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Integrals 201 to 246

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

verified

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

size

219 240 168 127 0 58 0 0 133 0

N.S.

1 1.10 0.77 0.58 0.00 0.26 0.00 0.00 0.61 0.00

time (sec)

N/A 0.453 21.240 1.007 0.000 0.085 0.000 0.000 0.440 0.000

Problem 202

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

196 216 160 122 0 53 0 0 115 0

N.S.

1 1.10 0.82 0.62 0.00 0.27 0.00 0.00 0.59 0.00

time (sec)

N/A 0.405 21.212 1.018 0.000 0.083 0.000 0.000 0.461 0.000

Problem 203

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

173 188 158 117 0 48 0 0 97 0

N.S.

1 1.09 0.91 0.68 0.00 0.28 0.00 0.00 0.56 0.00

time (sec)

N/A 0.369 21.211 1.148 0.000 0.081 0.000 0.000 0.482 0.000

Problem 204

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

150 160 150 112 0 43 0 0 81 0

N.S.

1 1.07 1.00 0.75 0.00 0.29 0.00 0.00 0.54 0.00

time (sec)

N/A 0.329 21.239 1.056 0.000 0.081 0.000 0.000 0.436 0.000

Problem 205

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

125 133 150 77 0 26 0 0 65 0

N.S.

1 1.06 1.20 0.62 0.00 0.21 0.00 0.00 0.52 0.00

time (sec)

N/A 0.297 21.209 0.934 0.000 0.079 0.000 0.000 0.409 0.000

Problem 206

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

142 156 90 108 0 50 0 0 86 0

N.S.

1 1.10 0.63 0.76 0.00 0.35 0.00 0.00 0.61 0.00

time (sec)

N/A 0.331 21.191 1.021 0.000 0.077 0.000 0.000 0.443 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

171 183 148 115 0 59 0 0 90 0

N.S.

1 1.07 0.87 0.67 0.00 0.35 0.00 0.00 0.53 0.00

time (sec)

N/A 0.365 21.193 1.003 0.000 0.076 0.000 0.000 0.412 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

192 212 150 124 0 64 0 0 166 0

N.S.

1 1.10 0.78 0.65 0.00 0.33 0.00 0.00 0.86 0.00

time (sec)

N/A 0.411 21.205 0.913 0.000 0.084 0.000 0.000 0.526 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

195 217 156 117 0 69 0 0 349 0

N.S.

1 1.11 0.80 0.60 0.00 0.35 0.00 0.00 1.79 0.00

time (sec)

N/A 0.426 21.230 1.030 0.000 0.079 0.000 0.000 0.569 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

178 193 150 112 0 87 0 0 331 0

N.S.

1 1.08 0.84 0.63 0.00 0.49 0.00 0.00 1.86 0.00

time (sec)

N/A 0.380 21.210 0.961 0.000 0.077 0.000 0.000 0.543 0.000

Problem 211

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

155 165 145 107 0 82 0 0 331 0

N.S.

1 1.06 0.94 0.69 0.00 0.53 0.00 0.00 2.14 0.00

time (sec)

N/A 0.340 21.203 1.003 0.000 0.084 0.000 0.000 0.515 0.000

Problem 212

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

151 161 140 107 0 82 0 0 347 0

N.S.

1 1.07 0.93 0.71 0.00 0.54 0.00 0.00 2.30 0.00

time (sec)

N/A 0.331 21.191 0.989 0.000 0.078 0.000 0.000 0.520 0.000

Problem 213

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

147 161 137 107 0 82 0 0 90 0

N.S.

1 1.10 0.93 0.73 0.00 0.56 0.00 0.00 0.61 0.00

time (sec)

N/A 0.328 21.188 0.988 0.000 0.080 0.000 0.000 0.544 0.000

Problem 214

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

168 185 137 108 0 99 0 0 648 0

N.S.

1 1.10 0.82 0.64 0.00 0.59 0.00 0.00 3.86 0.00

time (sec)

N/A 0.380 21.212 1.095 0.000 0.084 0.000 0.000 0.496 0.000

Problem 215

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

199 213 145 115 0 110 0 0 726 0

N.S.

1 1.07 0.73 0.58 0.00 0.55 0.00 0.00 3.65 0.00

time (sec)

N/A 0.412 21.212 0.986 0.000 0.079 0.000 0.000 0.505 0.000

Problem 216

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

222 238 150 124 0 115 0 0 584 0

N.S.

