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2.2.4 Integrals 301 to 330

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 C A A B A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 172 30 82 1701 50 0 0 85

N.S.

1 4.10 0.71 1.95 40.50 1.19 0.00 0.00 2.02

time (sec)

N/A 0.319 0.409 14.067 0.503 0.237 0.000 0.000 28.652

Problem 302

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 152 79 123 974 83 0 839 171

N.S.

1 1.38 0.72 1.12 8.85 0.75 0.00 7.63 1.55

time (sec)

N/A 0.429 1.514 217.824 0.314 0.249 0.000 11.515 32.421

Problem 303

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B A F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

49 49 127 211 139 56 0 0 45

N.S.

1 1.00 2.59 4.31 2.84 1.14 0.00 0.00 0.92

time (sec)

N/A 0.243 0.157 0.218 0.242 0.231 0.000 0.000 28.933

Problem 304

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 51 137 68 153 57 0 74 55

N.S.

1 0.88 2.36 1.17 2.64 0.98 0.00 1.28 0.95

time (sec)

N/A 0.235 0.118 265.292 0.256 0.239 0.000 1.115 28.872

Problem 305

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 137 68 162 57 0 83 38

N.S.

1 1.00 2.69 1.33 3.18 1.12 0.00 1.63 0.75

time (sec)

N/A 0.235 0.122 261.677 0.262 0.238 0.000 1.128 31.431

Problem 306

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

96 103 155 0 0 150 0 0 0

N.S.

1 1.07 1.61 0.00 0.00 1.56 0.00 0.00 0.00

time (sec)

N/A 0.321 1.318 0.000 0.000 0.244 0.000 0.000 0.000

Problem 307

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

71 112 128 0 0 150 0 0 0

N.S.

1 1.58 1.80 0.00 0.00 2.11 0.00 0.00 0.00

time (sec)

N/A 0.327 2.143 0.000 0.000 0.256 0.000 0.000 0.000

Problem 308

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

109 109 115 0 0 0 0 0 0

N.S.

1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.296 0.342 0.000 0.000 0.000 0.000 0.000 0.000

Problem 309

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 58 102 0 78 0 0 89

N.S.

1 1.00 0.98 1.73 0.00 1.32 0.00 0.00 1.51

time (sec)

N/A 0.281 0.114 1.195 0.000 0.083 0.000 0.000 27.529

Problem 310

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

109 109 411 0 0 0 0 0 0

N.S.

1 1.00 3.77 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.295 4.678 0.000 0.000 0.000 0.000 0.000 0.000

Problem 311

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 92 72 190 0 111 0 0 0

N.S.

1 0.98 0.77 2.02 0.00 1.18 0.00 0.00 0.00

time (sec)

N/A 0.358 0.131 1.318 0.000 0.088 0.000 0.000 0.000

Problem 312

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

109 109 174 0 0 0 0 0 0

N.S.

1 1.00 1.60 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.293 1.167 0.000 0.000 0.000 0.000 0.000 0.000

Problem 313

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 96 73 131 0 145 0 0 0

N.S.

1 0.98 0.74 1.34 0.00 1.48 0.00 0.00 0.00

time (sec)

N/A 0.356 0.170 1.451 0.000 0.084 0.000 0.000 0.000

Problem 314

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

110 110 377 0 0 0 0 0 0

N.S.

1 1.00 3.43 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.295 3.205 0.000 0.000 0.000 0.000 0.000 0.000

Problem 315

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 58 129 0 82 0 0 0

N.S.

1 1.00 0.98 2.19 0.00 1.39 0.00 0.00 0.00

time (sec)

N/A 0.280 0.096 1.224 0.000 0.093 0.000 0.000 0.000

Problem 316

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

109 109 186 0 0 0 0 0 0

N.S.

1 1.00 1.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.285 1.607 0.000 0.000 0.000 0.000 0.000 0.000

Problem 317

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 96 76 131 0 107 0 0 0

N.S.

1 0.98 0.78 1.34 0.00 1.09 0.00 0.00 0.00

time (sec)

N/A 0.357 0.152 1.316 0.000 0.087 0.000 0.000 0.000

Problem 318

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

110 110 579 0 0 0 0 0 0

N.S.

1 1.00 5.26 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.288 7.475 0.000 0.000 0.000 0.000 0.000 0.000

Problem 319

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 96 88 205 0 130 0 0 0

N.S.

1 0.98 0.90 2.09 0.00 1.33 0.00 0.00 0.00

time (sec)

N/A 0.358 0.156 1.317 0.000 0.086 0.000 0.000 0.000

Problem 320

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

122 138 367 0 0 0 0 0 0

N.S.

1 1.13 3.01 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.341 1.756 0.000 0.000 0.000 0.000 0.000 0.000

Problem 321

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

119 136 225 0 0 0 0 0 0

N.S.

1 1.14 1.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.339 13.656 0.000 0.000 0.000 0.000 0.000 0.000

Problem 322

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

123 134 181 0 0 0 0 0 0

N.S.

1 1.09 1.47 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.323 0.295 0.000 0.000 0.000 0.000 0.000 0.000

Problem 323

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

130 126 165 0 0 0 0 0 0

N.S.

1 0.97 1.27 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.333 2.284 0.000 0.000 0.000 0.000 0.000 0.000

Problem 324

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

130 126 466 0 0 0 0 0 0

N.S.

1 0.97 3.58 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.320 7.342 0.000 0.000 0.000 0.000 0.000 0.000

Problem 325

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

130 130 138 0 0 0 0 0 0

N.S.

1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.320 0.688 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 B F F F(-2) F F F(-1)

verified

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

size

129 126 441 0 0 0 0 0 0

N.S.

1 0.98 3.42 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.324 5.482 0.000 0.000 0.000 0.000 0.000 0.000

Problem 327

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

130 126 218 0 0 0 0 0 0

N.S.

1 0.97 1.68 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.319 1.720 0.000 0.000 0.000 0.000 0.000 0.000

Problem 328

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

139 170 169 0 0 0 0 0 0

N.S.

1 1.22 1.22 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.374 1.285 0.000 0.000 0.000 0.000 0.000 0.000

Problem 329

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

106 106 142 0 0 0 0 0 0

N.S.

1 1.00 1.34 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.317 0.948 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 A F F F F F F(-1)

verified

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

size

107 111 142 0 0 0 0 0 0

N.S.

1 1.04 1.33 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.291 0.760 0.000 0.000 0.000 0.000 0.000 0.000

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