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2.2.3 Integrals 201 to 234

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 201

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

229 251 375 2668 0 1002 0 0 0

N.S.

1 1.10 1.64 11.65 0.00 4.38 0.00 0.00 0.00

time (sec)

N/A 0.831 0.134 21.014 0.000 0.330 0.000 0.000 0.000

Problem 202

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

159 175 237 1776 0 600 0 0 0

N.S.

1 1.10 1.49 11.17 0.00 3.77 0.00 0.00 0.00

time (sec)

N/A 0.584 0.100 2.316 0.000 0.321 0.000 0.000 0.000

Problem 203

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 80 91 184 0 334 0 0 0

N.S.

1 1.08 1.23 2.49 0.00 4.51 0.00 0.00 0.00

time (sec)

N/A 0.355 0.024 1.514 0.000 0.284 0.000 0.000 0.000

Problem 204

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

15 15 17 15 17 17 0 3 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.00 0.20 1.13

time (sec)

N/A 0.216 0.702 0.199 1.528 0.285 0.000 105.033 0.818

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

351 437 442 6844 0 1269 0 0 0

N.S.

1 1.25 1.26 19.50 0.00 3.62 0.00 0.00 0.00

time (sec)

N/A 1.432 0.359 39.007 0.000 0.358 0.000 0.000 0.000

Problem 206

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

265 339 334 6494 0 1051 0 0 0

N.S.

1 1.28 1.26 24.51 0.00 3.97 0.00 0.00 0.00

time (sec)

N/A 1.027 0.900 4.400 0.000 0.334 0.000 0.000 0.000

Problem 207

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 237 287 352 0 813 0 0 0

N.S.

1 1.36 1.65 2.02 0.00 4.67 0.00 0.00 0.00

time (sec)

N/A 0.640 0.306 2.918 0.000 0.391 0.000 0.000 0.000

Problem 208

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

15 15 17 15 17 17 14 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.93 1.13 1.13

time (sec)

N/A 0.279 3.839 0.142 1.054 0.261 170.894 0.544 0.859

Problem 209

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

142 167 134 1404 129 292 0 0 0

N.S.

1 1.18 0.94 9.89 0.91 2.06 0.00 0.00 0.00

time (sec)

N/A 0.780 0.155 1.944 1.303 0.263 0.000 0.000 0.000

Problem 210

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

113 133 103 1368 107 246 0 0 0

N.S.

1 1.18 0.91 12.11 0.95 2.18 0.00 0.00 0.00

time (sec)

N/A 0.614 0.073 1.542 1.339 0.261 0.000 0.000 0.000

Problem 211

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 93 71 544 80 186 0 0 0

N.S.

1 1.18 0.90 6.89 1.01 2.35 0.00 0.00 0.00

time (sec)

N/A 0.423 0.105 1.670 1.303 0.262 0.000 0.000 0.000

Problem 212

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

19 19 21 17 73 36 0 19 20

N.S.

1 1.00 1.11 0.89 3.84 1.89 0.00 1.00 1.05

time (sec)

N/A 0.276 3.090 0.123 0.620 0.255 0.000 0.337 1.019

Problem 213

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

145 170 134 1410 129 292 0 0 0

N.S.

1 1.17 0.92 9.72 0.89 2.01 0.00 0.00 0.00

time (sec)

N/A 0.781 0.155 2.308 1.308 0.272 0.000 0.000 0.000

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

116 135 103 1374 106 246 0 0 0

N.S.

1 1.16 0.89 11.84 0.91 2.12 0.00 0.00 0.00

time (sec)

N/A 0.628 0.076 1.911 1.285 0.269 0.000 0.000 0.000

Problem 215

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 95 71 517 80 186 0 0 0

N.S.

1 1.16 0.87 6.30 0.98 2.27 0.00 0.00 0.00

time (sec)

N/A 0.427 0.093 1.872 1.283 0.253 0.000 0.000 0.000

Problem 216

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 81 36 0 19 20

N.S.

1 1.00 1.09 0.91 3.68 1.64 0.00 0.86 0.91

time (sec)

N/A 0.278 3.140 0.135 0.612 0.254 0.000 0.337 1.006

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

187 187 132 566 0 250 0 0 0

N.S.

1 1.00 0.71 3.03 0.00 1.34 0.00 0.00 0.00

time (sec)

N/A 0.838 0.258 224.515 0.000 0.288 0.000 0.000 0.000

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 59 53 34 40 0 0 0

N.S.

