 6.666

Problem 333

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1138 0 1181 0 0 0 0 0 0

N.S.

1 0.00 1.04 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 4.307 0.000 0.000 0.000 0.000 0.000 0.000

Problem 334

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

825 0 1254 0 0 2787 0 0 0

N.S.

1 0.00 1.52 0.00 0.00 3.38 0.00 0.00 0.00

time (sec)

N/A 0.000 3.212 0.000 0.000 0.626 0.000 0.000 0.000

Problem 335

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

524 0 998 1874 0 1611 0 0 0

N.S.

1 0.00 1.90 3.58 0.00 3.07 0.00 0.00 0.00

time (sec)

N/A 0.000 11.784 3.043 0.000 0.505 0.000 0.000 0.000

Problem 336

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 138 143 180 0 350 0 183 1320

N.S.

1 1.11 1.15 1.45 0.00 2.82 0.00 1.48 10.65

time (sec)

N/A 0.685 0.534 1.576 0.000 0.369 0.000 0.358 8.887

Problem 337

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

852 0 3039 0 0 0 0 0 0

N.S.

1 0.00 3.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 11.373 0.000 0.000 0.000 0.000 0.000 0.000

Problem 338

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

616 0 1752 0 0 2529 0 0 0

N.S.

1 0.00 2.84 0.00 0.00 4.11 0.00 0.00 0.00

time (sec)

N/A 0.000 9.801 0.000 0.000 0.496 0.000 0.000 0.000

Problem 339

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

386 0 915 1705 0 1419 0 0 0

N.S.

1 0.00 2.37 4.42 0.00 3.68 0.00 0.00 0.00

time (sec)

N/A 0.000 7.379 0.791 0.000 0.479 0.000 0.000 0.000

Problem 340

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 54 59 57 69 0 72 118

N.S.

1 1.00 0.90 0.98 0.95 1.15 0.00 1.20 1.97

time (sec)

N/A 0.306 0.073 0.300 0.190 0.273 0.000 0.318 6.350

Problem 341

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1144 0 3915 0 0 0 0 0 0

N.S.

1 0.00 3.42 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 8.232 0.000 0.000 0.000 0.000 0.000 0.000

Problem 342

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

840 0 973 0 0 3075 0 0 0

N.S.

1 0.00 1.16 0.00 0.00 3.66 0.00 0.00 0.00

time (sec)

N/A 0.000 5.900 0.000 0.000 0.592 0.000 0.000 0.000

Problem 343

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

517 0 1091 5310 0 1751 0 0 0

N.S.

1 0.00 2.11 10.27 0.00 3.39 0.00 0.00 0.00

time (sec)

N/A 0.000 12.252 2.818 0.000 0.546 0.000 0.000 0.000

Problem 344

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 123 146 155 0 396 0 221 1167

N.S.

1 1.18 1.40 1.49 0.00 3.81 0.00 2.12 11.22

time (sec)

N/A 0.671 0.906 1.317 0.000 0.361 0.000 0.376 8.137

Problem 345

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1432 0 4009 0 0 0 0 0 0

N.S.

1 0.00 2.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 10.309 0.000 0.000 0.000 0.000 0.000 0.000

Problem 346

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1051 0 5075 0 0 3131 0 0 0

N.S.

1 0.00 4.83 0.00 0.00 2.98 0.00 0.00 0.00

time (sec)

N/A 0.000 9.369 0.000 0.000 0.595 0.000 0.000 0.000

Problem 347

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

641 0 1666 5156 0 1707 0 0 0

N.S.

1 0.00 2.60 8.04 0.00 2.66 0.00 0.00 0.00

time (sec)

N/A 0.000 8.520 6.460 0.000 0.556 0.000 0.000 0.000

Problem 348

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 90 86 90 91 133 0 105 233

N.S.

1 0.94 0.90 0.94 0.95 1.39 0.00 1.09 2.43

time (sec)

N/A 0.337 0.137 2.951 0.185 0.310 0.000 0.353 6.516

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