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Integrals 801 to 838

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 801

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

681 725 2350 200671 0 0 0 0 206 0

N.S.

1 1.06 3.45 294.67 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 2.529 7.229 20.398 0.000 0.000 0.000 0.000 0.165 0.000

Problem 802

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

736 0 2172 919451 0 0 0 0 234 0

N.S.

1 0.00 2.95 1249.25 0.00 0.00 0.00 0.00 0.32 0.00

time (sec)

N/A 0.000 9.749 60.228 0.000 0.000 0.000 0.000 0.197 0.000

Problem 803

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

497 509 2012 97338 0 0 0 0 149 0

N.S.

1 1.02 4.05 195.85 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 1.503 6.468 10.672 0.000 0.000 0.000 0.000 0.183 0.000

Problem 804

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

489 501 2067 96893 0 0 0 0 69 0

N.S.

1 1.02 4.23 198.15 0.00 0.00 0.00 0.00 0.14 0.00

time (sec)

N/A 1.358 6.563 10.990 0.000 0.000 0.000 0.000 0.168 0.000

Problem 805

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

516 538 2102 119840 0 0 0 0 128 0

N.S.

1 1.04 4.07 232.25 0.00 0.00 0.00 0.00 0.25 0.00

time (sec)

N/A 1.504 6.601 15.720 0.000 0.000 0.000 0.000 0.155 0.000

Problem 806

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

688 720 2352 214174 0 0 0 0 206 0

N.S.

1 1.05 3.42 311.30 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 2.629 7.246 20.036 0.000 0.000 0.000 0.000 0.162 0.000

Problem 807

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

941 983 2669 381314 0 0 0 0 284 0

N.S.

1 1.04 2.84 405.22 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 4.206 7.827 32.020 0.000 0.000 0.000 0.000 0.160 0.000

Problem 808

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

25 25 27 25 27 27 0 27 27 27

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.00 1.08 1.08 1.08

time (sec)

N/A 0.227 3.289 0.352 1.727 0.279 0.000 0.917 0.158 18.712

Problem 809

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

312 311 0 0 0 0 0 0 71 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.23 0.00

time (sec)

N/A 0.781 0.000 0.000 0.000 0.000 0.000 0.000 0.177 0.000

Problem 810

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

230 229 200 0 0 0 0 0 40 0

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 0.17 0.00

time (sec)

N/A 0.446 0.467 0.000 0.000 0.000 0.000 0.000 0.170 0.000

Problem 811

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

104 104 120 0 0 0 0 0 14 0

N.S.

1 1.00 1.15 0.00 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.238 0.216 0.000 0.000 0.000 0.000 0.000 0.160 0.000

Problem 812

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

25 25 27 25 27 27 0 27 27 27

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.00 1.08 1.08 1.08

time (sec)

N/A 0.229 5.373 0.342 2.144 0.077 0.000 0.465 0.170 17.441

Problem 813

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

25 25 27 25 27 51 0 27 43 27

N.S.

1 1.00 1.08 1.00 1.08 2.04 0.00 1.08 1.72 1.08

time (sec)

N/A 0.235 6.732 2.063 23.739 0.165 0.000 0.515 0.182 21.699

Problem 814

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

25 25 27 25 27 75 0 27 59 27

N.S.

1 1.00 1.08 1.00 1.08 3.00 0.00 1.08 2.36 1.08

time (sec)

N/A 0.231 16.847 2.499 153.760 0.304 0.000 0.649 0.213 24.054

Problem 815

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

27 27 29 25 27 61 0 27 105 27

N.S.

1 1.00 1.07 0.93 1.00 2.26 0.00 1.00 3.89 1.00

time (sec)

N/A 0.252 39.114 0.381 2.811 0.353 0.000 1.091 0.216 29.238

Problem 816

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

27 27 29 25 27 27 0 27 63 27

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.00 1.00 2.33 1.00

time (sec)

N/A 0.253 13.734 0.356 1.339 0.194 0.000 0.908 0.185 18.948

Problem 817

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

27 27 29 25 27 27 26 27 26 27

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.96 1.00 0.96 1.00

time (sec)

N/A 0.247 0.275 0.342 1.308 0.182 3.664 0.574 0.156 18.550

Problem 818

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

27 27 29 25 27 27 26 27 38 27

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.96 1.00 1.41 1.00

time (sec)

N/A 0.241 7.879 0.363 1.334 0.184 1.084 0.514 0.155 22.751

Problem 819

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

27 27 29 25 27 63 26 27 54 27

N.S.

1 1.00 1.07 0.93 1.00 2.33 0.96 1.00 2.00 1.00

time (sec)

N/A 0.256 8.398 0.359 1.381 0.308 8.760 0.713 0.159 24.941

Problem 820

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

27 27 29 25 27 87 26 27 70 27

N.S.