1 1.00 1.69 1.51 0.97 1.14 0.00 0.00 0.00

time (sec)

N/A 0.227 0.019 0.820 0.308 0.284 0.000 0.000 0.000

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 63 58 50 0 65 0 0 0

N.S.

1 0.89 0.82 0.70 0.00 0.92 0.00 0.00 0.00

time (sec)

N/A 0.342 0.014 1.042 0.000 0.280 0.000 0.000 0.000

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 105 92 76 0 87 0 0 0

N.S.

1 1.02 0.89 0.74 0.00 0.84 0.00 0.00 0.00

time (sec)

N/A 0.491 0.014 1.694 0.000 0.255 0.000 0.000 0.000

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 49 83 95 63 103 0 0 0

N.S.

1 0.96 1.63 1.86 1.24 2.02 0.00 0.00 0.00

time (sec)

N/A 0.235 0.036 0.353 0.320 0.272 0.000 0.000 0.000

Problem 222

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 97 83 355 0 151 0 0 0

N.S.

1 0.94 0.81 3.45 0.00 1.47 0.00 0.00 0.00

time (sec)

N/A 0.399 0.013 0.802 0.000 0.356 0.000 0.000 0.000

Problem 223

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 159 133 413 0 187 0 0 0

N.S.

1 1.05 0.88 2.74 0.00 1.24 0.00 0.00 0.00

time (sec)

N/A 0.570 0.017 0.803 0.000 0.296 0.000 0.000 0.000

Problem 224

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

196 177 167 162 189 212 0 0 0

N.S.

1 0.90 0.85 0.83 0.96 1.08 0.00 0.00 0.00

time (sec)

N/A 0.525 0.114 1.250 0.339 0.283 0.000 0.000 0.000

Problem 225

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

250 484 250 678 0 304 0 0 0

N.S.

1 1.94 1.00 2.71 0.00 1.22 0.00 0.00 0.00

time (sec)

N/A 4.417 0.288 1.044 0.000 0.296 0.000 0.000 0.000

Problem 226

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

313 621 313 764 0 378 0 0 0

N.S.

1 1.98 1.00 2.44 0.00 1.21 0.00 0.00 0.00

time (sec)

N/A 4.231 0.228 1.543 0.000 0.303 0.000 0.000 0.000

Problem 227

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 33 27 25 19 28 19 21 22

N.S.

1 1.22 1.00 0.93 0.70 1.04 0.70 0.78 0.81

time (sec)

N/A 0.217 0.016 0.127 0.235 0.313 1.482 0.280 0.105

Problem 228

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 14 17 15 12 18 15

N.S.

1 1.00 1.00 0.82 1.00 0.88 0.71 1.06 0.88

time (sec)

N/A 0.206 0.091 0.299 0.230 0.264 0.217 0.279 0.140

Problem 229

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B F A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

47 44 61 1281 47 131 0 66 65

N.S.

1 0.94 1.30 27.26 1.00 2.79 0.00 1.40 1.38

time (sec)

N/A 0.320 0.060 1.248 0.310 0.276 0.000 0.293 0.877

Problem 230

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C A B F A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

103 104 146 1354 131 276 0 154 133

N.S.

1 1.01 1.42 13.15 1.27 2.68 0.00 1.50 1.29

time (sec)

N/A 0.478 0.084 6.524 0.331 0.296 0.000 0.298 1.009

Problem 231

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C A C F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

180 175 89 1323 167 258 0 0 164

N.S.

1 0.97 0.49 7.35 0.93 1.43 0.00 0.00 0.91

time (sec)

N/A 0.501 0.067 1.479 0.310 0.293 0.000 0.000 2.913

Problem 232

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C A C F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

180 175 89 1323 167 258 0 0 164

N.S.

1 0.97 0.49 7.35 0.93 1.43 0.00 0.00 0.91

time (sec)

N/A 0.497 0.065 1.320 0.309 0.285 0.000 0.000 2.739

Problem 233

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

103 104 145 855 169 221 0 154 135

N.S.

1 1.01 1.41 8.30 1.64 2.15 0.00 1.50 1.31

time (sec)

N/A 0.444 0.091 6.551 0.342 0.299 0.000 0.285 0.975

Problem 234

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

48 46 59 903 48 75 0 65 68

N.S.

1 0.96 1.23 18.81 1.00 1.56 0.00 1.35 1.42

time (sec)

N/A 0.316 0.053 1.352 0.310 0.284 0.000 0.284 0.863

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