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Integrals 301 to 344

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 Reduce Mupad

grade

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

verified

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

size

234 280 219 206 0 160 0 0 36 0

N.S.

1 1.20 0.94 0.88 0.00 0.68 0.00 0.00 0.15 0.00

time (sec)

N/A 0.672 5.527 2.178 0.000 0.081 0.000 0.000 0.172 0.000

Problem 302

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

131 143 176 218 0 162 0 0 38 0

N.S.

1 1.09 1.34 1.66 0.00 1.24 0.00 0.00 0.29 0.00

time (sec)

N/A 0.579 6.461 1.983 0.000 0.079 0.000 0.000 0.181 0.000

Problem 303

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

125 136 168 206 0 172 0 0 40 0

N.S.

1 1.09 1.34 1.65 0.00 1.38 0.00 0.00 0.32 0.00

time (sec)

N/A 0.495 5.120 1.727 0.000 0.076 0.000 0.000 0.172 0.000

Problem 304

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

57 62 123 142 0 88 0 0 40 0

N.S.

1 1.09 2.16 2.49 0.00 1.54 0.00 0.00 0.70 0.00

time (sec)

N/A 0.366 0.026 2.166 0.000 0.076 0.000 0.000 0.166 0.000

Problem 305

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

133 145 176 218 0 172 0 0 40 0

N.S.

1 1.09 1.32 1.64 0.00 1.29 0.00 0.00 0.30 0.00

time (sec)

N/A 0.563 6.423 2.034 0.000 0.075 0.000 0.000 0.185 0.000

Problem 306

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

131 148 140 218 0 172 0 0 40 0

N.S.

1 1.13 1.07 1.66 0.00 1.31 0.00 0.00 0.31 0.00

time (sec)

N/A 0.572 6.972 2.357 0.000 0.077 0.000 0.000 0.178 0.000

Problem 307

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

133 150 164 218 0 172 0 0 38 0

N.S.

1 1.13 1.23 1.64 0.00 1.29 0.00 0.00 0.29 0.00

time (sec)

N/A 0.535 6.660 2.376 0.000 0.090 0.000 0.000 0.180 0.000

Problem 308

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

59 64 99 121 0 83 0 0 40 0

N.S.

1 1.08 1.68 2.05 0.00 1.41 0.00 0.00 0.68 0.00

time (sec)

N/A 0.375 6.553 2.307 0.000 0.073 0.000 0.000 0.165 0.000

Problem 309

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

125 136 156 206 0 172 0 0 40 0

N.S.

1 1.09 1.25 1.65 0.00 1.38 0.00 0.00 0.32 0.00

time (sec)

N/A 0.504 5.138 1.782 0.000 0.074 0.000 0.000 0.169 0.000

Problem 310

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

133 145 164 218 0 172 0 0 40 0

N.S.

1 1.09 1.23 1.64 0.00 1.29 0.00 0.00 0.30 0.00

time (sec)

N/A 0.538 6.495 2.104 0.000 0.077 0.000 0.000 0.182 0.000

Problem 311

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

353 348 456 481 0 452 0 0 57 0

N.S.

1 0.99 1.29 1.36 0.00 1.28 0.00 0.00 0.16 0.00

time (sec)

N/A 0.769 10.628 0.549 0.000 0.089 0.000 0.000 0.211 0.000

Problem 312

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

358 353 469 482 0 456 0 0 58 0

N.S.

1 0.99 1.31 1.35 0.00 1.27 0.00 0.00 0.16 0.00

time (sec)

N/A 0.757 10.543 0.580 0.000 0.086 0.000 0.000 0.216 0.000

Problem 313

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

366 360 470 479 0 462 0 0 60 0

N.S.

1 0.98 1.28 1.31 0.00 1.26 0.00 0.00 0.16 0.00

time (sec)

N/A 0.760 10.519 0.554 0.000 0.082 0.000 0.000 0.215 0.000

Problem 314

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

371 363 464 479 0 460 0 0 59 0

N.S.

1 0.98 1.25 1.29 0.00 1.24 0.00 0.00 0.16 0.00

time (sec)

N/A 0.722 10.647 0.539 0.000 0.094 0.000 0.000 0.270 0.000

Problem 315

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

405 415 509 593 0 755 0 0 79 0

N.S.

