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Integrals 301 to 337

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 301

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 85 79 72 65 104 0 73 14 0

N.S.

1 1.00 0.93 0.85 0.76 1.22 0.00 0.86 0.16 0.00

time (sec)

N/A 0.279 0.057 0.806 0.038 0.094 0.000 0.125 0.260 0.000

Problem 302

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

101 101 91 97 81 130 0 91 17 0

N.S.

1 1.00 0.90 0.96 0.80 1.29 0.00 0.90 0.17 0.00

time (sec)

N/A 0.344 0.106 1.254 0.041 0.080 0.000 0.122 0.262 0.000

Problem 303

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

65 65 51 52 45 72 0 45 14 0

N.S.

1 1.00 0.78 0.80 0.69 1.11 0.00 0.69 0.22 0.00

time (sec)

N/A 0.269 0.050 0.757 0.039 0.080 0.000 0.131 0.238 0.000

Problem 304

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

65 65 71 48 47 76 0 49 16 0

N.S.

1 1.00 1.09 0.74 0.72 1.17 0.00 0.75 0.25 0.00

time (sec)

N/A 0.286 0.068 1.518 0.055 0.077 0.000 0.113 0.261 0.000

Problem 305

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

115 115 122 105 89 165 0 101 19 0

N.S.

1 1.00 1.06 0.91 0.77 1.43 0.00 0.88 0.17 0.00

time (sec)

N/A 0.384 0.244 1.549 0.044 0.079 0.000 0.134 0.251 0.000

Problem 306

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

110 110 102 100 90 211 0 106 20 0

N.S.

1 1.00 0.93 0.91 0.82 1.92 0.00 0.96 0.18 0.00

time (sec)

N/A 0.364 0.087 0.492 0.050 0.091 0.000 0.159 0.246 0.000

Problem 307

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

148 148 149 126 127 278 0 355 22 0

N.S.

1 1.00 1.01 0.85 0.86 1.88 0.00 2.40 0.15 0.00

time (sec)

N/A 0.418 0.462 1.170 0.136 0.106 0.000 0.139 0.280 0.000

Problem 308

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

239 239 286 207 200 443 0 223 22 0

N.S.

1 1.00 1.20 0.87 0.84 1.85 0.00 0.93 0.09 0.00

time (sec)

N/A 0.630 0.275 2.759 0.145 0.102 0.000 0.145 0.231 0.000

Problem 309

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

115 115 123 126 102 251 0 132 23 0

N.S.

1 1.00 1.07 1.10 0.89 2.18 0.00 1.15 0.20 0.00

time (sec)

N/A 0.535 0.177 0.567 0.040 0.089 0.000 0.132 0.264 0.000

Problem 310

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

161 161 220 158 143 334 0 387 25 0

N.S.

1 1.00 1.37 0.98 0.89 2.07 0.00 2.40 0.16 0.00

time (sec)

N/A 0.539 0.423 1.681 0.133 0.084 0.000 0.162 0.224 0.000

Problem 311

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

257 257 353 265 228 539 0 281 25 0

N.S.

1 1.00 1.37 1.03 0.89 2.10 0.00 1.09 0.10 0.00

time (sec)

N/A 0.856 0.516 4.444 0.141 0.099 0.000 0.138 0.264 0.000

Problem 312

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

133 133 104 117 105 216 0 132 20 0

N.S.

1 1.00 0.78 0.88 0.79 1.62 0.00 0.99 0.15 0.00

time (sec)

N/A 0.429 0.101 0.410 0.041 0.091 0.000 0.140 0.260 0.000

Problem 313

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

161 161 131 139 131 242 0 150 22 0

N.S.

1 1.00 0.81 0.86 0.81 1.50 0.00 0.93 0.14 0.00

time (sec)

N/A 0.462 0.154 0.998 0.040 0.087 0.000 0.137 0.244 0.000

Problem 314

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

271 271 214 234 211 426 0 264 22 0

N.S.

1 1.00 0.79 0.86 0.78 1.57 0.00 0.97 0.08 0.00

time (sec)

N/A 0.617 0.297 2.537 0.055 0.094 0.000 0.145 0.274 0.000

Problem 315

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

81 81 75 70 69 145 0 75 22 0

N.S.

1 1.00 0.93 0.86 0.85 1.79 0.00 0.93 0.27 0.00

time (sec)

N/A 0.369 0.213 0.447 0.044 0.088 0.000 0.134 0.259 0.000

Problem 316

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

128 128 179 101 100 254 0 107 24 0

N.S.

1 1.00 1.40 0.79 0.78 1.98 0.00 0.84 0.19 0.00

time (sec)

N/A 0.441 0.357 1.004 0.043 0.097 0.000 0.146 0.243 0.000

Problem 317

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

171 171 270 144 143 491 0 155 24 0

N.S.

1 1.00 1.58 0.84 0.84 2.87 0.00 0.91 0.14 0.00

time (sec)

N/A 0.532 0.836 2.547 0.043 0.110 0.000 0.136 0.277 0.000

Problem 318

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

140 140 165 147 127 321 0 172 25 0

N.S.

1 1.00 1.18 1.05 0.91 2.29 0.00 1.23 0.18 0.00

time (sec)

N/A 0.498 0.432 0.600 0.047 0.104 0.000 0.131 0.242 0.000

Problem 319

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

183 183 258 177 161 420 0 198 27 0

N.S.

