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2.2.9 Integrals 801 to 837

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 Mupad

grade

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

verified

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

size

25 25 27 25 27 27 0 27 27

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.00 1.08 1.08

time (sec)

N/A 0.204 2.852 0.530 2.100 0.485 0.000 0.911 11.057

Problem 802

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

311 311 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.719 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 803

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

228 229 195 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.415 0.408 0.000 0.000 0.000 0.000 0.000 0.000

Problem 804

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

104 104 117 0 0 0 0 0 0

N.S.

1 1.00 1.12 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.233 0.175 0.000 0.000 0.000 0.000 0.000 0.000

Problem 805

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

25 25 27 25 27 27 0 27 27

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.00 1.08 1.08

time (sec)

N/A 0.212 4.816 0.938 2.373 0.267 0.000 0.366 8.732

Problem 806

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

25 25 27 25 27 51 0 27 27

N.S.

1 1.00 1.08 1.00 1.08 2.04 0.00 1.08 1.08

time (sec)

N/A 0.211 5.948 2.234 24.043 0.396 0.000 0.439 13.071

Problem 807

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

25 25 27 25 27 75 0 27 27

N.S.

1 1.00 1.08 1.00 1.08 3.00 0.00 1.08 1.08

time (sec)

N/A 0.212 14.837 3.207 154.048 0.524 0.000 0.540 16.124

Problem 808

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

27 27 29 25 27 61 0 27 27

N.S.

1 1.00 1.07 0.93 1.00 2.26 0.00 1.00 1.00

time (sec)

N/A 0.227 35.911 0.639 3.309 0.573 0.000 1.040 21.007

Problem 809

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

27 27 29 25 27 27 0 27 27

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.229 12.730 0.628 1.704 0.443 0.000 0.837 11.448

Problem 810

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 25 27 27 26 27 27

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.96 1.00 1.00

time (sec)

N/A 0.218 0.228 0.139 1.526 0.398 2.698 0.513 10.170

Problem 811

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 25 27 27 26 27 27

N.S.

1 1.00 1.07 0.93 1.00 1.00 0.96 1.00 1.00

time (sec)

N/A 0.223 6.829 0.047 1.653 0.402 0.935 0.462 14.628

Problem 812

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 25 27 63 26 27 27

N.S.

1 1.00 1.07 0.93 1.00 2.33 0.96 1.00 1.00

time (sec)

N/A 0.232 7.796 0.049 1.653 0.533 7.592 0.631 17.231

Problem 813

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 25 27 87 26 27 27

N.S.

1 1.00 1.07 0.93 1.00 3.22 0.96 1.00 1.00

time (sec)

N/A 0.228 11.991 0.048 1.638 0.602 131.340 0.791 20.198

Problem 814

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

262 273 459 0 0 0 0 0 0

N.S.

1 1.04 1.75 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.151 11.702 0.000 0.000 0.000 0.000 0.000 0.000

Problem 815

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

196 199 307 0 0 0 0 0 0

N.S.

1 1.02 1.57 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.963 4.971 0.000 0.000 0.000 0.000 0.000 0.000

Problem 816

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

149 148 280 0 0 0 0 0 0

N.S.

1 0.99 1.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.501 2.032 0.000 0.000 0.000 0.000 0.000 0.000

Problem 817

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

171 181 0 0 0 0 0 0 0

N.S.

1 1.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.702 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 818

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

222 228 0 0 0 0 0 0 0

N.S.

1 1.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.082 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 819

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

113 113 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.602 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 820

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

288 306 294 0 0 0 0 0 0

N.S.

1 1.06 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.153 0.918 0.000 0.000 0.000 0.000 0.000 0.000

Problem 821

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

214 234 219 0 0 0 0 0 0

N.S.

1 1.09 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.641 0.428 0.000 0.000 0.000 0.000 0.000 0.000

Problem 822

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

163 183 128 0 0 0 0 0 0

N.S.

1 1.12 0.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.429 0.412 0.000 0.000 0.000 0.000 0.000 0.000

Problem 823

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

188 221 157 0 0 0 0 0 0

N.S.

1 1.18 0.84 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.641 0.168 0.000 0.000 0.000 0.000 0.000 0.000

Problem 824

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

279 305 197 0 0 0 0 0 0

N.S.

1 1.09 0.71 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.003 1.835 0.000 0.000 0.000 0.000 0.000 0.000

Problem 825

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

289 298 161 0 0 0 0 0 0

N.S.

1 1.03 0.56 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.553 1.248 0.000 0.000 0.000 0.000 0.000 0.000

Problem 826

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

208 203 132 0 0 0 0 0 0

N.S.

1 0.98 0.63 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.902 1.014 0.000 0.000 0.000 0.000 0.000 0.000

Problem 827

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

149 148 105 0 0 0 0 0 0

N.S.

1 0.99 0.70 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.513 0.407 0.000 0.000 0.000 0.000 0.000 0.000

Problem 828

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

195 216 1581 0 0 0 0 0 0

N.S.

1 1.11 8.11 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.754 16.384 0.000 0.000 0.000 0.000 0.000 0.000

Problem 829

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

305 320 1787 0 0 0 0 0 0

N.S.

1 1.05 5.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.866 18.768 0.000 0.000 0.000 0.000 0.000 0.000

Problem 830

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

409 418 2297 0 0 0 0 0 0

N.S.

1 1.02 5.62 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.013 20.150 0.000 0.000 0.000 0.000 0.000 0.000

Problem 831

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 29

N.S.

1 1.00 1.07 1.00 1.07 1.07 0.96 1.07 1.07

time (sec)

N/A 0.332 2.147 0.081 5.278 0.337 23.647 6.742 10.324

Problem 832

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

317 330 240 0 0 0 0 0 0

N.S.

1 1.04 0.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.090 0.830 0.000 0.000 0.000 0.000 0.000 0.000

Problem 833

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

228 242 195 0 0 0 0 0 0

N.S.

1 1.06 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.726 0.312 0.000 0.000 0.000 0.000 0.000 0.000

Problem 834

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

163 183 129 0 0 0 0 0 0

N.S.

1 1.12 0.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.433 0.152 0.000 0.000 0.000 0.000 0.000 0.000

Problem 835

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

195 231 1730 0 0 0 0 0 0

N.S.

1 1.18 8.87 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.666 16.806 0.000 0.000 0.000 0.000 0.000 0.000

Problem 836

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

306 346 1881 0 0 0 0 0 0

N.S.

1 1.13 6.15 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.844 18.334 0.000 0.000 0.000 0.000 0.000 0.000

Problem 837

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

405 450 2467 0 0 0 0 0 0

N.S.

1 1.11 6.09 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.992 19.284 0.000 0.000 0.000 0.000 0.000 0.000

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