1 1.07 0.68 0.56 0.00 0.52 0.00 0.00 2.63 0.00

time (sec)

N/A 0.460 21.217 1.030 0.000 0.079 0.000 0.000 0.513 0.000

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

252 282 187 272 0 137 0 0 736 0

N.S.

1 1.12 0.74 1.08 0.00 0.54 0.00 0.00 2.92 0.00

time (sec)

N/A 0.513 21.336 1.053 0.000 0.082 0.000 0.000 0.466 0.000

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

229 254 179 251 0 132 0 0 718 0

N.S.

1 1.11 0.78 1.10 0.00 0.58 0.00 0.00 3.14 0.00

time (sec)

N/A 0.466 21.324 0.984 0.000 0.083 0.000 0.000 0.457 0.000

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

206 219 177 232 0 127 0 0 700 0

N.S.

1 1.06 0.86 1.13 0.00 0.62 0.00 0.00 3.40 0.00

time (sec)

N/A 0.417 21.324 1.018 0.000 0.083 0.000 0.000 0.456 0.000

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

183 198 169 214 0 122 0 0 682 0

N.S.

1 1.08 0.92 1.17 0.00 0.67 0.00 0.00 3.73 0.00

time (sec)

N/A 0.395 21.318 0.992 0.000 0.081 0.000 0.000 0.442 0.000

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

183 194 167 214 0 122 0 0 664 0

N.S.

1 1.06 0.91 1.17 0.00 0.67 0.00 0.00 3.63 0.00

time (sec)

N/A 0.380 21.301 0.993 0.000 0.080 0.000 0.000 0.386 0.000

Problem 222

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

183 193 164 214 0 122 0 0 645 0

N.S.

1 1.05 0.90 1.17 0.00 0.67 0.00 0.00 3.52 0.00

time (sec)

N/A 0.383 21.298 0.981 0.000 0.081 0.000 0.000 0.448 0.000

Problem 223

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

175 189 165 214 0 122 0 0 630 0

N.S.

1 1.08 0.94 1.22 0.00 0.70 0.00 0.00 3.60 0.00

time (sec)

N/A 0.384 21.356 1.006 0.000 0.079 0.000 0.000 0.446 0.000

Problem 224

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

181 193 167 214 0 122 0 0 640 0

N.S.

1 1.07 0.92 1.18 0.00 0.67 0.00 0.00 3.54 0.00

time (sec)

N/A 0.384 21.288 1.040 0.000 0.087 0.000 0.000 0.520 0.000

Problem 225

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

202 220 167 240 0 139 0 0 743 0

N.S.

1 1.09 0.83 1.19 0.00 0.69 0.00 0.00 3.68 0.00

time (sec)

N/A 0.420 21.307 0.977 0.000 0.077 0.000 0.000 0.498 0.000

Problem 226

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

220 246 169 261 0 150 0 0 1119 0

N.S.

1 1.12 0.77 1.19 0.00 0.68 0.00 0.00 5.09 0.00

time (sec)

N/A 0.472 21.309 0.994 0.000 0.088 0.000 0.000 0.452 0.000

Problem 227

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

252 276 177 282 0 155 0 0 1119 0

N.S.

1 1.10 0.70 1.12 0.00 0.62 0.00 0.00 4.44 0.00

time (sec)

N/A 0.515 21.333 1.052 0.000 0.089 0.000 0.000 0.511 0.000

Problem 228

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

240 240 672 242 408 1350 11116 2736 1335 769

N.S.

1 1.00 2.80 1.01 1.70 5.62 46.32 11.40 5.56 3.20

time (sec)

N/A 0.462 2.369 1.050 0.077 0.107 0.938 0.266 0.344 11.648

Problem 229

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

155 155 289 154 230 573 4027 1142 590 405

N.S.

1 1.00 1.86 0.99 1.48 3.70 25.98 7.37 3.81 2.61

time (sec)

N/A 0.340 0.678 0.935 0.061 0.085 0.602 0.224 0.346 11.629

Problem 230

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

83 83 91 82 104 171 981 338 188 171

N.S.

1 1.00 1.10 0.99 1.25 2.06 11.82 4.07 2.27 2.06

time (sec)

N/A 0.248 0.187 0.086 0.042 0.081 0.332 0.230 0.332 11.319

Problem 231

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

196 172 135 0 0 0 0 0 92 0

N.S.