1 1.02 1.26 1.46 0.00 1.86 0.00 0.00 0.20 0.00

time (sec)

N/A 0.960 11.068 0.567 0.000 0.091 0.000 0.000 0.289 0.000

Problem 316

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

410 420 514 594 0 759 0 0 80 0

N.S.

1 1.02 1.25 1.45 0.00 1.85 0.00 0.00 0.20 0.00

time (sec)

N/A 0.927 10.942 0.572 0.000 0.095 0.000 0.000 0.289 0.000

Problem 317

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

400 373 468 474 0 470 0 0 58 0

N.S.

1 0.93 1.17 1.18 0.00 1.18 0.00 0.00 0.14 0.00

time (sec)

N/A 1.104 10.542 0.557 0.000 0.084 0.000 0.000 0.216 0.000

Problem 318

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

407 662 462 473 0 466 0 0 59 0

N.S.

1 1.63 1.14 1.16 0.00 1.14 0.00 0.00 0.14 0.00

time (sec)

N/A 1.458 10.671 0.559 0.000 0.090 0.000 0.000 0.216 0.000

Problem 319

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

407 664 458 464 0 474 0 0 59 0

N.S.

1 1.63 1.13 1.14 0.00 1.16 0.00 0.00 0.14 0.00

time (sec)

N/A 1.349 10.663 0.536 0.000 0.086 0.000 0.000 0.211 0.000

Problem 320

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

410 379 471 466 0 480 0 0 60 0

N.S.

1 0.92 1.15 1.14 0.00 1.17 0.00 0.00 0.15 0.00

time (sec)

N/A 0.907 10.527 0.537 0.000 0.096 0.000 0.000 0.215 0.000

Problem 321

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

81 81 81 81 85 77 87 83 87 72

N.S.

1 1.00 1.00 1.00 1.05 0.95 1.07 1.02 1.07 0.89

time (sec)

N/A 0.407 0.010 0.042 0.030 0.079 0.023 0.107 0.152 18.213

Problem 322

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

49 49 49 42 45 41 48 43 46 42

N.S.

1 1.00 1.00 0.86 0.92 0.84 0.98 0.88 0.94 0.86

time (sec)

N/A 0.328 0.004 0.036 0.025 0.060 0.019 0.113 0.148 0.023

Problem 323

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

20 20 20 17 16 16 15 16 19 16

N.S.

1 1.00 1.00 0.85 0.80 0.80 0.75 0.80 0.95 0.80

time (sec)

N/A 0.259 0.000 0.029 0.034 0.066 0.015 0.108 0.148 0.027

Problem 324

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

1 1 1 2 1 1 0 1 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.208 0.000 0.009 0.041 0.048 0.014 0.107 0.148 0.002

Problem 325

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

150 150 129 38 0 613 87 1026 351 763

N.S.

1 1.00 0.86 0.25 0.00 4.09 0.58 6.84 2.34 5.09

time (sec)

N/A 0.533 0.074 0.095 0.000 0.094 0.557 0.382 0.171 18.379

Problem 326

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

250 236 243 151 0 2309 394 2682 2409 6404

N.S.

1 0.94 0.97 0.60 0.00 9.24 1.58 10.73 9.64 25.62

time (sec)

N/A 0.697 0.300 0.220 0.000 0.172 103.570 0.373 0.313 19.663

Problem 327

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

355 361 372 331 0 4323 0 2707 6794 10979

N.S.

1 1.02 1.05 0.93 0.00 12.18 0.00 7.63 19.14 30.93

time (sec)

N/A 1.023 0.688 0.309 0.000 0.560 0.000 0.890 3.740 21.791

Problem 328

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

227 323 81 37 0 583 63 75 569 872

N.S.

1 1.42 0.36 0.16 0.00 2.57 0.28 0.33 2.51 3.84

time (sec)

N/A 1.029 0.033 0.174 0.000 0.097 0.385 0.115 0.171 17.429

Problem 329

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 47 43 32 0 269 257 31 70 85

N.S.

1 1.00 0.91 0.68 0.00 5.72 5.47 0.66 1.49 1.81

time (sec)

N/A 0.292 0.020 0.076 0.000 0.111 0.318 0.114 0.243 0.110

Problem 330

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

227 323 52 37 0 407 48 0 563 469

N.S.