1 1.00 1.41 0.97 0.88 2.30 0.00 1.08 0.15 0.00

time (sec)

N/A 0.602 0.939 1.608 0.043 0.097 0.000 0.136 0.257 0.000

Problem 320

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

300 300 478 302 263 847 0 352 27 0

N.S.

1 1.00 1.59 1.01 0.88 2.82 0.00 1.17 0.09 0.00

time (sec)

N/A 0.856 4.047 4.000 0.050 0.107 0.000 0.147 0.234 0.000

Problem 321

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

153 153 134 162 129 262 0 167 24 0

N.S.

1 1.00 0.88 1.06 0.84 1.71 0.00 1.09 0.16 0.00

time (sec)

N/A 0.578 0.183 0.487 0.042 0.083 0.000 0.131 0.240 0.000

Problem 322

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

219 219 183 210 185 341 0 223 26 0

N.S.

1 1.00 0.84 0.96 0.84 1.56 0.00 1.02 0.12 0.00

time (sec)

N/A 0.677 0.315 1.093 0.043 0.105 0.000 0.139 0.251 0.000

Problem 323

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

315 315 262 326 263 526 0 339 26 0

N.S.

1 1.00 0.83 1.03 0.83 1.67 0.00 1.08 0.08 0.00

time (sec)

N/A 0.825 0.606 2.821 0.057 0.087 0.000 0.142 0.260 0.000

Problem 324

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

154 154 185 160 139 324 0 181 26 0

N.S.

1 1.00 1.20 1.04 0.90 2.10 0.00 1.18 0.17 0.00

time (sec)

N/A 0.584 0.438 0.540 0.041 0.113 0.000 0.138 0.271 0.000

Problem 325

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

225 225 257 217 199 466 0 239 28 0

N.S.

1 1.00 1.14 0.96 0.88 2.07 0.00 1.06 0.12 0.00

time (sec)

N/A 0.709 1.427 1.308 0.044 0.096 0.000 0.139 0.271 0.000

Problem 326

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

323 323 501 326 287 851 0 369 28 0

N.S.

1 1.00 1.55 1.01 0.89 2.63 0.00 1.14 0.09 0.00

time (sec)

N/A 0.849 4.519 3.086 0.049 0.125 0.000 0.150 0.242 0.000

Problem 327

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

161 161 251 186 151 362 0 207 29 0

N.S.

1 1.00 1.56 1.16 0.94 2.25 0.00 1.29 0.18 0.00

time (sec)

N/A 0.662 0.965 0.636 0.048 0.120 0.000 0.138 0.229 0.000

Problem 328

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

239 239 339 249 215 516 0 271 31 0

N.S.

1 1.00 1.42 1.04 0.90 2.16 0.00 1.13 0.13 0.00

time (sec)

N/A 0.818 4.025 1.779 0.058 0.104 0.000 0.150 0.264 0.000

Problem 329

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

344 344 2991 384 315 939 0 427 31 0

N.S.

1 1.00 8.69 1.12 0.92 2.73 0.00 1.24 0.09 0.00

time (sec)

N/A 1.170 6.433 5.049 0.059 0.106 0.000 0.154 0.277 0.000

Problem 330

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

20 20 46 0 0 0 0 0 19 39

N.S.

1 1.00 2.30 0.00 0.00 0.00 0.00 0.00 0.95 1.95

time (sec)

N/A 0.196 0.216 0.000 0.000 0.000 0.000 0.000 0.227 0.166

Problem 331

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A F F B F F F B

verified

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

size

24 24 16 0 0 109 0 0 25 42

N.S.

1 1.00 0.67 0.00 0.00 4.54 0.00 0.00 1.04 1.75

time (sec)

N/A 0.199 0.031 0.000 0.000 0.089 0.000 0.000 0.261 2.020

Problem 332

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 47 64 0 0 0 0 0 21 110

N.S.

1 1.00 1.36 0.00 0.00 0.00 0.00 0.00 0.45 2.34

time (sec)

N/A 0.222 0.394 0.000 0.000 0.000 0.000 0.000 0.300 2.172

Problem 333

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

36 36 76 0 0 0 0 0 23 0

N.S.

1 1.00 2.11 0.00 0.00 0.00 0.00 0.00 0.64 0.00

time (sec)

N/A 0.233 0.099 0.000 0.000 0.000 0.000 0.000 0.230 0.000

Problem 334

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

30 30 26 25 36 23 41 36 62 24

N.S.

1 1.00 0.87 0.83 1.20 0.77 1.37 1.20 2.07 0.80

time (sec)

N/A 0.222 0.042 1.458 0.037 0.079 0.065 0.127 0.252 0.052

Problem 335

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A A B B

verified

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

size

56 56 51 52 81 54 85 75 114 48

N.S.

1 1.00 0.91 0.93 1.45 0.96 1.52 1.34 2.04 0.86

time (sec)

N/A 0.268 0.059 0.288 0.038 0.080 0.093 0.125 0.337 0.074

Problem 336

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

213 213 166 212 0 316 0 0 18 0

N.S.

1 1.00 0.78 1.00 0.00 1.48 0.00 0.00 0.08 0.00

time (sec)

N/A 0.721 0.349 0.522 0.000 0.092 0.000 0.000 0.215 0.000

Problem 337

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

271 271 220 376 0 671 0 0 21 0

N.S.

1 1.00 0.81 1.39 0.00 2.48 0.00 0.00 0.08 0.00

time (sec)

N/A 1.048 0.561 0.826 0.000 0.105 0.000 0.000 0.231 0.000

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