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Integrals 201 to 239

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 Reduce Mupad

grade

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

verified

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

size

177 189 210 1588 0 1178 0 1238 1308 0

N.S.

1 1.07 1.19 8.97 0.00 6.66 0.00 6.99 7.39 0.00

time (sec)

N/A 0.301 0.936 0.336 0.000 9.910 0.000 0.368 0.279 0.000

Problem 202

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

206 209 261 1417 0 1267 0 2589 1567 0

N.S.

1 1.01 1.27 6.88 0.00 6.15 0.00 12.57 7.61 0.00

time (sec)

N/A 0.333 0.342 0.332 0.000 29.931 0.000 0.514 0.269 0.000

Problem 203

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

232 247 223 302 0 656 0 3978 1732 528

N.S.

1 1.06 0.96 1.30 0.00 2.83 0.00 17.15 7.47 2.28

time (sec)

N/A 0.427 0.240 0.342 0.000 74.326 0.000 0.531 3.189 3.512

Problem 204

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

330 294 381 614 0 0 0 5705 2628 846

N.S.

1 0.89 1.15 1.86 0.00 0.00 0.00 17.29 7.96 2.56

time (sec)

N/A 0.469 0.380 0.348 0.000 0.000 0.000 0.685 0.364 3.687

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

432 343 581 1010 0 0 0 7493 3656 1177

N.S.

1 0.79 1.34 2.34 0.00 0.00 0.00 17.34 8.46 2.72

time (sec)

N/A 0.489 0.574 0.335 0.000 0.000 0.000 0.907 0.444 4.199

Problem 206

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

284 284 319 498 0 671 0 0 41 0

N.S.

1 1.00 1.12 1.75 0.00 2.36 0.00 0.00 0.14 0.00

time (sec)

N/A 0.408 19.158 3.335 0.000 0.128 0.000 0.000 8.750 0.000

Problem 207

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

229 210 214 219 0 310 0 0 33 0

N.S.

1 0.92 0.93 0.96 0.00 1.35 0.00 0.00 0.14 0.00

time (sec)

N/A 0.305 12.162 1.166 0.000 0.113 0.000 0.000 0.562 0.000

Problem 208

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

208 208 221 214 0 313 0 0 35 0

N.S.

1 1.00 1.06 1.03 0.00 1.50 0.00 0.00 0.17 0.00

time (sec)

N/A 0.302 12.186 1.305 0.000 0.115 0.000 0.000 0.578 0.000

Problem 209

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

208 208 219 214 0 312 0 0 96 0

N.S.

1 1.00 1.05 1.03 0.00 1.50 0.00 0.00 0.46 0.00

time (sec)

N/A 0.307 12.232 1.286 0.000 0.108 0.000 0.000 0.906 0.000

Problem 210

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

206 209 221 227 0 315 0 0 98 0

N.S.

1 1.01 1.07 1.10 0.00 1.53 0.00 0.00 0.48 0.00

time (sec)

N/A 0.293 12.279 1.342 0.000 0.116 0.000 0.000 0.888 0.000

Problem 211

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

145 139 309 604 0 1228 0 0 99 0

N.S.

1 0.96 2.13 4.17 0.00 8.47 0.00 0.00 0.68 0.00

time (sec)

N/A 0.296 16.270 12.842 0.000 0.104 0.000 0.000 9.839 0.000

Problem 212

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

208 222 312 729 0 1126 0 0 67 0

N.S.

1 1.07 1.50 3.50 0.00 5.41 0.00 0.00 0.32 0.00

time (sec)

N/A 0.369 18.370 4.535 0.000 0.114 0.000 0.000 13.022 0.000

Problem 213

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

92 92 289 288 0 194 0 0 45 0

N.S.

1 1.00 3.14 3.13 0.00 2.11 0.00 0.00 0.49 0.00

time (sec)

N/A 0.225 21.673 1.454 0.000 0.074 0.000 0.000 1.603 0.000

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

448 434 502 432 0 0 0 1026 4185 0

N.S.

1 0.97 1.12 0.96 0.00 0.00 0.00 2.29 9.34 0.00

time (sec)

N/A 0.521 2.235 1.776 0.000 0.000 0.000 0.418 0.839 0.000

Problem 215

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

406 376 472 372 0 696 0 735 2549 9140

N.S.

1 0.93 1.16 0.92 0.00 1.71 0.00 1.81 6.28 22.51

time (sec)

N/A 0.445 1.107 0.740 0.000 57.632 0.000 0.275 0.790 40.969

Problem 216

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

386 318 466 364 0 3716 0 599 1207 16501

N.S.

1 0.82 1.21 0.94 0.00 9.63 0.00 1.55 3.13 42.75

time (sec)

N/A 0.397 0.890 0.672 0.000 5.251 0.000 0.518 0.632 0.787

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

425 386 519 423 0 0 0 912 2870 373297

N.S.

1 0.91 1.22 1.00 0.00 0.00 0.00 2.15 6.75 878.35

time (sec)

N/A 0.445 3.567 0.724 0.000 0.000 0.000 0.804 0.843 17.237

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

493 458 112 495 0 0 0 1277 9649 0

N.S.

1 0.93 0.23 1.00 0.00 0.00 0.00 2.59 19.57 0.00

time (sec)

N/A 0.509 10.053 1.182 0.000 0.000 0.000 1.539 2.808 0.000

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

446 432 501 432 0 0 0 857 4185 0

N.S.