1 0.88 0.69 0.00 0.00 0.00 0.00 0.00 0.47 0.00

time (sec)

N/A 0.459 0.396 0.000 0.000 0.000 0.000 0.000 0.350 0.000

Problem 232

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

324 302 253 0 0 0 0 0 0 0

N.S.

1 0.93 0.78 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.724 0.911 0.000 0.000 0.000 0.000 0.000 0.380 0.000

Problem 233

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

281 281 618 0 0 0 0 0 25 0

N.S.

1 1.00 2.20 0.00 0.00 0.00 0.00 0.00 0.09 0.00

time (sec)

N/A 0.498 3.610 0.000 0.000 0.000 0.000 0.000 200.040 0.000

Problem 234

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

281 281 405 0 0 0 0 0 25 0

N.S.

1 1.00 1.44 0.00 0.00 0.00 0.00 0.00 0.09 0.00

time (sec)

N/A 0.430 2.077 0.000 0.000 0.000 0.000 0.000 200.037 0.000

Problem 235

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

281 281 234 0 0 0 0 0 25 0

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 0.09 0.00

time (sec)

N/A 0.414 1.598 0.000 0.000 0.000 0.000 0.000 200.033 0.000

Problem 236

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

281 281 234 0 0 0 0 0 48 0

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 0.17 0.00

time (sec)

N/A 0.449 1.724 0.000 0.000 0.000 0.000 0.000 0.716 0.000

Problem 237

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

281 281 272 0 0 0 0 0 114 0

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 0.41 0.00

time (sec)

N/A 0.436 2.393 0.000 0.000 0.000 0.000 0.000 8.948 0.000

Problem 238

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

281 281 237 0 0 0 0 0 234 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 0.83 0.00

time (sec)

N/A 0.431 4.756 0.000 0.000 0.000 0.000 0.000 156.556 0.000

Problem 239

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

277 277 232 0 0 0 0 0 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.424 0.651 0.000 0.000 0.000 0.000 0.000 0.374 0.000

Problem 240

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

390 443 210 0 0 0 0 0 0 0

N.S.

1 1.14 0.54 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.707 1.134 0.000 0.000 0.000 0.000 0.000 0.244 0.000

Problem 241

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 No Yes N/A TBD TBD TBD TBD TBD TBD

size

247 295 210 0 0 0 0 0 0 0

N.S.

1 1.19 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.457 0.721 0.000 0.000 0.000 0.000 0.000 0.243 0.000

Problem 242

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 No Yes N/A TBD TBD TBD TBD TBD TBD

size

175 211 210 0 0 0 0 0 1544 0

N.S.

1 1.21 1.20 0.00 0.00 0.00 0.00 0.00 8.82 0.00

time (sec)

N/A 0.310 0.554 0.000 0.000 0.000 0.000 0.000 0.246 0.000

Problem 243

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

122 158 268 0 0 0 0 0 650 0

N.S.

1 1.30 2.20 0.00 0.00 0.00 0.00 0.00 5.33 0.00

time (sec)

N/A 0.268 0.656 0.000 0.000 0.000 0.000 0.000 0.241 0.000

Problem 244

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 No No N/A TBD TBD TBD TBD TBD TBD

size

236 273 263 0 0 0 0 0 483 0

N.S.

1 1.16 1.11 0.00 0.00 0.00 0.00 0.00 2.05 0.00

time (sec)

N/A 0.415 0.676 0.000 0.000 0.000 0.000 0.000 0.235 0.000

Problem 245

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 No No N/A TBD TBD TBD TBD TBD TBD

size

274 314 289 0 0 0 0 0 892 0

N.S.

1 1.15 1.05 0.00 0.00 0.00 0.00 0.00 3.26 0.00

time (sec)

N/A 0.477 0.648 0.000 0.000 0.000 0.000 0.000 0.237 0.000

Problem 246

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 No No N/A TBD TBD TBD TBD TBD TBD

size

336 384 295 0 0 0 0 0 1048 0

N.S.

1 1.14 0.88 0.00 0.00 0.00 0.00 0.00 3.12 0.00

time (sec)

N/A 0.617 1.125 0.000 0.000 0.000 0.000 0.000 0.233 0.000

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