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Integrals 201 to 241

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

326 326 230 532 0 0 0 0 0

N.S.

1 1.00 0.71 1.63 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.611 9.678 8.067 0.000 0.000 0.000 0.000 0.000

Problem 202

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

442 442 7138 4161 0 0 0 0 0

N.S.

1 1.00 16.15 9.41 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.766 26.039 32.018 0.000 0.000 0.000 0.000 0.000

Problem 203

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

208 208 145 182 0 0 0 0 0

N.S.

1 1.00 0.70 0.88 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.131 3.778 17.243 0.000 0.000 0.000 0.000 0.000

Problem 204

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

216 216 251 281 0 0 0 0 0

N.S.

1 1.00 1.16 1.30 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.285 21.285 7.082 0.000 0.000 0.000 0.000 0.000

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

376 376 1138 2883 0 0 0 0 0

N.S.

1 1.00 3.03 7.67 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.491 13.360 14.500 0.000 0.000 0.000 0.000 0.000

Problem 206

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

495 495 1589 7173 0 0 0 0 0

N.S.

1 1.00 3.21 14.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.889 14.926 17.337 0.000 0.000 0.000 0.000 0.000

Problem 207

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

389 389 40517 510 0 0 0 0 0

N.S.

1 1.00 104.16 1.31 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.569 36.774 11.872 0.000 0.000 0.000 0.000 0.000

Problem 208

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 198 336 322 0 0 0 0 0

N.S.

1 1.00 1.70 1.63 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.131 5.315 10.626 0.000 0.000 0.000 0.000 0.000

Problem 209

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

598 598 1708 2444 0 0 0 0 0

N.S.

1 1.00 2.86 4.09 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.112 14.547 14.380 0.000 0.000 0.000 0.000 0.000

Problem 210

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

899 899 1990 18680 0 0 0 0 0

N.S.

1 1.00 2.21 20.78 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.676 7.333 17.709 0.000 0.000 0.000 0.000 0.000

Problem 211

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

744 744 1750 3569 0 0 0 0 0

N.S.

1 1.00 2.35 4.80 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.347 19.215 13.973 0.000 0.000 0.000 0.000 0.000

Problem 212

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

919 919 1960 15314 0 0 0 0 0

N.S.

1 1.00 2.13 16.66 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.149 7.166 16.550 0.000 0.000 0.000 0.000 0.000

Problem 213

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

1122 1122 2385 54551 0 0 0 0 0

N.S.

1 1.00 2.13 48.62 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.664 7.984 21.529 0.000 0.000 0.000 0.000 0.000

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

891 891 2026 18991 0 0 0 0 0

N.S.

1 1.00 2.27 21.31 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.232 7.027 16.321 0.000 0.000 0.000 0.000 0.000

Problem 215

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

1150 1150 2344 39100 0 0 0 0 0

N.S.

1 1.00 2.04 34.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.363 8.150 20.623 0.000 0.000 0.000 0.000 0.000

Problem 216

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No No No TBD TBD TBD TBD TBD

size

1428 1428 2979 88656 0 0 0 0 0

N.S.

1 1.00 2.09 62.08 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 6.175 9.058 23.698 0.000 0.000 0.000 0.000 0.000

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

652 0 50041 457 0 0 0 0 0

N.S.

1 0.00 76.75 0.70 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 37.554 17.069 0.000 0.000 0.000 0.000 0.000

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 198 325 322 0 0 0 0 0

N.S.

1 1.00 1.64 1.63 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.123 5.201 11.562 0.000 0.000 0.000 0.000 0.000

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

398 398 249 263 0 0 0 0 0

N.S.

1 1.00 0.63 0.66 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.497 3.141 13.405 0.000 0.000 0.000 0.000 0.000

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

622 763 1761 2867 0 0 0 0 0

N.S.

1 1.23 2.83 4.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.760 19.317 17.183 0.000 0.000 0.000 0.000 0.000

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 31 25 27 0 27 27 31

N.S.

1 1.00 1.07 0.86 0.93 0.00 0.93 0.93 1.07

time (sec)

N/A 0.215 14.574 0.667 0.731 0.000 1.101 0.912 99.948

Problem 222

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 31 25 27 0 27 27 31

N.S.