1 1.00 1.07 0.93 1.00 3.22 0.96 1.00 2.59 1.00

time (sec)

N/A 0.255 12.811 0.365 1.388 0.360 136.194 0.824 0.168 26.726

Problem 821

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

272 273 493 0 0 0 0 0 77 0

N.S.

1 1.00 1.81 0.00 0.00 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 1.245 17.526 0.000 0.000 0.000 0.000 0.000 0.168 0.000

Problem 822

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

203 199 342 0 0 0 0 0 56 0

N.S.

1 0.98 1.68 0.00 0.00 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 0.981 10.210 0.000 0.000 0.000 0.000 0.000 0.175 0.000

Problem 823

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

149 148 280 0 0 0 0 0 33 0

N.S.

1 0.99 1.88 0.00 0.00 0.00 0.00 0.00 0.22 0.00

time (sec)

N/A 0.543 2.240 0.000 0.000 0.000 0.000 0.000 0.158 0.000

Problem 824

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

171 181 0 0 0 0 0 0 28 0

N.S.

1 1.06 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 0.756 0.000 0.000 0.000 0.000 0.000 0.000 0.156 0.000

Problem 825

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

231 228 0 0 0 0 0 0 38 0

N.S.

1 0.99 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 1.141 0.000 0.000 0.000 0.000 0.000 0.000 0.172 0.000

Problem 826

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

113 113 0 0 0 0 0 0 34 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 0.625 0.000 0.000 0.000 0.000 0.000 0.000 0.166 0.000

Problem 827

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

299 306 297 0 0 0 0 0 90 0

N.S.

1 1.02 0.99 0.00 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 1.203 1.008 0.000 0.000 0.000 0.000 0.000 0.173 0.000

Problem 828

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

222 234 222 0 0 0 0 0 67 0

N.S.

1 1.05 1.00 0.00 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 0.703 0.496 0.000 0.000 0.000 0.000 0.000 0.166 0.000

Problem 829

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

163 183 128 0 0 0 0 0 42 0

N.S.

1 1.12 0.79 0.00 0.00 0.00 0.00 0.00 0.26 0.00

time (sec)

N/A 0.487 0.492 0.000 0.000 0.000 0.000 0.000 0.160 0.000

Problem 830

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

189 221 157 0 0 0 0 0 35 0

N.S.

1 1.17 0.83 0.00 0.00 0.00 0.00 0.00 0.19 0.00

time (sec)

N/A 0.687 0.197 0.000 0.000 0.000 0.000 0.000 0.163 0.000

Problem 831

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

288 305 216 0 0 0 0 0 45 0

N.S.

1 1.06 0.75 0.00 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 1.061 2.648 0.000 0.000 0.000 0.000 0.000 0.170 0.000

Problem 832

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A 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 TBD

size

27 27 29 27 29 29 26 29 34 29

N.S.

1 1.00 1.07 1.00 1.07 1.07 0.96 1.07 1.26 1.07

time (sec)

N/A 0.346 2.507 0.377 4.642 0.146 26.223 7.501 0.165 18.554

Problem 833

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

323 330 249 0 0 0 0 0 103 0

N.S.

1 1.02 0.77 0.00 0.00 0.00 0.00 0.00 0.32 0.00

time (sec)

N/A 1.182 1.089 0.000 0.000 0.000 0.000 0.000 0.178 0.000

Problem 834

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

231 242 198 0 0 0 0 0 74 0

N.S.

1 1.05 0.86 0.00 0.00 0.00 0.00 0.00 0.32 0.00

time (sec)

N/A 0.758 0.376 0.000 0.000 0.000 0.000 0.000 0.163 0.000

Problem 835

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

163 183 129 0 0 0 0 0 45 0

N.S.

1 1.12 0.79 0.00 0.00 0.00 0.00 0.00 0.28 0.00

time (sec)

N/A 0.460 0.176 0.000 0.000 0.000 0.000 0.000 0.159 0.000

Problem 836

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

204 231 1808 0 0 0 0 0 34 0

N.S.

1 1.13 8.86 0.00 0.00 0.00 0.00 0.00 0.17 0.00

time (sec)

N/A 0.738 17.398 0.000 0.000 0.000 0.000 0.000 0.178 0.000

Problem 837

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

322 346 1970 0 0 0 0 0 50 0

N.S.

1 1.07 6.12 0.00 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 0.931 19.984 0.000 0.000 0.000 0.000 0.000 0.171 0.000

Problem 838

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

428 450 2570 0 0 0 0 0 66 0

N.S.

1 1.05 6.00 0.00 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 1.140 20.307 0.000 0.000 0.000 0.000 0.000 0.178 0.000

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