1 0.97 1.12 0.97 0.00 0.00 0.00 1.92 9.38 0.00

time (sec)

N/A 0.532 2.033 1.291 0.000 0.000 0.000 0.404 0.697 0.000

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

404 374 472 369 0 451 0 623 2549 7103

N.S.

1 0.93 1.17 0.91 0.00 1.12 0.00 1.54 6.31 17.58

time (sec)

N/A 0.442 0.958 1.460 0.000 35.700 0.000 0.286 0.635 25.159

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

386 320 466 364 0 6174 0 644 1207 13287

N.S.

1 0.83 1.21 0.94 0.00 15.99 0.00 1.67 3.13 34.42

time (sec)

N/A 0.404 1.879 0.647 0.000 49.491 0.000 0.401 0.553 4.678

Problem 222

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

427 392 520 423 0 0 0 838 4618 413671

N.S.

1 0.92 1.22 0.99 0.00 0.00 0.00 1.96 10.81 968.78

time (sec)

N/A 0.456 10.343 0.779 0.000 0.000 0.000 0.787 0.835 18.759

Problem 223

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

495 464 112 495 0 0 0 1239 13315 0

N.S.

1 0.94 0.23 1.00 0.00 0.00 0.00 2.50 26.90 0.00

time (sec)

N/A 0.497 10.057 1.145 0.000 0.000 0.000 3.489 2.116 0.000

Problem 224

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

528 421 565 415 0 0 0 888 6541 0

N.S.

1 0.80 1.07 0.79 0.00 0.00 0.00 1.68 12.39 0.00

time (sec)

N/A 0.587 3.333 0.904 0.000 0.000 0.000 0.661 1.419 0.000

Problem 225

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

70 70 49 0 0 0 144 0 129 0

N.S.

1 1.00 0.70 0.00 0.00 0.00 2.06 0.00 1.84 0.00

time (sec)

N/A 0.209 0.109 0.000 0.000 0.000 0.516 0.000 0.166 0.000

Problem 226

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

70 70 49 0 0 0 379 0 129 0

N.S.

1 1.00 0.70 0.00 0.00 0.00 5.41 0.00 1.84 0.00

time (sec)

N/A 0.226 0.002 0.000 0.000 0.000 2.874 0.000 0.195 0.000

Problem 227

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

100 70 49 0 0 0 379 0 129 0

N.S.

1 0.70 0.49 0.00 0.00 0.00 3.79 0.00 1.29 0.00

time (sec)

N/A 0.199 0.099 0.000 0.000 0.000 2.982 0.000 0.174 0.000

Problem 228

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

100 100 86 0 0 0 379 0 129 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 3.79 0.00 1.29 0.00

time (sec)

N/A 0.221 0.208 0.000 0.000 0.000 2.766 0.000 0.171 0.000

Problem 229

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

242 223 180 0 0 0 0 0 0 0

N.S.

1 0.92 0.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.367 0.174 0.000 0.000 0.000 0.000 0.000 0.705 0.000

Problem 230

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

272 266 195 0 0 0 0 0 0 0

N.S.

1 0.98 0.72 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.378 0.202 0.000 0.000 0.000 0.000 0.000 1.231 0.000

Problem 231

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

264 260 205 0 0 0 0 0 29 0

N.S.

1 0.98 0.78 0.00 0.00 0.00 0.00 0.00 0.11 0.00

time (sec)

N/A 0.440 0.335 0.000 0.000 0.000 0.000 0.000 200.029 0.000

Problem 232

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

268 268 0 0 0 0 0 0 62 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 0.446 0.000 0.000 0.000 0.000 0.000 0.000 0.155 0.000

Problem 233

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 Yes N/A TBD TBD TBD TBD TBD TBD

size

283 283 208 0 0 0 0 0 92 0

N.S.

1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 0.33 0.00

time (sec)

N/A 0.418 0.294 0.000 0.000 0.000 0.000 0.000 0.156 0.000

Problem 234

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

277 277 215 0 0 0 0 0 132 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.48 0.00

time (sec)

N/A 0.402 0.343 0.000 0.000 0.000 0.000 0.000 0.182 0.000

Problem 235

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 Yes N/A TBD TBD TBD TBD TBD TBD

size

261 261 223 0 0 0 0 0 172 0

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 0.66 0.00

time (sec)

N/A 0.406 0.241 0.000 0.000 0.000 0.000 0.000 0.186 0.000

Problem 236

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 Yes N/A TBD TBD TBD TBD TBD TBD

size

558 577 508 0 0 0 0 0 212 0

N.S.

1 1.03 0.91 0.00 0.00 0.00 0.00 0.00 0.38 0.00

time (sec)

N/A 0.947 1.076 0.000 0.000 0.000 0.000 0.000 0.195 0.000

Problem 237

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

174 213 121 0 0 0 1647 0 0 0

N.S.

1 1.22 0.70 0.00 0.00 0.00 9.47 0.00 0.00 0.00

time (sec)

N/A 0.342 0.205 0.000 0.000 0.000 49.657 0.000 0.251 0.000

Problem 238

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

368 368 0 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 0.00

time (sec)

N/A 0.443 0.000 0.000 0.000 0.000 0.000 0.000 1.658 0.000

Problem 239

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

368 339 0 0 0 0 0 0 0 0

N.S.

1 0.92 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.509 0.000 0.000 0.000 0.000 0.000 0.000 1.723 0.000

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