1 1.00 1.07 0.86 0.93 0.00 0.93 0.93 1.07

time (sec)

N/A 0.100 87.531 0.527 1.028 0.000 10.451 1.231 105.691

Problem 223

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 31 25 27 0 0 27 0

N.S.

1 1.00 1.07 0.86 0.93 0.00 0.00 0.93 0.00

time (sec)

N/A 0.098 84.795 0.602 1.422 0.000 0.000 1.428 0.000

Problem 224

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 31 25 27 0 27 27 31

N.S.

1 1.00 1.07 0.86 0.93 0.00 0.93 0.93 1.07

time (sec)

N/A 0.243 14.913 0.646 0.777 0.000 3.792 1.683 107.171

Problem 225

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 31 25 27 0 27 27 31

N.S.

1 1.00 1.07 0.86 0.93 0.00 0.93 0.93 1.07

time (sec)

N/A 0.105 89.115 0.536 1.062 0.000 61.552 2.937 107.375

Problem 226

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 31 25 27 0 0 27 0

N.S.

1 1.00 1.07 0.86 0.93 0.00 0.00 0.93 0.00

time (sec)

N/A 0.101 87.715 0.593 1.396 0.000 0.000 5.147 0.000

Problem 227

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 31 25 27 0 27 27 31

N.S.

1 1.00 1.07 0.86 0.93 0.00 0.93 0.93 1.07

time (sec)

N/A 0.245 75.841 0.597 0.755 0.000 147.970 2.906 110.554

Problem 228

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 31 25 27 0 0 27 0

N.S.

1 1.00 1.07 0.86 0.93 0.00 0.00 0.93 0.00

time (sec)

N/A 0.110 98.957 0.546 1.148 0.000 0.000 3.674 0.000

Problem 229

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 31 25 27 0 0 27 0

N.S.

1 1.00 1.07 0.86 0.93 0.00 0.00 0.93 0.00

time (sec)

N/A 0.103 130.902 0.634 2.376 0.000 0.000 4.900 0.000

Problem 230

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 No N/A TBD TBD TBD TBD TBD

size

106 106 2425 0 0 0 0 0 0

N.S.

1 1.00 22.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.210 13.876 0.000 0.000 0.000 0.000 0.000 0.000

Problem 231

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

275 275 191 0 0 0 0 0 0

N.S.

1 1.00 0.69 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.493 1.789 0.000 0.000 0.000 0.000 0.000 0.000

Problem 232

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

205 205 152 0 0 0 0 0 0

N.S.

1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.300 0.753 0.000 0.000 0.000 0.000 0.000 0.000

Problem 233

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

156 156 124 0 0 0 0 0 0

N.S.

1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.184 0.135 0.000 0.000 0.000 0.000 0.000 0.000

Problem 234

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

208 208 159 0 0 0 0 0 0

N.S.

1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.332 0.632 0.000 0.000 0.000 0.000 0.000 0.000

Problem 235

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

248 248 215 0 0 0 0 0 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.544 1.516 0.000 0.000 0.000 0.000 0.000 0.000

Problem 236

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

27 27 29 27 29 29 26 29 33

N.S.

1 1.00 1.07 1.00 1.07 1.07 0.96 1.07 1.22

time (sec)

N/A 0.141 6.636 1.290 4.191 0.313 5.086 0.878 15.968

Problem 237

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

296 296 278 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.587 0.816 0.000 0.000 0.000 0.000 0.000 0.000

Problem 238

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

211 211 200 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.395 0.427 0.000 0.000 0.000 0.000 0.000 0.000

Problem 239

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

156 156 125 0 0 0 0 0 0

N.S.

1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.227 0.184 0.000 0.000 0.000 0.000 0.000 0.000

Problem 240

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 No N/A TBD TBD TBD TBD TBD

size

206 206 5411 0 0 0 0 0 0

N.S.

1 1.00 26.27 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.627 32.619 0.000 0.000 0.000 0.000 0.000 0.000

Problem 241

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 No N/A TBD TBD TBD TBD TBD

size

322 322 14108 0 0 0 0 0 0

N.S.

1 1.00 43.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.628 46.813 0.000 0.000 0.000 0.000 0.000 0.000

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