1 1.42 0.23 0.16 0.00 1.79 0.21 0.00 2.48 2.07

time (sec)

N/A 0.922 0.025 0.187 0.000 0.086 0.298 0.000 0.223 17.380

Problem 331

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B B B B B B B B

verified

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

size

17 17 37 26 25 25 26 29 25 11

N.S.

1 1.00 2.18 1.53 1.47 1.47 1.53 1.71 1.47 0.65

time (sec)

N/A 0.245 0.004 0.062 0.031 0.083 0.076 0.135 0.223 0.038

Problem 332

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

24 24 24 18 17 17 20 17 16 17

N.S.

1 1.00 1.00 0.75 0.71 0.71 0.83 0.71 0.67 0.71

time (sec)

N/A 0.245 0.010 0.082 0.111 0.080 0.061 0.104 0.219 0.052

Problem 333

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

57 71 91 54 53 53 70 53 51 83

N.S.

1 1.25 1.60 0.95 0.93 0.93 1.23 0.93 0.89 1.46

time (sec)

N/A 0.404 0.052 0.075 0.109 0.083 0.091 0.125 0.223 0.101

Problem 334

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

137 202 41 31 0 147 899 143 231 210

N.S.

1 1.47 0.30 0.23 0.00 1.07 6.56 1.04 1.69 1.53

time (sec)

N/A 0.720 0.028 0.173 0.000 0.075 0.531 0.211 0.218 17.255

Problem 335

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

270 359 324 124 0 8845 0 0 66 25137

N.S.

1 1.33 1.20 0.46 0.00 32.76 0.00 0.00 0.24 93.10

time (sec)

N/A 1.555 0.350 0.270 0.000 0.352 0.000 0.000 200.040 23.569

Problem 336

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

108 119 122 146 0 66 0 0 152 0

N.S.

1 1.10 1.13 1.35 0.00 0.61 0.00 0.00 1.41 0.00

time (sec)

N/A 0.484 6.910 2.582 0.000 0.099 0.000 0.000 0.259 0.000

Problem 337

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

80 86 112 136 0 57 0 0 116 0

N.S.

1 1.08 1.40 1.70 0.00 0.71 0.00 0.00 1.45 0.00

time (sec)

N/A 0.402 5.646 2.450 0.000 0.095 0.000 0.000 0.247 0.000

Problem 338

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

48 53 59 114 0 44 0 0 80 0

N.S.

1 1.10 1.23 2.38 0.00 0.92 0.00 0.00 1.67 0.00

time (sec)

N/A 0.341 4.216 1.972 0.000 0.088 0.000 0.000 0.229 0.000

Problem 339

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

12 12 18 43 0 9 0 0 30 0

N.S.

1 1.00 1.50 3.58 0.00 0.75 0.00 0.00 2.50 0.00

time (sec)

N/A 0.240 0.006 0.494 0.000 0.102 0.000 0.000 0.241 0.000

Problem 340

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

57 58 80 119 0 74 0 0 251 0

N.S.

1 1.02 1.40 2.09 0.00 1.30 0.00 0.00 4.40 0.00

time (sec)

N/A 0.349 0.028 1.889 0.000 0.104 0.000 0.000 0.274 0.000

Problem 341

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 91 107 143 0 117 0 0 50 0

N.S.

1 1.07 1.26 1.68 0.00 1.38 0.00 0.00 0.59 0.00

time (sec)

N/A 0.409 10.071 2.375 0.000 0.093 0.000 0.000 0.229 0.000

Problem 342

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

113 124 117 153 0 157 0 0 58 0

N.S.

1 1.10 1.04 1.35 0.00 1.39 0.00 0.00 0.51 0.00

time (sec)

N/A 0.498 10.097 2.379 0.000 0.113 0.000 0.000 0.179 0.000

Problem 343

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

52 53 59 114 0 44 0 0 80 0

N.S.

1 1.02 1.13 2.19 0.00 0.85 0.00 0.00 1.54 0.00

time (sec)

N/A 0.373 0.028 1.571 0.000 0.101 0.000 0.000 0.174 0.000

Problem 344

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

12 12 18 43 0 9 0 0 30 0

N.S.

1 1.00 1.50 3.58 0.00 0.75 0.00 0.00 2.50 0.00

time (sec)

N/A 0.262 0.006 0.500 0.000 0.105 0.000 0.000 0.167 0.000

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